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Lecture Notes for

Facilities Design

Spring 2003

Michael G. Kay

Department of Industrial Engineering North Carolina State University

Raleigh, NC 27695-7906

These notes are provided for the use of the students in IE 453: Facilities Design at North Carolina State University.

Copyright © 2003 Michael G. Kay. All rights reserved for all original material.

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Contents 1. Introduction 1

1.1 Facilities Planning in Production 1 1.1.1 Facility Planning Hierarchy 1 1.1.2 The Production Process 2

2. Economic Analysis 5 2.1 Introduction 5 2.2 Costs 7

2.2.1 Fixed and Variable Costs 7 2.2.2 Total and Average Costs 8 2.2.3 Long-Run and Short-Run Costs 9 2.2.4 Product Cost 11

2.3 Scale and Scope 12 2.3.1 Facility Size 12 2.3.2 Firm Size 16

2.4 Discounting 17 2.4.1 Basic Formulas 17 2.4.2 Effective Cost vs. Capital Recovery Cost 18 2.4.3 Further Issues in Discounting 20

2.5 Capital Budgeting 21 2.5.1 Introduction 21 2.5.2 Formal Capital Budgeting Analysis 23 2.5.3 Issues in Capital Budgeting 26

2.6 Cost Accounting 30 2.6.1 Break-Even Analysis 30 2.6.2 Cost Indifference Analysis 31

2.7 Problems 34

3. Capacity Planning 36 3.1 Production Charts 36 3.2 Factory Physics 39

3.2.1 Line Yield 40 3.2.2 Throughput Feasibility 41 3.2.3 Machine Sharing and Setups 43 3.2.4 Cycle-Time Feasibility 44 3.2.5 Basic Capacity Planning Procedure 46

3.3 Problems 47

4. Facility Layout 51 4.1 Flow Processes 51

4.1.1 Material Flow System 52 4.1.2 Total Cost of Material Flow and Material Transport 52

4.2 Machine Layout 55

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4.2.1 Flow Requirements 55 4.2.2 Types of Machine Layouts 58 4.2.3 Flow Patterns within Manufacturing Departments 58 4.2.4 QAP Model of Machine Layout 59 4.2.5 QAP Model with Fixed Costs 69

4.3 Department Layout 70 4.3.1 Flow Patterns between Departments 70 4.3.2 Block Layout Representations 71 4.3.3 CRAFT 72 4.3.4 Activity Relationships 74

4.4 Space and Personnel Requirements 75 4.4.1 Personnel Requirements 76 4.4.2 Space Requirements 77

4.5 Problems 81

5. Material Handling 85 5.1 Introduction 85

5.1.1 Definitions of Material Handling 85 5.1.2 Scope of Material Handling 86 5.1.3 Design of MH Systems 87 5.1.4 Principles of Material Handling 88 5.1.5 Characteristics of Materials 89 5.1.6 Material Handling Equipment 90

5.2 The Unit Load Concept 93 5.2.1 Unit Load Design 93

5.3 Unit Load Formation Equipment 95 5.3.1 Pallets 101

5.4 Positioning Equipment 105 5.5 Conveyors 110 5.6 Cranes 120 5.7 Industrial Trucks 122

5.7.1 Counterbalanced Lift Trucks 131 5.7.2 Narrow-Aisle Lift Trucks 136 5.7.3 Automatic (or Automated) Guided Vehicle (AGV) Systems 137

5.8 MH Equipment Selection 138 5.9 Problems 139

6. Storage and Warehousing 145 6.1 Introduction 145

6.1.1 The Need for Storage and Warehousing 145 6.1.2 Storage/Warehousing Functions and Elements 146 6.1.3 Sortation Systems 148

6.2 Storage System Design 149 6.2.1 Storage Terminology 150 6.2.2 Storage Policies 150 6.2.3 Cube Utilization and Honeycomb Loss 152 6.2.4 Dedicated Storage Assignment Problem (DSAP) 155

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6.2.5 Warehouse Design 157 6.3 Storage Equipment 160 6.4 Automated Storage/Retrieval Systems 168

6.4.1 Components of an AS/RS 168 6.4.2 AS/RS Design 169

6.5 Identification and Control Equipment 173 6.6 Problems 175

Bibliography 181

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1. Introduction

1.1 Facilities Planning in Production A facility represents the tangible fixed assets associated with a locus of economic activity. Economic activities are those activities associated with the production, distribution, and consumption of goods and/or services. Facilities are built or established to support these activities. Examples of facilities include manufacturing plants or factories, warehouses, distribution centers, retail stores, hospitals, offices, airports, and schools. Broadly speaking, facility planning involves determining the type, quantity, arrangement, and location of tangible fixed assets to best achieve the objectives of the economic activity. For example, a factory that enables low-cost production of a product can be utilized to maximize the profit of a firm.

Facility Planning

Facility Design Facility Location

Structural Design

Facility Layout

Material Handling

Figure 1.1. Facilities Planning Hierarchy.

1.1.1 Facility Planning Hierarchy Following Tompkins et al. (1996), the subject of facilities planning can be divided into two general areas: facility design and facility location. With respect to a particular facility, the location of the facility refers to where the facility is in relation to its suppliers, customers, and other facilities with which it interacts, while the design of the facility refers to how the components within the facility, which interact with each other, are arranged.

1

1. INTRODUCTION LECTURE NOTES FOR FACILITIES DESIGN

• Facility Planning: Determine how tangible fixed assets in the form of facilities can best be utilized to support the production and distribution of goods and/or services, including (1) determining the need for facilities and (2) evaluating alternative facility plans.

• Facility Location: Determine where facilities should be located to best support the production and distribution of goods and/or services.

For example: determining in which city a new manufacturing plant should be located to minimize transportation costs to customers located throughout the country.

• Facility Design: Determine how the components of a facility should be configured to best support the production and distribution of goods and/or services, where the components of the facility consist of the structure, the layout, and the material handling systems.

• Structural Design: Determine the detailed design of a facility, including the building and such services as gas, water, power, heat, light, air, and sewage.

• Facility Layout: Determine the arrangement and shape of space-consuming entities (i.e., “activities”) in a facility, where the activities interact with each other through flows of material, personnel, and/or information.

Examples of activities: machines, work centers, production areas, offices, and departments.

• Material Handling System Design: Determine the processes, equipment, and systems that transfer and manage the transfer of material between activities in a facility.

1.1.2 The Production Process As shown in Figure 1.2, production can be described as the process of transforming input factors (resources) into outputs (products).

tangible fixed assets

personnel

materials & supplies

energy

product

scrap

Production Process

Figure 1.2. The production process.

Facility planning involves making strategic decisions concerning the tangible fixed assets used in the production process. The difference in the planning horizon for each of the different levels of analysis used in the production process listed in Table 1.1 is due to the different mix of fixed versus variable production factors present at each level of analysis:

• Fixed factors are input factors that cannot be immediately changed, resulting in constraints on the analysis of the production process—factors become fixed because they cannot be easily and/or economically changed in a short period of time;

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SPRING 2003 1.1. FACILITIES PLANNING IN PRODUCTION

• Variable factors are input factors that can be changed and, in many cases, the objective of the analysis is to minimize the costs associated with these factors;

• Planning level ⇒ most factors are variable ⇒ long planning horizon ⇒ strategic decisions

• Control level ⇒ most factors are fixed ⇒ short “planning” horizon ⇒ tactical decisions

• In facilities planning, almost all of the output factors are initially variable; once facilities planning is complete, many of the factors (e.g., the location and design of a manufacturing plant) become fixed (e.g., a new plant can not be built in minutes if demand for a product suddenly increases).

• In machine-level control, almost all of the factors are fixed; the only variable factors and tactical decisions required are the operational state of the machines (e.g., a machine can be turned on in seconds if a product needs processing and turned off if there are no products).

The decisions associated with each of the levels of analysis of the production process listed in Table 1.1 only concern those input factors that are variable during the period of analysis. In the table, the planning horizon of quality control is meant to concern decisions relating only to current production; quality assurance, which includes quality control, also considers quality issues relating to product design and process planning.

Table 1.1. Planning Horizon Associated with Production Analysis

Planning Horizon Level of Analysis

Months–Years Facilities Planning

Months–Years Product Design and Process Planning

Weeks–Months Production Planning

Hours–Weeks Production Control

Minutes–Hours Quality Control

Seconds–Minutes Machine-level Real-time Control

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2. Economic Analysis

2.1 Introduction The principle objective of a firm in a market economy is to maximize the profit associated with providing “products” (i.e., goods and/or services) to its customers (i.e., individuals, other firms, or the government). In particular, the objective of the firm is to maximize the difference between the revenue received from the sale of the product to customers and the cost of producing and delivering the product to customers. Profit can be maximized by increasing revenue and/or decreasing cost:

Profit q Revenue q Cost qb g b g b g= -

Revenue equals the price at which each unit of the product is sold times the quantity of product sold. Price and quantity are inversely related to each other and together constitute customers’ demand for a product. It is not possible for a firm to select both price and quantity: at a particular price, the quantity of product that can sold depends upon customers’ demand, and, conversely, to sell a particular quantity of product depends upon the price at which the product is offered for sale. While a firm may be able to influence customers’ demand for a product through, for example, advertising, thereby increasing revenue, the typical objective of the production-related activities of the firm is to meet a specified demand for the product at the lowest possible cost. Thus, production contributes to the overall goal of maximizing profits by minimizing the cost of producing the specified demand; in particular, the typical objective in facility planning is to minimize the facility-related costs.

Product demand is specified in terms of desired quantities of product to be available for sale at specific times. Product demand drives the desired production rate, which, in turn, drives the planning of facilities. Time can be an important factor in overall profitability because a new product that can be brought quickly to market can, for a short time at least, command a high price. A product that can be produced at what may be a high-cost facility that will be operational in a few months may be able to command a much higher price for several years and may result in greater overall profits than a product produced in a low-cost facility that will take several years to become operational; by then, other firms will also be producing the product, resulting a greater overall supply of the product and a correspondingly lower price at which it can be sold.

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2. ECONOMIC ANALYSIS LECTURE NOTES FOR FACILITIES DESIGN

The cost to a firm of producing and delivering a product includes both costs that can be directly attributed to the product (e.g., material costs) and, if the firm produces more than one product, some portion of the costs associated with operating the firm that can not be attributed to any individual product (e.g., the cost of operating the firm’s central office).

The total cost to a firm to produce and deliver a product is the sum of the costs associated with each of the following elements:

• Administrative—overall management of the firm, especially strategic planning;

• Finance—obtains and manages the funds necessary for the firm’s fixed asset expenditures;

• Research and development (R&D)—product design (and new manufacturing technologies and future technological trends);

• Marketing—determine quantity and price of a product (and future product opportunities);

• Procurement—delivery of materials required to produce a product;

• Production—actual manufacture of a product;

• Distribution (and sales)—(sale and) delivery of a product to a customer.

While the costs associated with all of these elements affect the profitability of the firm, it is useful in facilities planning to consider the costs associated with all of the elements except procurement, production, and distribution as being fixed.

The typical objective in facilities planning is to plan facilities that minimize the costs of procurement, production, and distribution. The other elements can be considered to provide inputs to and constraints on the facilities planning process. For example, marketing and R&D together determine the characteristics of a product and a target price at which a particular quantity of the product can be sold, and finance determines the cost of capital; the design of a product and the quantity to be produced determine the basic characteristics of a facility used to produce the product, and the cost of capital determines a large portion of the cost of establishing and operating the facility.

The location of a facility has a direct impact on procurement and distribution costs (e.g., transportation costs usually increase with distance) and a somewhat more indirect impact on production costs (e.g., labor costs, taxes, energy, etc.); while the design of a facility has a direct impact on production costs (principally through the costs of material flow) and a more indirect impact on distribution costs (where, typically, distribution costs serve to constrain the maximum economic scale of the facility).

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SPRING 2003 2.2. COSTS

2.2 Costs

2.2.1 Fixed and Variable Costs For a particular planning horizon, the input factors of the production process have costs that can be considered to be either fixed or variable depending on whether or not the factors themselves are fixed or variable. When a new facility is being planned, almost all inputs can be varied; once the location of the facility is selected, the cost of some of the inputs become fixed (e.g., transportation costs of raw materials and finished products to/from the facility, and the prevailing labor rate for that location); and once the design of the facility is selected, the cost of even more of the inputs become fixed (e.g., material handling equipment costs).

Stage of Facility Planning Process

Cos

t

Planning Designing Building Installing Commis- sioning

Modification

$ Cost of making changes to a facility

Figure 2.1. Cost of making changes to a facility.

Input factors can become fixed because they can not be easily and/or economically changed in a short period of time due to the following reasons:

• Transactions costs—changing the input would incur too high a transactions cost (e.g., it is expensive to sell a facility if there is a temporary decrease in demand);

• Specialized resources—some inputs are specialized to a particular production process and would have little or no value to others (e.g., a custom machine that is only useful as part of a specific production process not used by others to produce the same products, or a worker with special skills);

• Indivisible resources—some inputs are “lumpy,” that is, the cost of utilizing the input is the same over a range of outputs (e.g., the labor costs to set up a machine are the same whether one or 100 parts are produced).

Due to the creation of an ever greater number of fixed costs at each successive stage of the facilities planning process, the planning horizon in planning a facility should be long because the cost of making changes to a facility will increase at each stage (see Figure 2.1)—although at any particular stage, all previous costs should be considered to be “sunk costs” with respect their impact on current plans.

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q0

$

$/q

Cos

t

qmaxOutput Quantity

q0Output Quantity

Cos

t per

Uni

t Out

put

F

qmax

TC

V

AC

AVCMC

Slope = AC

Slope = AVC

Figure 2.2. Total costs (top) and average costs (bottom) curves.

2.2.2 Total and Average Costs In general, the total cost to produce (and distribute) a particular output quantity of a product is the sum of cost of each of the inputs. Letting F be the sum of fixed costs (of the fixed factors) and V(q) be a function that represents the sum of the variable costs (of the variable factors) for different output quantities q, then the following functions of q represent related costs:

Total Cost: TC q F V q( ) ( )= + (2.1)

Total Variable Cost: V q TC q F( ) ( )= - (2.2)

Average Cost: AC q TC qq

F V qq

( ) ( ) ( )= = + (2.3)

Average Variable Cost: AVC q V qq

( ) ( )= (2.4)

Marginal Cost: MC q TC qq

q dTC qdq

q( ) ( ) ( )= =DD

(discrete ) (continuous ) (2.5)

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As shown in Figure 2.2, starting from the level of fixed costs F incurred independently of any output, the total cost function TC(q) rises throughout as output increases, first possibly at a decreasing rate but ultimately at an increasing rate—until the maximum producible quantity qmax is attained. When one or more input factors are held fixed, increasing the other inputs will only increase the quantity produced up to a point (qmax) due to the “Law of Diminishing Returns,” an observed physical law, and increasing these inputs further can even interfere with the production process enough to actually reduce the quantity produced.

Note: the minimum of an average cost curve can be determined geometrically from its corresponding total cost curve by noting that the slope (i.e., rise over run) of the line from the origin to a point along the total cost represents the average cost since AC(q) = TC(q)/q.

2.2.3 Long-Run and Short-Run Costs If the price at which a firm can sell a product is less than the minimum attainable average variable cost AVC, a competitive firm will not produce at all; but at zero output and zero revenues, if the fixed cost F continues the firm will be incurring a loss (and will continue to incur a loss at any price below the minimum AC). The distinction between short-run and long-run costs provides an explanation of how a firm can stay in business when operating at a loss:

Long-run costs ⇔ all inputs can be varied ⇒ only variable costs

Short-run costs ⇔ some inputs are fixed ⇒ both variable and fixed costs

How long is the long run? The long run for a competitive firm is sufficient the time alter all of the inputs to a production process in response to a change in price, including, possibly, having the firm go out of business.

The long-run total cost (LRTC) and average cost (LRAC) functions represent the total and average cost, respectively, of producing any output q when all inputs are allowed to vary. The short-run total cost (SRTC) and average cost (SRAC) functions apply when one or more inputs are held fixed at a constant cost F.

The relationships between total short-run and long-run costs are shown in Figure 2.3 (top). The short-run total cost function SRTC1 applies when the fixed factors are held constant at a level appropriate for small-scale production (q1); similarly, SRTC2 and SRTC3 are associated with the higher levels of fixed cost appropriate for medium-scale (q2) and large-scale (q3) production, respectively. The corresponding average cost functions are shown in Figure 2.3 (bottom).

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q0

$

$/q

Tota

l Cos

t

q1 q2 q3

Output Quantity

q0 q1 q2 q3

Output Quantity

Ave

rage

Cos

t

LRTC

SRTC

3

SRTC

2

SRTC

1

LRACSRAC3

SRAC2

SRAC1

F1

F2

F3

Figure 2.3. Long- and short-run cost curves: Total cost (top) and average cost (bottom).

In the absence of transactions costs, and if only unspecialized and divisible resources were used as inputs, there would be no difference between “long run” and “short run” costs; but, once a facility has been established, the presence of costs associated with the sale and purchase of inputs and the fact that some resources become specialized and/or indivisible results in fixed input factors and a corresponding distinction between the short run and the long run.

Since it is not possible to change fixed inputs immediately (or otherwise they would not be fixed), the response of a firm to a change in demand (and corresponding change in output quantity) or to a change in price depends on whether or not the change is regarded as temporary or permanent:

Temporary change in demand ⇒ do not change fixed inputs ⇒ stay on current short-run curve

Permanent change in demand ⇒ change fixed inputs ⇒ move to new short-run curve

Shutdown Decision A firm makes a profit if a product can be sold at a price that equals or exceeds the cost of producing the product. Assume that a firm is currently making a profit producing a product and that its facility is the only fixed input factor involved in the production; all of the other factors

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are variable. In response to a change in the demand and/or price of the product in the market, the product can now be produced for AC (inclusive of facility costs) and AVC (exclusive of facility costs) and can be sold for P. If the change is temporary, then the costs and/or price will return to their previous values. Given the new AC, AVC, and P, the firm should make following decisions concerning the production of the product in response to the change:

P ≥ AC ⇒ Continue production

AVC ≤ P < AC and Temporary change ⇒ Continue production

P < AVC and Temporary change ⇒ Stop production and Keep facility

P < AC and Permanent change ⇒ Stop production and Sell (change) facility

2.2.4 Product Cost In order for a product to be profitable in the long run (i.e., so that a non-negative net present value is actually realized), a firm needs to recover all of the costs associated with providing the product. The revenues received from the sale of the product are used to recover these costs. The total cost to the firm of providing a product for sale has two principal components, with the majority of the costs of each component being incurred at different stages in the project’s life cycle:

• Investment costs. Multi-period (typically multi-year) costs associated with acquiring the fixed assets used to provide the product.

Investment costs, the majority of which are incurred prior to the start of actual production, are associated with the tangible fixed assets (e.g., land, buildings, and equipment) and the intangible fixed assets (e.g., R&D costs for basic research, product design, and production process design) used to provide the product.

• Operating costs. Single-period (typically less than a year) costs associated with acquiring the current assets used to produce the product.

Operating costs, the majority of which are incurred during actual production, are associated with the current assets used to produce the product (e.g., raw materials, purchased components, labor, and facility and general administrative operating costs) and to provide the finished product to its customers (e.g., finished goods inventory, sales and marketing, transport, customer service, and warranty costs).

Although most of the investment costs are incurred prior to the start of the actual production of a product, they can (in most cases) only be recovered from the revenues generated from the final sale of the product to customers. For some products like pharmaceuticals, the costs associated with R&D and sales and marketing can be many times greater than the product’s actual production costs.

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2.3 Scale and Scope

2.3.1 Facility Size In the short run (once a facility is established), the total cost function associated with production at the facility ultimately starts to increase at an increasing rate due to the Law of Diminishing Returns. In the long run (e.g., when a new facility is being planned or a major modification is being planned to an established facility), the shape of the total cost function is governed by the economies and diseconomies of scale associated with different levels of production at the facility. These economies set a minimum efficient scale (MES) for the facility. The MES is the point or range where the long-run average cost function is at a minimum, and corresponds to the most efficient size for the facility.

$/q

qOutput Quantity

Ave

rage

Cos

t

MES2

MES1MES3

LRAC2

LRAC1

LRAC3

Figure 2.4. Minimum efficient scales of facilities.

In some industries, the MES of facilities may determine market structure. In Figure 2.4, LRAC1, with steep cost gradients and a single optimum size (MES1), would result in all facilities in the industry being about the same size; LRAC2, with gentle cost gradients and a wide range of optimal sizes (MES2), would result in facilities at nearly any size; and LRAC3, with a optimal size (MES3) that may extend beyond the firm’s or the entire market’s total size, would result in a single facility being capable of supplying all output (a possible “natural monopoly”).

An economy of scale exists when larger output is associated with lower average costs (i.e., the downward sloping portion of an average cost function); a diseconomy of scale exists when larger output is associated with higher average costs (i.e., the upward sloping portion of an average cost function).

In the short run, the Law of Diminishing Returns causes diseconomies of scale to occur as output is increased; in the long run, the Law of Diminishing Returns will also “eventually” cause diseconomies of scale to occur as output is increased, but level of output at which this condition is encountered can be well beyond the market’s total size. Within the relevant range of possible outputs, the interplay of both economies and diseconomies of scale determine the shape of the long-run average cost function and the resulting MES of facilities.

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SPRING 2003 2.3. SCALE AND SCOPE

Economies of Scale Possible sources of economies of scale for a facility include the following:

Specialization As a facility’s work force expands in response to increasing output, it can be used for more specialized tasks; through the “division of labor,” each worker can learn to perform a specific task more rapidly and precisely, the loss in time and effort associated with shifting among tasks is reduced, and (as noted by Babbage) highly skilled workers are not required to perform low-skilled tasks that could be performed by lower wage workers. Machines can also become more specialized and thereby more efficient; although specialized machines are often more expensive, the long production runs possible when output increases serve to reduce the cost per unit of output (i.e., average cost) because the fixed cost of the machines can be spread out over the larger output.

Physical laws Physical laws associated with a production process often favor large size. “Volume–surface” and “area–perimeter relationships” are examples: the surface area of a sphere increases as the two-thirds power of its volume and the perimeter of a circle increases as the square root of its area, thus energy losses across the surface or perimeter are reduced as size increases; the cost of building and operating many process-industry facilities increases roughly as the two-thirds power of their capacity—at least within a range. Also, some forces operate most efficiently at large scale; for example, a single twenty-ton stamping machine is more efficient than five hundred hammers.

Risk pooling Because of the law of large numbers, the effects of uncorrelated random events tend to cancel each other out when there is a number of events. This can result in a natural economy of scale, for example, with respect to the amount of inventory needed to achieve a specific level of service [Carlton and Perloff].

The Law of Multiples Specialization and physical laws can cause indivisibilities between the inputs used in a production process because certain inputs must be at least a minimum size (i.e., “lumpy” inputs). When several inputs are lumpy, the most efficient combined size may be the least common multiple of the minimum size for each; for example, if a product requires three different operations on three different types of machines and the first machine is most efficient at 4 units per hour, the second at 3 units per hour, and the third at 2 units per hour, then the minimum efficient scale (MES) is 12 units per hour (the least common multiple) using 3 machines for the first operation, 4 for the second, and 6 for the third operation.

If, due to the Law of Multiples, the gradient of the average cost function is steep around the MES, there are ways to offset the impact of the law to enable efficient production at lower outputs: (a) sell or inventory or use in another product (see Item 0, below) the “excess” produced by an input that has a large minimum size; (b) increase the output of an input that has a small

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minimum size (a “bottleneck” input or resource) by increasing its utilization (e.g., adding an extra shift, reducing setup times, etc.); and (c) purchasing “extra” input on the market.

Shared resources A facility producing a variety of products may permit certain inputs (or resources) that are common to each product to be shared, which has the potential of reducing the per-unit cost of utilizing these resources (also termed an “economy of scope” with respect to these products). This can help mitigate large individual product demands implied by the Law of Multiples because, even though the demand for each individual product produced at the facility may be far below its individual MES of production, the aggregate demand for several products sharing common resources may be closer to the aggregate MES to produce all of the products. When a product is produced below its individual MES, some of the resources used in its production are underutilized; when additional products can share these resources, the resources can be more fully utilized. Also, if the demand for each product produced at the facility fluctuates independently of the other products during a period of time, then common resources are more likely to be better utilized during the period of time. The degree of resource sharing can range from just sharing a common building and administration staff (i.e., factory overhead) to sharing common machines and operators to sharing common raw materials.

Cheaper inputs A facility producing a large volume of output may be able to buy some or all of its inputs more cheaply due to economies of scale in the procurement process (e.g., full vs. partial truck loads) and in the production and marketing activities of its suppliers.

$/q

qOutput Quantity

Ave

rage

Cos

t

q1q2

LRAC-Tran

LRAC-Prod

LRAC-Prod&Tran

Figure 2.5. Reduction in MES from q1 to q2 due to transport costs.

Diseconomies of Scale. Possible sources of diseconomies of scale for a facility include the following:

Transport costs When the “value-to-density ratio” of a product is low, transport costs can become a large share of the total cost to produce and distribute the product. Since average transport costs increase when customers are located further from a facility, the density of the market for a low value-to-

14

SPRING 2003 2.3. SCALE AND SCOPE

density product limits the effective size of a facility; for example, ready-mix cement is usually produced locally, while a single semiconductor manufacturing facility can serve a worldwide market.

In Figure 2.5, the MES of a facility with respect to production costs would be larger (q1 on LRAC-Prod) except for the diseconomy of scale associated with transport costs (LRAC-Tran) which reduces the effective MES of the facility (q2 on LRAC-Prod&Tran).

More costly inputs When the size of facility increases, certain inputs can be more costly to purchase as output increases; for example, the supply of trained labor in the vicinity of the facility may be limited and will result in costly training and/or relocation, and the cost of land may increase if the facility requires a large site with flat terrain. In addition, some of the sources of economies can become diseconomies when they are pushed too far; for example, task specialization can become excessive, resulting in careless work and low quality.

When an increase in the size of the facility is associated with an expansion in output of the whole industry, then the price of some or all of the input factors used in production may increase due to the “factor-price effect” as each firm in the industry bids up the price of the inputs. The price increase will be the greatest in the short run, but even in the long run the price of some inputs will remain high due to supply limits (e.g., good ore veins).

Risk When the size of an entire firm increases, there is usually a decrease in its overall financial risk (which can, e.g., lower its cost of capital); but when the size of an individual facility increases (possibly one of many facilities owned by a single firm), there is usually an increase in the risk associated with the particular facility. Although most environmental risks like fire, flood, and earthquakes can be insured against so that there is no financial risk to the firm, other risks are difficult or impossible to insure against. (The lack of any type of crop insurance is one explanation for why medieval farmers typically traveled long distances between multiple small plots of land located in areas subject to different environmental risks instead of tending to a single large plot [Landsburg].)

Most of these uninsurable risks are associated with the use of specialized resources in the face of uncertainty. Specialized resources may be difficult to modify or sell if for some reason circumstances change and the resources are no longer needed in their current form. In some cases, this type of risk can be reduced by using more flexible, modular, or marketable resources—but there is a tradeoff because less specialized resources may result less efficient production. In some cases the sheer physical size of a building may carry a high risk; for example, two smaller warehouses located close together at a site might be preferable to one large warehouse because, even though the two warehouses might be slightly less efficient to operate, it may be much easier in the future to either sell one of the smaller warehouses or modify it for other uses.

15


2.3.2 Firm Size The economies and diseconomies of scale that lead to the MES of a single facility are somewhat different from the factors that determine the economies and diseconomies of scale (or size) of a firm—a firm that may own and operate several separate facilities. While the size of facilities is mainly dictated by the technology of the production process, the size of the firms that operate the facilities is determined in large part by control or organizational requirements and financial considerations. One of the principle reasons for factory-based manufacturing is that it provides firms with a means to efficiently execute the internal control of production-related activities. In a market economy, the size and scope of a firm extends to those activities that can be coordinated more efficiently through internal controls than by external market transactions. The presence of viable firms in the economy demonstrates that there must be benefits associated with use of internal controls, while the limited size of these firms demonstrates that, beyond some level, market transactions are more efficient for controlling economic activities.

The benefits of market transactions are due to the information provided by prices concerning the relative value of the resources used in the production process; price information enables efficient resource allocation without requiring centralized control (some large firms use internal prices, also termed “transfer prices,” to allocate goods and services between the separate divisions of the firm). The benefits of internal controls are due to the elimination of the transaction costs associated with market transactions; these transaction costs include the costs associated with creating a market, price negotiations, and contract enforcement. The costs of internal controls are the monitoring costs associated with ensuring efficient internal resource utilization and allocation. The overall effectiveness of a firm can diminish with increasing size if it is difficult to identify (and reward) the individual effort of each employee. Although stock ownership in the firm, in addition to wages, can be used to reward employees so that they work hard even when they are not being monitored, in a large firm each employee will own only a small portion of the firm. In a small firm, in contrast, an employee might also be the owner of the firm, resulting in monitoring costs of zero since any and all of the “employee’s” efforts will be rewarded. Also, as the size of a firm increases beyond the ability for direct management control, layers of bureaucracy are added to management. Bureaucracy adds to overhead costs and reduces the quality of decision making due to distortions in information as it is passed up to top management. For a particular facility, the costs and benefits of internal controls can result in both economies and diseconomies of scale.

Another factor associated with firm size that has an impact on facility size is financial risk. While the uninsurable risk of using specialized resources can be a diseconomy of scale for a single facility, the financial impact of this risk can be reduced if the facility is owned by a large firm. A large firm will likely have a lower cost of capital as compared to a smaller firm due to the “portfolio effect” associated with the larger firm’s ability to spread the risk of a single facility over many other investments. The smaller firm might be out of business with one unfavorable investment.

16

SPRING 2003 2.4. DISCOUNTING

2.4 Discounting The discounting process involves the use of the following compound interest formulas. Let

N = number of compounding periods

r = effective interest or discount rate (in decimal form) per compounding period

FV = future value of a cash flow

PV = present value of a cash flow or uniform series of cash flows

Ct = cash flow occurring at the end of period t

Given N periods, the index t can range from 0 to N, where t = 0 corresponds to the beginning of the first period (or the end of period 0), t = 1 corresponds to the end of the first period (and the beginning of the second period), and t = N corresponds to the end of the Nth period.

2.4.1 Basic Formulas

Future value For t = 0, FV = PV; for t = 1, FV = PV(1 + r); for t = 2, FV = PV(1 + r)(1 + r) = PV(1 + r)2; and, in general, the future value at the end of period t of the present value of a single cash flow (or payment) is

Future value of single payment: FV PV FV PV r t PV r t= =, %,b g 1+b g . (2.6)

Present value Using (2.6) and solving for PV, the present value of a single payment occurring at the end of period t is

Present value of single payment: PV FV PV FV r t FVr t=

+, %,b g b g1

= . (2.7)

Net present value The net present value of a series of cash flows Ct, t = 0, 1, . . . , N, is, using (2.7),

Net present value: ( )( )0 0

, %,1

N Nt

t tt t

CNPV C PV FV r tr= =

= =+

∑ ∑ . (2.8)

Uniform series of cash flows If C is the cash flow per period of a uniform series of N end-of-period cash flows (also termed an “annuity”), where C = Ct, t = 1, . . . , N, then, using (2.7),

( )( )

( )1 1

, %, 11

N Nt

tt t

CPV C PV FV r t C rr

−

= =

= = =+

∑ ∑1

N

t=+∑

17


( ) ( )11 1 NC r r−= + + + +−

1

. (2.9)

Multiplying (2.9) by (1 + r),

( ) ( ) ( ) ( )11 1 1 1NPV r C r r r− − + = + + + + +

( ) ( )11 1 1 NC r r− − += + + + + + , (2.10)

and subtracting (2.9) from (2.10) results in

( ) ( )1 1 1 NPV r PV C r − + − = − + ,

which, assuming r ≠ 0 and solving for PV, reduces to

Present value of uniform series: ( ) ( )1 1, %, , 0

NrPV C PV C r N C r

r

− − + = = ≠

. (2.11)

If r = 0, then (2.9) reduces to , which can also be derived via (2.11) through the use of l’Hôpital’s rule:

C N⋅

( ) ( ) 1

0 0

1 1 1lim lim

1

N N

r r

r N rN

r

− −

→ →

− + + −

= = .

The present value of the uniform series of cash flows in (2.11) does not include a cash flow for the beginning of period 0 (i.e., t = 0). If the cash flow C0 occurring at the beginning of the first period is added to the uniform series of N cash flows C occurring at the end of each period, then the net present value is

( )0 , %,NPV C C PV C r N= + . (2.12)

Using (2.11) and solving for C, the capital recovery cost of a single cash flow (or payment) PV occurring at the beginning of the first period is

( )( )

: , %,1 1 N

rCapital recovery cost C PV C PV r N PV rof single payment r −

= = − +

, 0≠ . (2.13)

If r = 0, then (2.13) reduces to PV N .

2.4.2 Effective Cost vs. Capital Recovery Cost “Effective cost” and “capital recovery cost” represent two alternate ways of determining the full opportunity cost of an investment in fixed assets. They represent, respectively, either the net present value or the uniform per-period cost associated with the loss in value (or depreciation) of the fixed assets and the cost of the capital used to finance the assets (i.e., the interest on long-

18

SPRING 2003 2.4. DISCOUNTING

term debt and the required return on equity). In facilities planning, they can be used to equate the (multi-period) investment costs of fixed assets with the (per-period) operating costs of the assets.

Given a cost of capital of r per period, the “effective cost” (IVeff) for fixed assets with an initial investment cost of IV and a salvage value of SV at the end of N periods is equal to the initial investment cost IV minus the present value (2.7) of the salvage value SV:

Effective cost: IV . (2.14) IV SV PV FV r N IV SVr N

eff = - = -+

, ,b g b g1

If SV = 0, then the effective cost of the fixed assets is equal to their initial investment cost.

Using the capital recovery cost of a single payment (2.13) to convert the effective cost (2.14) to an equivalent uniform series of end-of-period costs, the capital recovery cost per period (CCR) of the fixed assets is equal to the following:

Capital recovery cost: ( ) ( )CR eff , ,1 (1 ) N

rIV C PV r N IV SV SV rr −

= = − − +

C , (2.15) + ⋅

where CCR ( )eff , ,IV C PV r N= (1 ) 1 (1 )N N

SV rIVr r −

= − + − +

(1 )1 (1 ) 1 (1 )

N

N

r r rIV SVr r

−

− N−

+= − − + − +

( )1 (1 )

1 (1 ) 1 (1 )

N

N

r r rrIV SVr r

−

− N−

− − + = − − + − +

( )1 (1 ) N

rIV SV SV rr −

= − + ⋅ − +

( ) ( ), ,IV SV C PV r N SV r= − + ⋅ .

If SV = 0, then CCR = C, the capital recovery cost of the single payment IV.

The capital recovery cost (2.15) provides the following insights concerning investments:

1. If IV = SV, then (2.15) reduces to SV r◊ , which is equal to IV r◊ since IV = SV. Since the initial investment is fully recovered and not reduced in value (e.g., working capital, bonds, and most land), the capital recovery cost is just the opportunity cost of the funds invested, as represented by the cost of capital (e.g., the interest payments on a bond, the principal of which is repaid at the bond’s maturity date).

2. As N Æ• , then (2.15) reduces to IV r◊ . Since the salvage value will never be realized, the capital recovery cost is equal to the initial investment cost times the capital recovery cost in perpetuity (see Eq. (2.17) in Sec. 2.4.3 ).

19


3. If IV represents the amount of an amortized loan (e.g., a home mortgage), where SV = 0 from the lender’s point of view, then the capital recovery cost is the amount of loan times the capital recovery cost of the single payment (2.13) from the lender to the borrower; it represents the payment required per period from the borrower to the lender to cover principal and interest on the loan.

2.4.3 Further Issues in Discounting

Perpetuity A “perpetuity” is an infinite series of uniform end-of-period cash flows. If r > 0, then

as 1 0+ Æ-r Nb g N Æ• so that, using (2.11), the present value of C, the cash flow per period of the perpetuity, is

Present value of perpetuity: ( ) ( )1 1, %, lim

N

N

r CPV C PV C r Cr r

−

→∞

− + = ∞ = =

. (2.16)

Likewise, taking the limit of (2.13) as N Æ• or solving (2.16) for C, the capital recovery cost in perpetuity of PV is

Capital recovery cost in perpetuity: ( ), %,C PV C PV r PV r= ∞ = ⋅ . (2.17)

Nominal interest rates A “nominal interest rate” is an interest rate specified for a basis period (e.g., a year) that (1) can be different from the compounding period (e.g., a month) and, if different, (2) does not include the effects of inter-compounding-period discounting during the basis period. If rnom is the nominal interest rate per basis period, there are Nnom basis periods, and there are M compounding periods during each basis period, then r, the effective interest rate per compounding period, and N, the number of compounding periods, are as follows:

r rM

N M N= =nomnomand ◊

=

The nominal interest rate is equal to the effective interest rate if the basis period is the same as the compounding period.

The most common basis period for specifying nominal interest rates is a year. For example, 12% compounded monthly is usually understood to refer to a nominal interest rate of 12% per year, corresponding to an effective interest rate of 1% per month (or b g 12.68% per year, which is also termed the “annual percentage rate” (APR)).

1 0 01 112+ -.

Nonintegral number of compounding periods When a cash flow does not occur at the beginning or end of a compounding period, it is possible to use a nonintegral number of compounding periods to discount the cash flow. If N is a nonintegral number of compounding periods such that N = N + λ, where N is the integral portion and λ, 0 < λ < 1, is the fractional portion of N, then N corresponds to N complete

20

SPRING 2003 2.5. CAPITAL BUDGETING

compounding periods and λ of the ( N + 1)th period. For example, the future value FV of an amount PV after N periods is the following:

FV PV FV PV r N FV PV r PV r rN= =, %, , %,c hb g b g b g 1 1+ +

= + = + =+PV r PV r PV FV PV r NN N1 1b g b g b , %, g.

2.5 Capital Budgeting

2.5.1 Introduction Capital budgeting is the process of planning investments in fixed assets. In facilities planning, it provides a formal means of evaluating alternative facility plans. Fixed assets (also termed “capital assets” or “capital goods” or just “capital”) are assets whose benefits or returns are expected to extend beyond one year, while current assets (e.g., cash, accounts receivable, and inventories) are assets whose returns are expected within a year—the investment in current assets is termed “working capital.” Fixed assets can either be tangible (e.g., the land, buildings, and equipment that comprise a facility) or intangible (e.g., research and development (R&D) expenses for a product).

Since fixed assets provide returns for multiple years into the future, the discounting process is used in capital budgeting to recognize the time value or opportunity costs of the investment funds used to acquire the fixed assets. Discounting gives explicit consideration to the fact that, all else being equal, a dollar received immediately is preferable to a dollar received at some future date. Discounting is not typically an important issue in current asset analysis, and is usually ignored.

Project interdependence In capital budgeting, each separate configuration of fixed assets to be considered for acceptance (i.e., selection or acquisition) is termed a project. Associated with each project are the costs and benefits (i.e., negative and positive cash flows, respectively) that would occur if the project is accepted. If only a single project is being considered, the project should be accepted only if its benefits meet or exceed its costs; if more than one project is being considered, the degree of interdependence between the projects has to be taken into account in the capital budgeting analysis. The possible degrees of interdependence between two projects, A and B, are as follows:

• Prerequisite—project A is possible only if project B is accepted;

• Complement—the benefits (costs) of project A would increase (decrease) if B is accepted;

• Independent—project A is not affected by the acceptance of project B, that is, accepting one project does not influence the acceptance of any other project (except with respect to the availability of funds);

21


• Substitute—the benefits (costs) of project A would decrease (increase) if B is accepted;

• Mutually exclusive—project A is not possible if project B is accepted, that is, accepting one project implies rejecting the other.

In facilities planning, capital budgeting analysis can be used to determine which facilities, each at different locations and/or producing different products, should be built (independent projects), or to select a single design to build a facility at a site from several alternate designs that are available for the facility (mutually exclusive projects). If a project (A) is a prerequisite of another project (B), then both projects together can be considered to be a single project (A&B) that is mutually exclusive with respect to the other (A) by itself. Since in a capital budgeting analysis it can be difficult to quantitatively determine all of the combinations of costs and benefits between projects that are complements or substitutes of each other, it may be reasonable to assume that the projects are either independent or mutually exclusive; in this case, a qualitative description of the interdependencies between the projects should, at least, be provided in addition to the quantitative analysis.

Project categories Facility-related projects are frequently classified into the following categories:

• Maintenance—expenditures to maintain the current level of performance of a facility;

• Cost reduction—expenditures to lower the cost of producing the current level of output at a facility;

• Expansion—expenditures to increase the future level of output of a facility;

• Construction—expenditures to establish a new facility;

• Mandatory—expenditures required at a facility to comply with, for example, government regulations, insurance requirements, or labor agreements.

Different analysis procedures are often used for the different categories of projects. The cost of capital (i.e., discount rate) and the level of detail of the analysis used for each project category are related to the magnitude of the expenditures and the uncertainty of the costs and benefits associated with the typical projects that occur in each category. Little or no analysis may be required for routine maintenance projects or mandatory projects (that, if avoided, would result in large fines or possible shutdown of the facility); simple procedures like the “payback method” may be used for small-scale cost reduction projects suggested by the engineering staff and approved by the plant manager at the facility level; while formal capital budgeting procedures may be required for large-scale expansion projects and new facility construction, with final approval at the corporate headquarters level.

Incremental cash flows In capital budgeting, a project is evaluated based on the magnitude and timing of the incremental (explicit and implicit) cash flows that would be induced if the project were to be accepted. For a profit-maximizing firm in a market economy, cash outflows and inflows, as signaled through prices, provide the ultimate measure of the costs and benefits (to the firm) associated with

22


engaging in any economic activity. The benefit to the firm from the production of a good or service is the revenue (i.e., cash receipts) received from its sale at a price in the market. The cost to the firm to produce a good or service is the sum of the payments (i.e., cash expenditures) required to attract the input factors or resources necessary for its production. The payments required are the market prices of the resources and are made to the owners of the resources. The market price of a resource represents the amount sufficient for the owner of the resource to forgo the opportunity to receive the benefits associated with the best alternative use of the resource.

2.5.2 Formal Capital Budgeting Analysis The same type of capital budgeting analysis can be used to determine whether one or more independent projects should be accepted, or to select a single project from among several mutually exclusive projects (including combinations of prerequisite projects); a more complicated analysis is required for projects that are complements or substitutes of each other.

Given M projects, the basic elements used for a capital budgeting analysis of the projects are the following:

r = weighted average cost of capital (effective interest or discount rate in decimal form) per compounding period at which the cash flows associated with the projects are to be discounted;

Nj = expected life (number of compounding periods) of project j;

IVj = investment costs, where IV0 is the initial investment expenditure (negative cash flow) to acquire at beginning of period 0 (or time 0) the fixed assets and working capital associated with project j, and SVj = jNIV− is the salvage value (positive or negative cash flow) received at end of period Nj from the disposal of the fixed assets and recovery of working capital associated with project j;

Rjt = revenue (or receipts) exclusive of SVj that would occur during period t if and only if project j is accepted;

OCjt = operating costs (or expenditures) that would occur during period t if and only if project j is accepted, excluding interest expenses of any long-term debt used to finance the investment in the project;

Cjt = net cash flow of project j at the end of period t.

= , 0, ,jt jt jt jR OC IV t N= …− −

Assumptions The following assumptions are made to simplify the presentation.

1. The cost of capital r is the same for all projects under consideration.

2. IVj and OCjt are specified as non-negative values (and, thus, are subtracted in determining the net cash flow).

23


3. All of the initial investment expenditures associated with each project j are incurred at time 0, the start of the project; if these expenditures are incurred over several periods, then IVj should represent their present value at time 0.

4. Any and all of the salvage value from each project j is received at the end of period Nj; if the salvage value is received over several periods, then SVj should represent their future value at the end of period Nj.

5. All projects under consideration are either all independent or all mutually exclusive.

NPV of project Using Eq. (2.8), the net present value of project j can be determined as follows:

( )( )0 0

, %,1

j jN Njt

j jt j tt t

CNPV C PV FV r N

r= =

=+

∑ = ∑ . (2.18)

If project j is accepted, the value of the firm will increase by the amount NPVj.

Cost of Capital (r) = 0.20Project A

Period Revenues Oper Cost Invest Cost Net Cash Flow PV/FV Present Value(N) (R) (OC) (IV) (C) (1/(1+r)^N) C*(1/(1+r)^N)

0 $0 $0 $1,000,000 ($1,000,000) 1.0000 ($1,000,000)1 500,000 300,000 0 200,000 0.8333 166,6672 1,000,000 500,000 0 500,000 0.6944 347,2223 1,000,000 500,000 0 500,000 0.5787 289,3524 1,000,000 500,000 0 500,000 0.4823 241,1275 500,000 375,000 (250,000) 375,000 0.4019 150,704

Net Present Value (NPV) = $195,071 Figure 2.6. Use of a spreadsheet to calculate the NPV of a project.

Using a spreadsheet In Figure 2.6, a spreadsheet is used to calculate NPVA = $195,071, the net present value of Project A. In the spreadsheet, relative addressing is used for all the calculations except for the cost of capital, 0.20, which is referenced as an absolute address (in MS Excel, it is referenced as $C$1 (third column, first row)).

Projects with different lives When two or more mutually exclusive projects have different lives, it is not appropriate, in general, to base the acceptance decision on just the NPVj given in (2.18) because the projects with longer lives would have more time to accrue positive cash flows, thereby increasing their net present values and biasing the capital budgeting decision in their favor. To eliminate this bias, the projects must somehow be converted to projects that have equal lives.

One means of accomplishing this conversion is to assume that each project j will be replaced with an “identical” project at the end of every Nj periods. This series of replacements, termed a

24


“replacement chain,” can either be extended out to the least common multiple of all the projects’ lives, or assumed to continue in perpetuity (i.e., an infinite series of replacement projects). Unlike a positive NPVj, which represents the amount by which the value of a firm will increase if project j is accepted, a positive net present value for a replacement chain does not represent the actual increase in the value of the firm; but its use will lead to a correct capital budgeting decision relative to the other mutually exclusive projects being considered.

An alternative to the explicit use of replacement chains (and net present value in general) is to use (2.17) to convert NPVj to the equivalent uniform end-of-period net cash flow (also known as “annual worth”) of project j, where an infinite series of replacements is implicit since it is necessary to assume that the uniform series of cash flows will continue at the same uniform level forever.

The replacement projects are considered to be identical to the initial project in a replacement chain if the timing and magnitude of all of their cash flows are the same as the cash flows of the initial project, except for being shifted a multiple of Nj periods into the future. In some cases, it is not reasonable to assume that all of the cash flows associated with the initial project will be repeated when the project is replaced; for example, the salvage value of existing equipment that, once salvaged at time 0, will not be available for salvage in the future. Such one-time cash flows should not be include in the replacement projects.

Project acceptance criteria Given M projects that are either all independent or all mutually exclusive, determine, using (2.18), the net present value NPVj of the cash flows associated with each project j, j = 1, . . . , M. Projects can then be accepted based on the following criteria.

1. Independent projects: Accept all projects with a non-negative NPVj; reject all projects with a negative NPVj.

2. Mutually exclusive projects with equal lives (all Nj equal): Accept the project with the largest non-negative NPVj; reject all other projects. (Reject all projects if all NPVj’s are negative.)

3. Mutually exclusive projects with different lives (all Nj not equal): Accept the project with the largest non-negative equivalent uniform end-of-period net cash flow Cj, where Cj =

( , %,jNPV C PV r N )j ; reject all other projects. (Reject all projects if all Cj’s are negative.)

Payback Method The payback method is an alternative means of evaluating projects. It is typically used for evaluating small cost-reduction projects. The payback period of a project is the number of periods it takes to recover the initial investment expenditure from the project’s future (undiscounted) positive net cash flows. The payback period of a project can be used in place of determining the net present value of the project. If the project provides a uniform series of positive end-of-period net cash flows C and has an initial investment expenditure of IV at time 0, then the payback period of the project is

25


Payback period IVC

= . (2.19)

The principal advantages of using the payback method to evaluate projects are the following:

1. It is (arguably) easier to understand and explain to others;

2. There is no need to determine a cost of capital;

3. It gives the same relative ranking of mutually exclusive projects as the NPV approach if the projects all have the same C and all SV = 0.

For small cost-reduction projects at large firms, there is typically a fixed budget for these types of projects with no implied cost of capital associated with the budget. The principal disadvantages of using the payback method are the following:

1. It ignores discounting (i.e., assumes a 0% cost of capital);

2. It ignores salvage values;

3. It ignores cash flows that occur beyond a project’s payback period.

The third disadvantage is not a problem if, as assumed in (2.19), the project provides a uniform series of returns and SV = 0. Cost-reduction projects (the bread and butter of most industrial engineers) typically provide uniform returns because, once the project is implemented, their returns (e.g., the cost savings associated with a process improvement) continue to be realized at a constant magnitude until the production process changes.

Projects will long payback periods are usually considered risky because more distant cash flows are usually more uncertain. In addition, a firm may not be in business at the point in time at which the returns beyond a project’s payback period could be realized. As a rule of thumb:

• small cost-reduction projects with payback periods not exceeding two or three years are usually considered good candidates for acceptance;

• projects with payback periods of a year or less are almost always accepted and given high priority;

• projects with payback periods of greater than two or three years are usually not accepted (or maybe given further consideration only after a more detailed analysis).

2.5.3 Issues in Capital Budgeting

Opportunity costs All costs are opportunity costs: the cost of any activity is the loss of the opportunity to receive the benefits associated with the best alternate activity available. If the full opportunity costs of a project are used to determine its net present value NPV, then any amount NPV > 0 represents the “economic profit” possible from the project; a NPV = 0 represents a project with “normal profit.”

For a profit-maximizing firm, the opportunity costs of a project are both

26


• the cash outflows that will occur, if and only if the project is accepted, and

• the cash inflows that will not occur, if and only if the project is accepted.

While it is usually not too difficult to identify the “explicit” cash flows associated with a project, it can be much more difficult to identify the “implicit” cash flows that will or will not occur as a result of the project’s impact on the existing resources and the future activities of the firm not directly related to the project under consideration. (The term “opportunity costs” is sometimes used to refer to just “implicit costs” in order to distinguish these costs from the “explicit costs” considered in the context of accounting.)

For example, if a project will be using space in a facility that is currently empty, then the opportunity cost of using the space might be zero if the space would otherwise remain empty during the life of the project; but if it possible to rent the space to others or use it for future projects, then the (implicit) opportunity costs induced by accepting the project would be the rental receipts forgone or the costs of expanding the facility to accommodate future projects. If several mutually exclusive projects are being considered that represent all current and future uses of the space (including renting or selling the space), then the opportunity cost of using the space for one particular project is difference between the maximum net present value available from all of the projects and the net present value of the particular project.

Sunk costs Sunk costs are cash outflows that have either already occurred and cannot be recovered, or have not yet occurred but cannot be avoided. As such, sunk costs should not be considered in capital budgeting decisions. Cash flows that have already occurred (e.g., past purchases) or cannot be avoided (e.g., future lease payments) have no impact on the incremental cash flows that will occur if a project currently under consideration is accepted. In the short run, the portion of fixed costs that are not recoverable are sunk costs. The only impact that the project can have on the existing fixed assets of a firm is through a change in their salvage value that would occur as a result of the project being accepted. For example, if a project can utilize an existing machine that currently has excess capacity, the opportunity cost of using the machine is any reduction in the future salvage value of the machine; the initial investment expenditures that have already occurred to acquire the machine are sunk costs and should not affect the decision to accept the current project under consideration.

Cost of capital The cost of capital (also termed the “minimum acceptable rate of return”) used in capital budgeting should be the weighted average of the cost of the different types of funds a firm uses to finance investments (e.g., the after-tax interest rate on new debt and the cost of equity, weighted by the proportion of debt and equity in a firm’s capital structure). The cost of capital for a project represents the opportunity cost of the funds invested in the project—if the funds are not invested in the project, they can be invested in other ways to provide revenues at least equal to the cost of capital. The cost of capital can be adjusted upwards or downward to reflect the riskiness of a project.

27


For example, if a firm’s investment funds are obtained using 50% long-term debt, at an after-tax interest rate of 7% per year, and 50% equity, at 13% per year, then the weighted cost of capital is (0.5)·7 + (0.5)·13 = 10%. If $10 of revenue will be received per year from $100 of investment (composed of $50 debt and $50 equity), then $50·(0.07) = $3.50 is the interest on the debt and 10 – 3.50 = $6.50 is the return on equity.

Timing of cash flows Many of the cash flows induced by a project may not occur at the beginning or end of the time period used in the capital budgeting analysis. If cash flows occur a multiple times throughout a period (e.g., monthly sales revenues for a year time period), then it is common practice to use to as an end-of-period amount the simple sum (i.e., without in-period discounting) of the cash flows that occur during the period (e.g., the sum of the monthly sales revenues). If a cash flow occurs at a single point in time, then either the beginning or end of the closest time period, or a nonintegral number of compounding periods, can be used.

Inflation As long as all of the cash flows associated with a project are expected to increase at the same rate of inflation, the effects of inflation can essentially be ignored in capital budgeting by both:

1. Stating the future cash flows in terms of “current” (i.e., not including future inflation) dollar amounts, as opposed to the “actual” (i.e., including future inflation) dollar amounts received throughout the project, and

2. Using the “real,” as opposed to the actual or “nominal,” cost of capital.

If r is the nominal cost of capital and i is the rate of inflation, then

r ri

r ii

r ii

rreal =++

- =+ - +

+= -

+ª -1

11

1 11 1b g i (2.20)

is the real cost of capital, where it is assumed that the basis period of the nominal cost of capital or interest rate is the same as the compounding period so that the nominal rate equals the effective rate.

For example, if the nominal cost of capital is 10% per year (compounded annually) and the inflation rate is expected to be 4% per year, then the net present value of current-dollar cash flows discounted at a real cost of capital of 5.77% (≈ 6%) is the same as the net present value of the actual-dollar cash flows that will occur discounted at the nominal cost of capital 10%. If the cash flows associated with a project are expected to increase at different rates of inflation (which is possible since “the” rate of inflation determined by the government is only a weighted average of a selected number or basket of goods and services in the economy), then their actual dollar amounts and the nominal cost of capital should be used in the capital budgeting decision.

Taxes As long as the impact of taxes on the cash flows associated with each project are similar in proportion, then the effects of taxes can be ignored as an initial approximation in capital

28


budgeting since the relative differences in cash flows will be the same. Taxes should be included in order to estimate absolute cash flows. Unless the goal of tax policy is to change economic decisions, tax effects are usually designed to limit their impact on decision-making.

Depreciation Depreciation represents the decline in value of a fixed asset as a result of the asset being used for a project—the difference between the value of the asset at the start of a time period and its (salvage) value at the end of the time period. For tax purposes, a certain amount of depreciation can be considered as a cost (i.e., deductible expense) each year to represent the decline in value of fixed assets (except land). During the life of the project, the depreciation of the asset does not generate any cash flows. The only cash flows that may result from the asset being used for the project are expenditures to purchase the asset and any cash flows associated with the disposal of the asset (which may be positive or negative). In capital budgeting, the only impact of depreciation on each period’s cash flow is through the reduction in income tax expense that it provides. The capital recovery cost of a fixed asset provides a per-period cost that is equivalent to the asset’s net present value. “Sinking-fund” depreciation plus interest on the initial investment, both at the cost of capital, is the only depreciation method that provides per-period costs that are equivalent to the asset’s capital recovery cost (“straight-line” depreciation is equivalent to using a 0% cost of capital to discount the sinking fund).

Cost of capital budgeting Since performing a capital budgeting analysis is itself not a costless operation, it is important to consider the level of detail required for the analysis in comparison to its potential costs and benefits. Once the idea for a project has occurred and prior to starting a formal capital budgeting analysis of the project, the costs associated with analysis itself are part of the project’s costs; once performed, the analysis becomes a sunk cost whether or not the project is accepted.

The principal cost of many cost reduction projects in a facility is the labor of the engineering staff during the projects’ planning stages. Because of these considerations, it is useful to perform a preliminary analysis of a project to decide what level of detail will be required to make a decision concerning its acceptance. For example, it may be decided that the “payback period” of a project provides enough information to make a reasonable decision, or it may be judged that the positive net present value of the readily identifiable cash flows associated with a project provide enough of a safety margin to more than outweigh the possible impact of the more difficult to determine opportunity costs (e.g., implicit costs) of the project—the cost of a more detailed analysis would only reduce the project’s net benefits without changing the final decision.

Externalities Although the cash flows associated with a project correspond to the costs and benefits of the project to a firm, they do not necessarily correspond to the costs and benefits of the project to an individual or to society as a whole. The costs and benefits of a project that are external to the firm and are not compensated by the firm are termed “externalities.” For example, if as a result of a project an employee of the firm has to work harder at no increase in salary, then the project

29


has increased the personal, non-monetary cost to the employee of his or her job; the firm itself does not incur a cash outflow associated with the increased labor provide by the employee, and, unless the employee owns stock in the firm, he or she will not realize any of the cash benefits resulting from the project. One of the functions of the legal system is to require firms to consider externalities: fines and legal liability serve to attach a cash cost to actions that would otherwise result in externalities. A firm may be required by a regulatory agency of the government to undertake a mandatory project that will not result in any cash inflows; the cash cost to the firm of not accepting the mandatory project would be a fine or possible shutdown.

2.6 Cost Accounting Cost accounting is the process of determining and recording the cost of producing a product or providing a service. Cost accounting information can be used for many purposes:

• it provides the basic data for financial and managerial accounting reports and budgets;

• it can be used to determine the effectiveness of past performance;

• it can be used as the basis for many short-term managerial decisions;

• it can be used to determine contract bid prices; and

• it can be used in capital budgeting as a starting framework for estimating future cash flows.

Capital budgeting involves long-term managerial decisions concerning fixed assets; once a project has been accepted and its fixed assets have become fixed (sunk) costs, cost accounting information provides a means of measuring the current effectiveness of the project (e.g., measuring errors in the original cash flow estimates) and of estimating the short-run costs associated with subsequent short-term decisions.

Many managerial decisions concerning a product involve the relationships between its cost, volume (output quantity), and sales price; examples include break-even analysis for a product and make-or-buy decisions concerning the product or its component parts. For these decisions, it is necessary to distinguish between the fixed and the variable costs to produce the product. As already discussed in Section 2.2.1 , fixed costs are those costs that do not change with product volume and variable costs are those costs that do change with product volume.

2.6.1 Break-Even Analysis Given a particular production process for a product, the output quantity at which total costs equal total revenues is termed its “break-even point.” Break-even analysis can be used to determine the expected profitability of a product at different output quantities so that preliminary decisions can be made concerning, for example, product pricing (which is possible if a firm is not a “price-taker” and has some control over a product’s price, e.g., in a contract bid). If the product cost includes the full opportunity costs of all of the input factors used to produce the product, then the

30

SPRING 2003 2.6. COST ACCOUNTING

firm will breakeven (i.e., earn normal profits) at the break-even point; if all costs are not included (e.g., return on equity), an additional “profit margin” can be added to account for these costs.

Although the short-run total cost function (SRTC) for most products will not be linear over the entire range of possible outputs, increasing steeply as qmax is approached due to the Law of Diminishing Returns, there typically is some “relevant range” of outputs over which the function is approximately linear. Assuming that over a relevant range of outputs that the total cost (TC) to produce q units of output is TC = F + v·q, where F is the fixed cost and v is the variable cost per unit (i.e., a linear average variable cost defined in Eq. (2.4), where AVC = V q = v), and that the total revenue (TR) received from the sale of q units (also a linear function) is TR = p·q, where p is per unit price for the product, then the break-even point (q

q( )

B) is the output quantity at which TR = TC:

TR TC= p q F v q◊ = + ◊

p v q F- =b g

so that

Break-Even Point: q . (2.21) Fp vB =-

In Figure 2.7, the relevant range of outputs is between qmin and qmax. The break-even points for Alternates 1 and 2, qB1 and qB2, are within the relevant range; the break-even point for Alternative 3 is at zero output since the purchase price, v3, is less than the sale price, P.

2.6.2 Cost Indifference Analysis Cost indifference analysis can be used to make make-or-buy and how-to-make decisions. Given two different alternatives for providing a product (or a component part of a product), the output quantity at the total costs for the two alternatives are equal is termed the “cost indifference point.” Make-or-buy decisions arise when one of the alternatives is to purchase (buy) the product and the other alternative is produce (make) the product. If the alternatives are two different processes for producing the product, then how-to-make decisions can be made concerning which process is less costly at different output quantities. How-to-make type decisions arise whenever there is a need to select between alternatives that have different fixed and variable costs (e.g., many material handling equipment selection decisions).

31


q0

$To

tal C

ost o

r Tot

al R

even

ue

qB2 qI2&3

Output QuantityqB1 qI1&3 qI1&2

Revelent Range of Outputs

F2

F1

TR = P·q

TC3 = V 3·q

TC2 = F2 + V2·q

TC1 = F1 + V1·q

qmin qmax

Figure 2.7. Break-even points and cost indifference points for Alternative 1 (make),

Alternative 2 (make), and Alternative 3 (buy).

Given fixed costs of F1 and F2 and variable costs of v1 and v2 for Alternative 1 and Alternative 2, respectively, and assuming total costs are linear over the relevant range, then the cost indifference point is the output quantity (qI1&2) at which TC1 = TC2:

TC TC1 2=

F v q F v q1 1 2 2+ ◊ = + ◊

F F v v1 2 2 1- = -b gq

so that

Cost Indifference Point: q . (2.22) F Fv vI1 2

1

2 1& = -

-2

If one of the alternatives is to purchase the product (Alt. 3 in Figure 2.7), then the fixed cost for that alternative will be zero and its variable cost will be its purchase price. If the variable costs of both alternatives are equal, then the cost indifference point is undefined (division by zero) and the alternative with the lowest fixed cost will have the lowest total cost.

In Figure 2.7, between outputs qmin and qI2&3, the product should be purchased (i.e., Alternative 3); between qI2&3 and qI1&2, the product should be produced using the process defined by Alternative 2; and between qI1&2 and qmax, the product should be produced using the process defined by Alternative 1.

Operating leverage Everything else being equal between two alternatives, the alternative with larger fixed costs provides a greater degree of operating leverage and associated business risk: an increase in the output quantity beyond the cost indifference point between the two alternatives will result in

32

SPRING 2003 2.6. COST ACCOUNTING

greater profits for the alternative with greater operating leverage, while a decrease in the output quantity below their cost indifference point will result in a greater reduction in profits (or, possibly, increase in losses).

33


2.7 Problems 2.1. Why, if the NPV of an independent project is equal to zero, should the project still be

accepted, i.e., is the project still profitable?

2.2. Why is it not appropriate to use just the interest rate on debt as your cost of capital when performing an economic analysis?

2.3. Given that $800 is the most you can afford for a monthly mortgage payment, what is the largest loan amount you can borrow assuming the loan will be for 30 years with a 6% nominal annual interest?

2.4. A firm is buying a facility for $150,000. The facility will be used for 25 years, at which time it will be sold for $75,000. All of its purchase cost is to be financed using an amortized loan. The loan period is for 30 years with a 6% nominal annual interest rate and monthly compounding. Determine the monthly loan payment.

2.5. Under what conditions is it reasonable to ignore the impact of inflation in a capital budgeting decision?

2.6. How is it possible for a decrease in transportation costs to increase the scale of operation of a production process?

2.7. A firm is currently considering the construction of a widget factory. The total investment cost (for land, building, and machines) is $8 million and an estimated net cash flow from operations of $1 million occurring at the end of each year. The estimated salvage value of the factory at the end of 20 years is 50% of its original investment cost, and the cost of capital is 12% compounded annually. Determine if the firm should build the factory.

2.8. A firm is currently considering two options for constructing a widget factory. The first option (1) is to build a highly automated factory for a total investment cost (for land, building, and machines) of $8 million and an estimated net cash flow from operations of $1.5 million occurring at the end of each year; the second option (2) is to build a low-tech factory for a total investment cost of $1 million and estimated net cash flow from operations of $600,000 occurring at the end of each year. The estimated salvage value of either factory at the end of 20 years is 50% of its original investment cost, and the cost of capital is 12% compounded annually. Determine which option, if any, the firm should choose.

2.9. A firm is currently considering two options for constructing a factory that will produce one million widgets per year. The first option (1) is to build a highly automated factory for a total investment cost (for land, building, and machines) of $8 million and an

34

SPRING 2003 2.7. PROBLEMS

estimated average operating cost (for materials and labor) of $1.50 per unit; the second option (2) is to build a low-tech factory for a total investment of $1 million and an estimated average operating cost (for materials and labor) of $2.50 per unit. The estimated salvage value of either factory at the end of 20 years is 50% of its original investment cost, and the cost of capital is 12% compounded annually.

(a) Determine which option, if any, the firm should choose.

(b) What annual demand would result in the two options having the same cost (i.e., the cost indifference point)?

2.10. Currently, a manual machine (MM) is being used in the plant to produce widgets. The plant manager would like to know if it’s a good idea to replace the manual machine with new automated machine (AM). The operating cost is the sum of the material cost and the labor cost per widget. Although it requires five minutes to produce each widget using either machine, the AM only requires the machine operator for two minutes to load (1 min) and unload (1 min) widgets, while MM requires the operator for the full five minutes. The fully burdened labor rate of the operator is $8.00 per hour, and the operator can perform other productive tasks (valued at ≥ $8.00/hr) when not operating the AM. The current salvage value of MM is $4,000 and the cost to purchase the AM is $15,000. Demand is 7,500 widgets per year, for 15 years. Calculate the following information associated with replacing the MM with the AM:

(a) What is the payback period (in years) associated with replacing the MM with the AM?

(b) What is the net present value (NPV) associated with replacing the MM with the AM, assuming a 12% cost of capital with annual compounding and that, at the end of 15 years, the salvage value of MM and AM will be $0 and $7,500, respectively?

(c) How is it possible to make a decision concerning whether or not AM should be purchased if the material cost is not included in the analysis?

(d) If material cost is $0.50 per widget, what is the average cost per widget for both alternatives as a sum of material, labor, and equipment costs?

(e) Why is it incorrect to determine the average cost by dividing the present value of all of the costs by 15 times the annual demand?

(f) What is the annual widget demand that would result in both MM and AM having the same cost (i.e., a cost indifference point)?

35

3. Capacity Planning

3.1 Production Charts Production charts are graphical representations used to plan and document production processes. The most common types of production charts include the following:

• Assembly drawing

• Component part drawings

• Parts list

• Bill of materials

• Precedence diagram

• Route sheets

• Assembly chart

• Operation process chart

• Flow process chart

• Production schedule

All of the charts are drawn using symbols standardized by the American Society of Mechanical Engineers in 1947. The five basic manufacturing activities are represented using the following symbols:

Operation—an intentional change in one or more characteristics of objects (the symbol is also used to represent component parts in an assembly chart).

Transportation—a movement of an object or operator that is not an integral part of an operation or inspection.

Inspection—an examination of an object to determine quality or quantity.

Delay—an interruption between the action just completed and the next planned action.

Storage—an object is stored under controlled conditions, i.e., its withdrawal requires authorization.

“Combined”—combining two symbols indicates simultaneous activities; e.g., the symbol shown indicated that inspection is conducted at the same time an operation is performed.

36

SPRING 2003 3.1. PRODUCTION CHARTS

Assembly vs. Fabrication It is useful to describe all manufacturing operations as being assembly, decomposition, or fabrication operations:

• Assembly operations—the fitting or joining of two or more component parts or subassemblies into a complete structure or unit that is “stable enough” for subsequent handling.

Common in discrete-part manufacturing; the methods used for joining can include screw fastening, riveting, welding, soldering, adhesive joining, pressing, and brazing, and may require the use of “consumable” materials or supplies (e.g., glue or solder) that are not identified as distinct parts.

• Separation operations—separation or disassembly of a single raw material or component part into two or more identifiable component parts; opposite of an assembly operation.

Common in process industries, e.g., oil refining; in discrete-part manufacturing, includes operations such cutting bar stock, etc.

• Fabrication operations—the intentional change in the characteristics of a single component part or subassembly.

All manufacturing operations that are not assembly or decomposition operations are fabrication operations, and can involve changing the shape of material, machining parts to a fixed dimension, obtaining a surface finish, or other methods of changing the physical properties of objects; may include operations such as painting where material is added.

Precedence Diagrams Assembly, operation process, and flow process charts constrain operations and inspections to a serial order. Precedence diagrams are used to represent only the essential constraints on the order with which operations and inspections can occur. Operations and inspections that are not constrained to occur in a particular order are represented in a precedence diagram as parallel paths; this serves to indicate that there is flexibility in the order of their occurrence, even though only a single ordering of these operations and inspection is represented in the other charts. A precedence diagram showing all operations and inspections can be used to represent the full range of possible assembly and operation process charts. A precedence diagram are particularly useful prior to developing an operation process chart because the sequence with which assembly operations can occur is typically more constrained than the sequence with which fabrication operations can occur.

Assembly Charts An assembly chart represents the order in which a product can be assembled. Unless the product’s output is known, each assembly operation in the chart should represent the minimum amount of assembly required so that the resulting assembly is just stable enough for handling; this increases the flexibility of the chart because, depending on the product’s required output,

37

3. CAPACITY PLANNING LECTURE NOTES FOR FACILITIES DESIGN

handling may be required between each assembly operation (high volume) or several assembly operations may be able to be combined into a single operation (low volume).

An assembly chart is a tree graph. Each node in the tree is either an assembly operation, an inspection, or a component part. The root (bottom) of the tree is the final assembly operation or inspection, and all of the leaves of the tree are component parts. The arcs are typically not shown as being directed because the order of the assembly in the chart is understood to be from left to right and from top to bottom. Each assembly node has two or more input arcs from component part nodes or previous assembly or inspection nodes, and (except for the root) one output arc to the next assembly or inspection node. Component part inspections that occur prior to the part’s first assembly are usually not included in the assembly chart.

Operation Process Charts An operation process chart is an assembly chart that also represents the fabrication operations associated with a production process. Excluding any decomposition or rework/repair operations, the operation process chart is a tree graph. Assembly operations are the branch nodes in the tree; fabrication operations and inspections, the remaining nodes in the tree, have a single input arc and a single output arc; and component parts are represented as input arcs to operations. The path from each leaf arc to the root of the tree represents a single sequence of operations and inspections used to transform a component part into a portion of the final product. If rework or repair operations are included, then cycles occur in the graph and the chart may not be a tree because different paths (i.e., sequences of operations) are possible depending on whether or not rework or repair is required; if decomposition operations are included, the chart may still be a (inverted) tree as long as there are no assembly operations.

Flow Process Charts A flow process chart is an operation process chart that also represents the transportation, delay, and storage activities associated with a production process. The flow process chart is used during facility layout and material handling system design. It adds detail to an operation process chart concerning the flow of material between operations and inspections. A sequence of operations represented in an operation process chart may be performed on a single general-purpose machine or on several special-purpose machines; in a flow process chart, the transportation symbol can be used to represent movement between different machines. Depending on the need, a flow process chart can be represented different ways: as a graph (i.e., a more detailed operation process chart); in a tabular format (using standard preprinted forms); or drawn to scale on top of a layout of the facility as part of a flow diagram.

38

SPRING 2003 3.2. FACTORY PHYSICS

3.2 Factory Physics “Factory physics” is a term used by Hopp and Spearman (2000) to refer to an approach to analyzing production systems that uses queuing approximation formulas to estimate system performance. With respect to capacity planning, factory physics provides a middle ground between the simple “rough cut” approach traditionally used and the more detailed and time-consuming simulation approach. More details concerning the queuing approximation formulas used in factory physics can be found in Suri et al. (1993).

Approximation formulas for a production system’s cycle time is related to its throughput via Little’s Law:

Little’s Law: TH WIPCT

= (3.1)

where

TH = throughput

= average output of a production system per unit time (e.g., parts per hour)

WIP = work-in-process

= inventory between the start and end points of a product routing

CT = cycle time

= average time from release of a job at the beginning of the routing until it reaches an inventory point at the end of the routing

Figure 3.1 shows a graphical depiction of Little’s Law, where the throughput corresponds to the slope of the lines representing the cumulative number of arrivals and departures.

Arriva

ls

Depart

ures

time

cum

ulat

ive

num

ber

smoothed

CT

WIP

slope

= TH

Figure 3.1. Little's Law

(adapted from Fig. 1.1 in Taylor and Karlin (1998)).

39


3.2.1 Line Yield Fabrication and assembly operations may result in defective parts due to many factors. The defective part may be identified during the operation or later during a subsequent operation or an inspection. For each fabrication operation, its yield fraction represents an estimate of the percentage of nondefective parts produced by and identified during the operation; for each assembly operation, the fraction represents an estimate of the percentage of nondefective parts produced by and/or identified during the operation; and for each inspection, it represents the percentage of nondefective parts identified during the inspection.

Yield fractions are estimates of the long-run average percentage of nondefective parts that are produced and/or identified. During any particular short period of time, the estimate is not likely to be accurate. A large number of defective parts are likely immediately following machine setups or when a process is out of control. Factors that can influence the percentage of scrap include: whether the operation is performed using manual or automated equipment, the tolerances specified, the grade of material, and equipment maintenance.

Let yi = yield fraction of ith operation, i.e., the long-run average percentage of nondefective parts produced or identified

rd,i = departure rate (desired output) of nondefective parts from ith operation

ra,i = input rate of nondefective parts to ith operation.

For each component part, let ra,1 be the number of units per period required at the start of its first operation (a leaf node of the operation process chart) and let ra,N be the number of units per period of nondefective final product required (i.e., the product’s throughput rate) after the last operation or inspection (the root node of the operation process chart). A total of N operations and inspections are performed on the component part as it is transformed into the final product. Since ra,N is known, and assuming the y1, …, yN yield fractions have been estimated, ra,1 can be determined as follows:

,,1

d Na

N

rrY

= , (3.2)

where

1

i

ij

Y=

= jy∏ (3.3)

is the cumulative yield (or line yield) from operation 1 to i.

Example A four workstation routing is shown in Figure 3.2, where workstation 1 (W/S 1) has three machines (M/C), W/S 2 has six M/C, etc. Because of yield loss, 14.04 parts must be started at W/S 1 to get 10 nondefective parts from W/S 4. Table 3.1 shows the spreadsheet calculations used to determine the line yield, where the shaded cells correspond to input values. Alternatively,

40


the cumulative yield at the last operation can be used to determine the required input to the first operation:

,4,1

4

10 10 14.04070.85 0.9 0.95 0.98 0.71222

da

rrY

= = = =⋅ ⋅ ⋅

. (3.4)

,2 ,3d ar r=,1 ,2d ar r= ,3 ,4d ar r= ,4dr,1ar

W/S 1 W/S 2 W/S 3 W/S 4

1011.9314.04 10.74 10.20

Figure 3.2. Four-workstation routing.

Table 3.1. Line Yield

W/S 1 2 3 4 Arrival Rate (ra, q/hr) 14.0407 11.9346 10.7411 10.2041

Yield (y) 0.85 0.9 0.95 0.98 Departure Rate (rd, q/hr) 11.9346 10.7411 10.2041 10

Rework In addition to final good products, defective parts (or scrap) is produced at a rate of r y, (1 )a i i− at each operation i. If significant, this output must somehow be accommodated when planning material flow. Possible uses for scrap include the following:

• reworking it so that it can be reused upstream or downstream in the production process,

• reworking it so that it can be sold as second quality product,

• selling it as is without rework, or paying to have it removed.

3.2.2 Throughput Feasibility The throughput requirement of each workstation corresponds to the desired output rate of nondefective parts from the workstation

. (3.5) *throughput requirement departure ratedTH r= ≡ =

Increasing the departure rate to account for yield loss results in the required arrival rate to the station, a dr r= y , from which the minimum number of identical machines required at the workstation can be determined so that the effective capacity or service rate of the workstation strictly exceeds the arrival rate to the station:

arrival rate service ratea er r= < = , (3.6)

41


which is equivalent to the requirement that the utilization of the workstation be strictly less than one:

utilization 1a a e

e

r r tur m

= = = < , (3.7)

where

ra = arrival rate to workstation

re = e

mt

= service rate (or effective capacity)

m = number of identical machines in workstation (m ≥ 1a er t + )

te = 0tA

= effective mean process time with failures (preemptive outages)

t0 = natural mean process time

A = MTTFMTTF MTTR+

= availability

MTTF = mean time to failure

MTTR = mean time to repair.

Equation (3.7) can then be used to determine the minimum number of identical machines needed at the workstation in order to satisfy the throughput requirements:

1a em r t= + (3.8)

(Note: Using won’t work since it is possible that , which would result in a utilization of 100%.)

a em r t= a e a er t r t=

Example Continuing with the example shown in Table 3.1, Table 3.2 and Table 3.3 show the spreadsheet calculations used to determine the minimum number of machines necessary to produce a throughput of 10 parts per hour from the routing shown in Figure 3.1 (i.e., a throughput feasible capacity plan).

42


Table 3.2. Throughput Feasible Capacity Plan

W/S 1 2 3 4 Arrival Rate (ra, q/hr) 14.0407 11.9346 10.7411 10.2041

Natural Process Time(t0, hr/q) 0.2 0.5 0.25 0.15 MTTF(hr) 40 100 MTTR(hr) 2 5

Availability (A) 0.95238 1 0.95238 1 Effective Process Time(te, hr/q) 0.21 0.5 0.2625 0.15

Number of M/C(m) 3 6 3 2 Utilization (u) 0.98285 0.99455 0.93985 0.76531

Yield (y) 0.85 0.9 0.95 0.98 Departure Rate (rd, q/hr) 11.9346 10.7411 10.2041 10

Table 3.3. Spreadsheet Formulas Used in Table 3.2

A B C D 1 W/S 1 22 Arrival Rate (ra, q/hr) =C11/C10 =D11/D10 3 Natural Process Time (t0, hr/q) 0.2 0.5 4 MTTF (hr) 40 5 MTTR (hr) 2 6 Availability (A) =IF(ISBLANK(C4), 1, C4/(C4 + C5))=IF(ISBLANK(D4), 1, D4/(D4 + D5))7 Effective Process Time (te, hr/q) =C3/C6 =D3/D6 8 Number of M/C (m) =FLOOR(C2*C7 + 1,1) =FLOOR(D2*D7 + 1,1) 9 Utilization (u) =C2*C7/C8 =D2*D7/D8 10 Yield (y) 0.85 0.9 11 Departure Rate (rd, q/hr) =D2 =E2

3.2.3 Machine Sharing and Setups If several of the operations used to produce a product use the same type of machine, or several products are produced that have operations that use the same type of machine, then it is possible to reduce the number of machines required by sharing machines among the operations. It is not possible to just add the equipment fractions of each operation sharing the same type of machine together to determine the total number of shared machines required. Unless the parts produced for each operation are almost identical, there is usually some additional time required to reconfigure a machine to produce each batch of different part types. This additional time when the machine is stopped and can not be operating is termed the machine’s internal setup time; in contrast, the machine’s external setup time is the time required to prepare to produce a particular part on the machine that does not require the machine to be stopped (e.g., fixture preparation). A machine’s “down time” represents the percentage of time the machine is not available for production due to repair or planned maintenance—it does not include internal setup time because the machine is still available for production during this time.

43


Internal setup time is essentially an additional fixed cost associated with sharing machines among several operations. This additional cost is offset by the savings in equipment costs associated with not having to dedicate underutilized machines to individual operations. In order to spread this fixed cost over a number of units, multiple units of a part type (production batches) can be produced on a machine before switching to produce a different part type. Large production batch (or lot) sizes can reduce the average setup cost per unit, but they can cause increases in work-in-process (WIP) inventory, making it difficult to control production, and they can result in entire batches being scrapped or reworked because of the delay in getting feedback from subsequent operations. One method of reducing batch size without increasing per unit setup cost is to convert internal setup actions to external setup actions (a technique often associated with “Just-In-Time” (JIT) production). Small production batch sizes can increase the average setup cost per unit and can increase equipment costs if additional machines are required due to increases in down time to perform internal setups. In practice, determining the most cost effective batch size is a difficult task.

In many cases, several operations may require many of the same setup actions on the machine. The setup time to switch between these operations is less than the time required for a full machine setup. By grouping these operations together on a shared machine, the time spent on setups can be reduced. The process of grouping together related “families” of operations or products to be performed in “cells” of shared machines is termed “group technology.”

3.2.4 Cycle-Time Feasibility The following queuing approximation formulas can be used to estimate the cycle time of a single machine workstation (G/G/1) or a workstation with m identical machines (G/G/m). Equation (3.11) is used to estimate the arrival squared coefficient of variation (SCV) of a workstation based on the departure SCV of the previous workstation in the routing, where the arrival SCV of the first workstation in the routing must be initially specified:

G/G/1: 2 2

time process timeutilizationvariability

queuing time

2 1

q e

a ee e

CT CT t

c c u t tu

= +

+ = − + (3.9)

G/G/m: ( )

( )

2( 1) 12 2

2 1

ma e

ec c uCT t t

m u

+ − + = − e+ (3.10)

44


Departure (SCV): ( )

( )( ) ( )

2 2 2 2

2 22 2 2

1 , if

1 1 1 1 , if 1

e a

da e

u c u c mc uu c c m

m

+ − =

= + − − + − >

1 (3.11)

where

u = a er tm

= utilization

m = number of identical machines in workstation (m ≥ 1a er t + )

ra = arrival rate

= 2ac

2

2a

atσ = arrival SCV (squared coefficient of variation)

ta = mean time between arrivals

2aσ = variance of arrival time (= 0, deterministic; = , exponential) 2

at

te = effective mean process time with failures (preemptive outages)

= 2ec

22 202

0(1 ) (1 )e

re

MTTRc c A Att

σ= + + − = effective process time SCV with failures

20σ = = variance of natural process time 2 2

0 0t c

2eσ =

2 202

( r2

0)MTTR tMTTFA

σ ++

σ = variance of effective process time with failures

= natural process time SCV (squared coefficient of variation) 20c

2rσ = variance of repair time

= 2rc

2

2r

MTTRσ = repair time SCV.

Example Continuing with the example shown Table 3.2, Table 3.4 shows the calculations used to estimate the cycle time of the routing shown in Figure 3.1 and to determine the total cost of the machines used in the routing. Note: The arrival rate, ra, is used to calculate the WIP instead of the throughput, TH = rd, due to the (conservative) assumption that all failures are identified at the end of processing.

45


Table 3.4. Cycle Time and Total Machine Cost Estimation

W/S 1 2 3 4 Total Arrival Rate (ra, q/hr) 14.0407 11.9346 10.7411 10.2041 Arrival SCV (c2

a) 1 1.08758 0.59714 0.90558 Natural Process Time (t0, hr/q) 0.2 0.5 0.25 0.15 Natural Process SCV (c2

0) 0.25 0 0 0.5 MTTF (hr) 40 100 MTTR (hr) 2 0 5 0

Repair Time SCV (c2r) 1 0 0 0

Availability (A) 0.95238 1 0.95238 1 Effective Process Time (te, hr/q) 0.21 0.5 0.2625 0.15 Eff Process Time SCV (c2

e) 1.15703 0 0.90703 0.5 Number of M/C (m) 3 6 3 2

Utilization (u) 0.98285 0.99455 0.93985 0.76531 Yield (y) 0.85 0.9 0.95 0.98

Departure Rate (ra*y) (rd, q/hr) 11.9346 10.7411 10.2041 10 Departure SCV (c2

d) 1.08758 0.59714 0.90558 0.75381 Cycle Time in Queue (CTq, hr) 4.26486 8.19096 0.97673 0.15241 13.58496

Cycle Time at W/S (CT, hr) 4.47486 8.69096 1.23923 0.30241 14.70746WIP in Queue (ra*CTq) (q) 59.8816 97.7558 10.4912 1.55518 169.6839

WIP at W/S (q) 62.8302 103.723 13.3108 3.08579 182.9499M/C Cost ($000) 10 18 2 6 W/S Cost ($000) 30 108 6 12 156

3.2.5 Basic Capacity Planning Procedure In traditional “rough cut” capacity planning, only enough capacity is planned at each workstation to meet its throughput (TH*) requirements; cycle time is ignored. In the factory physics approach, both throughput (TH*) and cycle time (CT*) requirements are met as part of the design process.

BASIC CAPACITY PLANNING PROCEDURE FOR A SINGLE WORKSTATION

0. Given: ra ⇒ TH* (throughput), and CT* (cycle time) requirements.

1. (Throughput feasible) Determine initial number of machines:

1a em r t= + (3.12)

2. Calculate CT using (3.9) or (3.10).

3. (Cycle time feasible) If CT ≤ CT*, then STOP; else, either

(a) Add machine: m ⇐ m + 1

(b) Or make some other change to workstation

and GOTO Step 2.

46


3.3 Problems 3.1. Why is it sometimes not necessary to have a route sheet for each component part of a

product?

3.2. Given an operation process chart, how is it possible to distinguish between fabrication operations and assembly operations?

3.3. How does an operation process chart differ from an assembly chart?

3.4. Given Parts A–D, Subassemblies E–F, and Final Assembly G, how many A–D are needed to produce one G if E = A(4) + B(2) + C, F = D(4) + E(2), and G = B(2) + E(3) + F?

3.5. Given the opportunity to reduce a machine’s internal setup time, with a corresponding increase in its external setup time, why might overall setup costs be reduced even though the total time required for the setup has not changed?

3.6. Why is the expected cycle time for an item likely to higher if it is produced using a machine that is shared with other items as compared to the same machine if it is dedicated to the item?

3.7. Given the desired output from a series of three fabrication operations of 125 nondefective finished parts, how many parts should be input to the first operation if the yield fractions of the operations are 0.85, 0.92, and 0.90, respectively?

3.8. If 100 units of raw material are input to a workstation during a shift and the workstation has a yield fraction of 0.80, why is it unlikely that 80 nondefective units will have been produced at the end of the shift?

3.9. How is it possible to estimate the average amount of time each unit of product spends in production on a line if all that is known is the monthly output of the line and the average number of units in process on the line?

3.10. If the daily output of a production line is 25 units and the average number of units in process on the line is 50, what is the average amount of time each unit of product spends in production on a line?

3.11. Why is it not possible to release work into a production line at an average rate equal to the average capacity of the line?

3.12. Compute the capacity (jobs per day) for a single machine with a mean process time of three hours and an SCV of one. There are 10 hours per day.

47


3.13. Compute the capacity (jobs per day) for workstation with 12 machines in parallel, each having a natural mean process time of two hours. There are 10 hours per day. The machines have a mean time to failure of 80 hours with a mean time to repair of four hours.

3.14. Given an arrival rate to a workstation of 12 units per hour and an effective process time of 15 minutes, what is the minimum number of identical machines that would be required at the workstation?

3.15. Given a desired output rate of 90 nondefective units per hour from a workstation, a yield fraction of 0.9, a natural process time of 2.16 minutes, and machines that have a mean time to failure of 45 hours with a mean time to repair of 5 hours, what is the minimum number of machines that would be required at the workstation?

3.16. Given that the desired output rate from a workstation is 10 nondefective units per hour, the average time between arrivals is expected to be totally random, it takes exactly 12 minutes to process each unit, the yield fraction of the machines is 0.85, with a mean time to failure of 15 hours and a mean time to repair of exactly 2 hours, (a) what is the expected average cycle time associated with minimizing the number of machines required at the workstation and (b) what is the expected work in process at the workstation?

3.17. The following information is available as part of the throughput feasible design of a new three-station serial production line. A single product will be produced using a routing of stations 1, 2, and 3, and the line will be designed to meet a maximum demand of 24,000 nondefective units per year, operating for five eight-hour shift per week, fifty weeks per year. The average time between arrivals is expected to be totally random. For stations 1–3, each machine: costs $65,000, $250,000, and $120,000, respectively; has a yield fraction of 0.85, 0.95, and 0.75, respectively; has a natural process time of 18, 7, and 11 minutes, respectively; the machines never breakdown; and the variance of the natural process time of any machine is equal to the square of its average natural process time. What will be the total machine costs for the line?

3.18. The following information is available as part of the throughput feasible design of a new three-station serial production line. A single product will be produced using a routing of stations 1, 2, and 3. The product’s annual demand is expected to be 96,000 units per year for the next 10 years, the line will operate for two eight-hour shift per day, 250 days per year. For stations 1–3, each machine has: an initial investment cost of $65,000, $80,000, and $125,000, respectively; a salvage value equal to 25% of its initial investment cost at the end of 10 years; a yield fraction of 0.80, 0.75, and 0.80, respectively; a natural process time of exactly 6, 12, and 15 minutes, respectively; and the machines never breakdown. Raw material costs $1.50 per unit delivered and any scrapped material is not recovered. Direct labor costs are $8.00 per hour, fully burdened, and one operator is assigned to each machine. Assuming the cost of capital is 15%, with annual

48


compounding, what are (a) the average machine costs per unit, (b) the average labor per unit, and (c) the average material costs per unit? Please state all of the assumptions used in your analysis.

49

4. Facility Layout

Facility layout involves determining the arrangement, and possibly the shape, of space-consuming entities (i.e., activities) in a facility. Examples of activities include machines, workstations, workcenters, production areas, offices, and departments. Activities interact with each other through flows of material, personnel, and/or information. Facility layout can be divided into two areas: machine layout and department layout.

Machine layout involves determining only the arrangement (i.e., position and orientation) of space-consuming entities that have a fixed shape. The term “machine” layout is used because the activities usually considered are the machines and workstations in a manufacturing department, which have a fixed shape.

Department layout involves determining both the arrangement and shape of space-consuming entities. The term “department” layout is used because the activities usually considered are the workcenters, production areas, offices, and departments in a facility, which, unlike machine layout, are not restricted to having a fixed shape. In general, determining a department layout is more “difficult” than determining a machine layout because a large number of different shapes are possible for each activity and the shape of one activity constrains the shapes of other activities.

4.1 Flow Processes In the design of a production system, material flow related issues include the following:

1. How raw materials and component parts get to their first operation (or inspection).

2. How work-in-process moves from operation to operation—prior to material flow analysis, it is usually assumed that the output of an operation is immediately available as input to the next operation.

3. How finished product is removed from its last operation or inspection.

All of these considerations relate to flow processes:

• Discrete, identifiable items ⇒ discrete flow processes

51

4. FACILITY LAYOUT LECTURE NOTES FOR FACILITIES DESIGN

• Continuous or bulk, unidentifiable items ⇒ continuous flow processes

The overall flow process for a facility is referred to as its logistics system (see Figure 4.1).

4.1.1 Material Flow System The material flow system of a facility refers to the flow of items “within” the facility. The type of flow is determined by the activities among which materials flow. The following flow planning hierarchy in Table 4.1 describes the different levels at which material flow can be analyzed. The flow within a workstation or machine will be assumed to be given and will not be considered further with respect to its impact on facility design.

suppliers

customers

Material Management System

Material Flow System

Physical Distribution SystemLogi

stic

s Sy

stem

into facility

within facility

from facility

Figure 4.1. Logistics system of a facility.

Table 4.1. Flow Planning Hierarchy

Flow Within Activities Analysis Level

Workstation or machine Motions Motion studies and ergonomics

Department Machines and workstations Machine layout

Facility Departments Department layout

4.1.2 Total Cost of Material Flow and Material Transport The following measure can be used to represent both the total cost of material flow (TCMF) within a facility and the total cost of material transport (TCtran) to/from the facility. The measure represents the total cost of material movement between physical entities termed “activities.” Material flow refers to material movement within a facility, and material transport refers to material movement to/from a facility. TCMF can be used as a criterion for making facility design decisions, where an activity would correspond to, for example, an individual machine, workcenter, storage area, or department. TCtran can be used as a criterion for making facility location decisions, where the activities would correspond to the facility and its suppliers and customers.

52

SPRING 2003 4.1. FLOW PROCESSES

(4.1) TC TC TC f h dij ij ijj

M

i

M= = = ◊ ◊

==ÂÂMF tran

11

where

M = number of activities between which material moves

fij = flow volume between activities i and j, measured in moves per time period

dij = distance (or move-time) between activities i and j

hij = cost per move between activities i and j per unit distance (or per unit move-time).

TC measures the total cost of material movement per time period. It can be used as the criterion with which to compare alternate facility designs (TCMF) or alternate facility locations (TCtran).

Facility design In facility design, the (initial) flow requirements between activities, the fij’s, can be determined once the initial PP&S design is completed; the dij’s and the hij’s remain unknown, and are only determined during facility design. Once the facility layout is completed so that each activity is assigned a position in the facility, the distances (or move-times) between activities, the dij’s, can be determined; once the material handling system design is completed, the handling costs between activities, the hij’s, can be determined.

Facility Layout

Total Cost Material

Flow (TC MF)

Flow Requirements

MH System Design

f

d

f

h h

d

f d

h

Figure 4.2. Use of total cost of material flow in facility design.

Problem: the “best” layout of the facility (i.e., the layout that minimizes TCMF) depends on knowing the flow volumes and the handling costs, and the “best” material handling system design (i.e., the design that minimizes TCMF) depends on knowing the flow volumes and the distances between activities; thus, facility layout and material handling system design are interdependent (and even PP&S design and facility design are interdependent since the flow requirements may be revised after the initial facility design is completed).

53


Facility location In (4.1), the total cost of material transport (TCtran) used for facility location has the same form as the total cost of material flow (TCMF) used for facility design. In the (minisum) location problem for a single facility, the location of the facility that minimizes TCtran is determined. The activities are the facility, its suppliers of raw materials and component parts, and the customers for its finished product(s); it is assumed that the locations of the suppliers and customers are known.

In facility location, the (initial) transport requirements between the facility and its suppliers and customers, the fij’s, correspond to the number of shipments of material to, and finished product from, the facility during a period of time. The initial PP&S design can be used as a starting point to determine the shipping and receiving schedules for the facility. Due to the economies of scale associated with the transport of large shipments, one shipment may correspond to the input/output requirements of several production periods (shifts); the period of time used to define the facility’s transport requirements may correspond to several shifts, with inventories used to balance the transport to/from the facility with the input/output requirements of each shift. In JIT production, the transport requirements may correspond to a single shift’s input/output requirements, with little or no inventories of materials and/or finished product between shifts.

Transport Requirements

Facility Location

Total Cost Transport (TC tran)

Transport System Design

f

d

f

h h

d

f d

h

Figure 4.3. Use of total cost of material transport in facility location.

Once the transport requirements have been determined, the design of the transport system involves determining the mode of transport to be used between each activity (e.g., truck, rail, air, or sea) and the cost per unit of distance (or move-time), the hij’s, for each. Assuming the locations of the facility’s suppliers and customers are known, each potential site at which the facility can be located will result in a different set of dij’s. Given the transport requirements and the transport system design, the location selected for the facility should be a site that minimizes TCtran.

54

SPRING 2003 4.2. MACHINE LAYOUT

4.2 Machine Layout Once the initial production system design has been completed for all of the products to be produced in the facility, decisions will have been made concerning the routing to be used to produce each item (or product), the number of each type of machine required for each operation in each workstation, and whether each machine or workstation is dedicated to a single operation or shared among several operations.

For the machine layout problem, the principal relationships between the activities will be assumed to be the quantitative measure of the flow of material between the activities as defined by their flow requirements. Other quantitative and qualitative measures of the relationships between activities are possible (e.g., adjacency) and can be considered in more general facility layout problems.

4.2.1 Flow Requirements Given a routing for each item k and the total number of each item to be produced, the flow requirements between all pairs i and j of machines can be determined once some measure of the “cost” of each move has been determined.

Unit load sizes The number of items transferred with each move is termed the unit load (or transportation batch) size. The transportation batch size is usually less than or equal to the production batch size of each operation. Unit load sizes are typically determined during material handling system design.

Equivalence factors During the initial machine layout, little or no information is usually available concerning the type of material handling to be used to transport unit loads between machines. When this information is not available, it is impossible to determine the actual “cost” to transfer each load; instead, an equivalence factor (not an actual cost) can be used for each move to reflect the “relative difficulty” of transferring each unit load—that is, the estimated relative handling-related effort of transferring each load of a move as compared to the effort of transferring the loads of each of the other moves.

If the unit load sizes are not known, then a unit load size of one can be assumed for all moves and equivalence factors can be used to reflect the relative differences in handling-related effort between the items moved; for example, if an item is twice the size of another item, then half the number of items will be able to be placed into any equal sized transfer container (e.g., a tote) and twice the number containers will be required to transfer the same number of items—an equivalence factor for the larger item that is double that of the smaller item will reflect the fact that twice the number of containers are required (and, if a single container is transferred with each move, will translate into twice the number of required moves).

55


Equivalent flow volumes The flows from all of the items that move from machine i to machine j can be converted into the following single “weighted” measure of flow, termed the “equivalent flow volume,” between machines i and j:

Equivalent Flow Volume:1

P

ij ijk ijkk

w f=

h= ⋅∑ . (4.2)

where P = total number of items (or products) considered

fijk = number of moves from machine i to machine j for item k during a time period

hijk = equivalence factor for moves from machine i to machine j for item k

Machine layout criterion Given M different machines, the flow requirements between the machines are determined once each wij has been determined. The flow requirements can be represented in an M × M matrix (or “from/to chart”) W of equivalent flow volumes. Different layouts of the machines can be compared using the following criterion that represents what could be termed the “total weighted distance of material flow” between the machines:

∫ wij

. (4.3) w dij ijj

M

i

M◊

==ÂÂ

11

This criterion is similar to the total cost of material flow criterion, TCMF, discussed in Eq. (4.1), except that it does not represent the actual cost of the material flow because only relative equivalence factors are used in place of actual handling costs.

Example In this example, A, B, and C are P = 3 different types of items transferred between M = 4 machines shown in Figure 4.4. The total number of each item to be produced is fi,j,A = fA = 8, fi,j,B = fB = 5, and fi,j,C = fC = 12. The routings are:

A(8): 1–2–3–4; B(5): 2–4–1–2–3; C(12): 3–4–1–2–4

If no information is available concerning unit load sizes and, as shown in Figure 4.5, item A is three times the size of item C and item B is twice the size of item C, then equivalence factors of 3, 2, and 1 can be used for items A, B, and C, respectively, to reflect the likely relative handling effort required for each item so that, for example, hi,j,A = hA = 3, hi,j,B = hB = 2, and hi,j,C = hC = 1. If a common unit load container is to be used to transport the items, then, as shown in Figure 4.6, then 2 A’s, 3 B’s, and 6 C’s can be placed on each container and handling effort is likely to be inversely proportional to the number of items that can be placed on the container; for this example, hA = 1

2 , hB = 13 , and hC = 1

6 .

56


Machine1

Machine2

Machine3

Machine4

1

1

1

2

2

2

2

3

3

3

4

4

4

A

B

C

4

Figure 4.4. Routings for items A, B, and C.

A B C

Figure 4.5. Relative sizes of items A, B, and C.

A

A

B B B

C

C

C

C

C

C

Figure 4.6. Common unit load container for items A, B, and C.

The resulting flow requirements for this example can be represented in the following 4 × 4 matrix of equivalent flow volumes (with nonzero values shown for the actual moves between machines):

1,2

2,3 2,4

3,4

4,1

0 0 0 0 46 0 00 0 0 0 34 220 0 0 0 0 0 36

0 0 0 22 0 0 0

ij

ww ww w

w

≡ = =

W .

57


4.2.2 Types of Machine Layouts Four types of machine layouts are typically used in manufacturing departments:

1. Fixed product layout—product difficult to move ⇒ machines are either at fixed locations adjacent to the product or are brought to product when they are needed

2. Product layout (production line)—large stable demand for a small number of products ⇒ many dedicated machines and workstations ⇒ a few dominate flows exist ⇒ most material flow between adjacent machines/workstations ⇒ fixed-path material handling possible

3. Group layout (or product family, or cellular layout)—several groups of products with related processing requirements and medium total demand for the products in each group ⇒ most machines and workstations dedicated to group and shared within group ⇒ little material flow between groups ⇒ each group can be considered a separate manufacturing department for layout purposes ⇒ product layout may be possible within group

4. Process layout (job shop)—low demand for a large number of unrelated products ⇒ many shared machines and workstations ⇒ no dominate flows exist ⇒ little material flow between adjacent machines/workstations ⇒ variable-path material handling likely

Product layouts can result in the lowest average cost of production if demand is large enough; process layouts can result in increased machine utilization if demand is low, at the cost of increased setup time and material flow; group layouts can realize many of the advantages of both product and process layouts, even when demand is not large, without as high setup and material flow costs.

4.2.3 Flow Patterns within Manufacturing Departments The flow pattern within a manufacturing department depends on the type of machine layout.

Fixed product layout Flow of operations to/from the product at a fixed location results in many of the machines being mobile.

Product layout Most flow of product is between adjacent machines/workstations. Flow patterns depend on whether or not operators are shared between machines/workstations:

Dedicated operators ⇒ end-to-end, back-to-back, or odd-angle flow patterns.

Operator shared between two machines/workstations ⇒ front-to-front flow patterns.

Operator shared between several machines/workstations ⇒ circular or U-shaped flow patterns (U-shaped flow patterns are often used in JIT production systems).

58


Group layout Little flow between groups results in process layout flow patterns between groups, and product or process layout flow patterns within each group.

Process layout The use of variable-path material handling results in most flow occurring between machines/workstations and aisles. Flow pattern depends on machine–aisle arrangement:

Two-way aisles ⇒ parallel or perpendicular flow patterns

One-way aisles ⇒ diagonal flow patterns

4.2.4 QAP Model of Machine Layout Machine layout can be modeled as a Quadratic Assignment Problem (QAP) if each activity (machine) is restricted to occupy one of a finite number of fixed potential locations (sites).

The QAP is solved to find the minimum “cost” assignment of M machines to N fixed sites.

QAP for Layout: Minimize (4.4) TC c x xijkl ik jll

N

j

M

k

N

i

M=

====ÂÂÂÂ

1111

M

◊ ◊

N= 1, ,

i M

subject to xÂ (4.5) kiki

==

11

, for all sites …

xikk

N=

=1

1, for all machines …= 1, ,Â (4.6)

x = l q (4.7) ik 0 1,where

xik = 10,,

if machine is assigned to site otherwise

i kRST cijkl = “cost” of assigning machine i to site k when machine j is assigned to site l.

The objective function (4.4) of the QAP is quadratic because of the xik·xik terms. Constraints (4.5) assure that each site is assigned a (possibly dummy) machine. Constraints (4.6) assure each machine is assigned a unique site. Constraints (4.7) make the QAP a 0–1 integer program.

If M > N (i.e., more machines than sites), then the problem is not well defined and has no solution; if M < N, the N – M “dummy machines” are added so that M + (N – M) = N, each with no interactions with any other machines (i.e., the flow volumes of the dummy machines are all equal to zero). Unless otherwise stated, it will be assumed that M = N.

Heuristic (i.e., non-optimal) procedures are typically used to solve QAP’s since it is computationally infeasible to find a (globally) optimal solution when M is much greater than 20. With M = N, M! possible solutions (i.e., possible assignments) would have to be (at least

59


implicitly) examined to find an optimal solution, which becomes infeasible for M > 20 (e.g., even M = 12 ⇒ M! = 12! = 479,001,600 possible solutions to examine). M! is the number of possible permutations of the integers 1 to M.

Steepest Descent Pairwise Interchange Heuristic for QAP The Steepest Descent Pairwise Interchange (SDPI) heuristic is a simple procedure for finding “locally optimal” solutions to a QAP. The locally optimal solution may or may not be the globally optimal solution.

Let W = M × M machine weight matrix (equivalent flow volumes between all pairs of M machines).

D = N × N site distance matrix (“distances” between all pairs of the N sites).

a = a a a N( ), ( ), , ( )1 2 … = 1 × N machine-to-site assignment (or permutation) vector, where a(k) = i represents the assignment of machine i to site k.

The distance measure used in machine layout is problem-dependent: it may represent the straight line (or Euclidean) distance between two sites if the layout is in a large unobstructed open area; it may represent the rectilinear (or city block) distance if the travel between sites is along aisles; it may represent the actual travel distance a material handling device would travel between sites; or it may represent the time it would take for a material handling device to transport a load between sites.

Each element of W represents a machine-to-machine weight and each element of D represents a site-to-site distance. In order to be able to multiply elements of W with elements of D to determine the total weighted distance (TC), the elements of W and D must be made commensurate either by translating machine-to-machine weights to site-to-site weights, or by translating site-to-site distances to machine-to-machine distances.

Given M machines, each element w(i, j) of W represents some measure of the “weight” between machine i and machine j. The assignment vector a can be used to translate machine weights to the weights between sites. Given a(k) = i and a(l) = j, the wei d site l is equal to the following element of the machine weight matrix W: w a = w(i, j).

ght between site k angk a l( ), ( )b

For a given a, W, and D,

TC w a k a l dkll

N

k

N( ) ( ), ( )a =

==ÂÂ b g

11◊

vector a

(4.8)

represents the objective function value for a.

It is also possible to translate site distances to the distances between machines by using the 1 × M site-to-machine assignment –1= a a a M- - -1 1 11 2( ), ( ), , (… )

g-1 i

, which is the inverse permutation of a, where a a = k, for k = 1, . . . , N, so that k-1 ( )b (4.9) TC w d a i a jij

j

M

i

M( ) ( ), ( )a- -

=== ◊ÂÂ1 1

11d

60


represents the objective function value for a–1. The only difference between the two representations is that site-to-site weights are compared to site-to-site distances using a and machine-to-machine weights are compared to machine-to-machine distances using a–1.

Given an initial machine-to-site assignment vector a0, a simple heuristic is to determine which pairwise interchange of machines results in the greatest decrease in TC. If no interchange reduces TC, then keep the initial assignment; otherwise, make the pairwise interchange and then continue by looking at pairwise interchanges of the machines in the new assignment vector.

For a given assignment vector a, let akl be the assignment vector resulting from the interchange of the machines located at sites k and l. There are FHG

M2IKJ = M M( )-1 2 pairwise interchanges of M

machines.

SDPI HEURISTIC

0. Given a0, W, and D, let a ← a0 and determine TC(a).

1. Determine ¢ = aarg min ( )TC k lklm < ra , where a is an assignment that resulted in the ¢minimum TC(akl) for all M M( )-1 2 possible pairwise interchanges of machines in a.

2. If TC(a ) ≥ TC(a), then stop, with a as a locally optimal assignment vector; ¢otherwise, a ← a , TC(a) ← TC(a ), and go to Step 1. ¢ ¢

As stated, the heuristic is not deterministic because the a determined in Step 1 may be one of several different assignments that have the same minimum TC. One possible rule to make the heuristic deterministic (for computer implementation) is to choose a based on lexicographic order so that the a chosen is the first such assignment encountered in a traversal from 1 to N of the k and l indices; for example, a

¢

¢¢

1,2 would be chosen over a1,3 and a2,1. In Step 2, TC(a ) is required to be strictly less than TC(a) for an interchange to occur. This requirement eliminates the need to check for the possibility of cycling.

¢

Pairwise interchange graph In order to illustrate the operation of the SDPI heuristic, a “pairwise interchange graph” can be constructed for small (i.e., less than five machines/sites) problems. In such a graph, each node ax, x = 1, … , M!, represents one of the M! possible assignment vectors and each arc (ax,ay) represents a pairwise interchange that transforms assignment ax into ay and assignment ay into ax. Each node is connected via arcs to M(M – 1)/2 other nodes, representing all of the possible pairwise interchanges from this assignment. The value assigned to each node ax is the total cost TC(ax). Although the global optimum assignment can be read off the graph for small problems, there would be too many nodes to make this feasible for larger problems. The advantage of the SDPI heuristic for larger problems is that only O(M3) nodes are considered as compared to all M! nodes.

61


a1=[1234]:3830

a2=[1243]:3680

a3=[1342]:5660

a4=[1324]:5330

a5=

[142

3]:4

330

a6=

[143

2]:4

810

5490:[2431]=a

7

5520:[2413]=a

8

4820:[2314]=a

9

4640:[2341]=a10

4020:[2143]=a11

4170:[2134]=a12

5350:[3124]=a13

5680:[3142]=a14

4320:[3241]=a15

4500:[3214]=a16

4180

:[341

2]=

a 17

3670

:[342

1]=

a 18 a

19 =[4321]:3770

a20 =

[4312]:4280

a21 =

[4213]:5300

a22

=[4231]:5270

a23

=[4132]:4930

a24

=[4123]:4450

Figure 4.7. Pairwise interchange graph for 4-machine–4-site layout problem.

An example pairwise interchange graph is shown in Figure 4.7 corresponding to an M = N = 4 machine layout problem. There are 4! = 24 nodes in the graph corresponding to all of the possible assignments of 4 machines to 4 sites. The arc from a1 to a2 represents a2,3, the interchange of machines 2 and 3 located at sites 2 and 3. The global optimum assignment is a18, corresponding to TC = 3,670.

MATLAB implementation of SDPI heuristic The SDPI heuristic has been implemented as the MATLAB function sdpi. In addition, the function rte2W is available to convert routings to a W matrix, the function dists is available to determine the (lp norm) distances between each pair of site locations, and the function dijk is available to determine the shortest paths between each pair of site locations.

62


function [TC,a] = sdpi2(W,D,a) %SDPI2 Steepest Descent Pairwise Interchange Heuristic for QAP. % [TC,a] = sdpi2(a,W,D) % M = number of machines and sites % W = M x M machine-machine weight matrix % D = M x M site-site distance matrix % a = M-element initial assignment vector % %(SDPI2 differs from SDPI in not error checking and not allowing fixed costs) M = length(a); TC0 = Inf; TC = sum(sum(W(a,a).*D)); % Initial TC disp(' '),disp([TC a]) while TC < TC0 TC0 = TC; a0 = a; for i = 1:M-1 for j = i+1:M aij = a0; aij([j i]) = aij([i j]); % Pairwise interchange of i and j TCij = sum(sum(W(aij,aij).*D)); % Calc. TC of interchange if TCij < TC TC = TCij; a = aij; end end end disp([TC a]) end

Figure 4.8. Code listing for MATLAB function SDPI2.

Example 1 of SDPI heuristic: 1-D distances Continuing the previous example (where the equivalent flow volume matrix W was determined for items A, B, and C): Let M = N = 4,

,

0 46 0 0 0 10 35 500 0 34 22 10 0 25 40, and0 0 0 36 35 25 0 1522 0 0 0 50 40 15 0

= =

W D

where the site distance matrix D is determined from the site locations, represented as circles, as shown in Figure 4.9.

0 10 35 50

1 2 3 4

Figure 4.9. Site locations.

63


In order to use the SDPI heuristic, an initial assignment vector is needed; let

[ ] [ ]0 (1), (2), (3), (4) 4,1, 2, 3a a a a= =a ,

which corresponds to node a24 in the pairwise interchange graph shown in Figure 4.7 and to the initial assignment of machines (squares) to sites (circles) shown in Figure 4.10.

0 10 35 50

14

21

32

43

Figure 4.10. Initial machine–site assignment.

Step 0: Given a0, W, and D, let a ← a0 and

TC(a) ( )4 4

1 1( ), ( ) 4,450kl

k lw a k a l d

= =

= ⋅∑∑ =

Step 1 (1st pass): Of the nodes a5, a11, a13, a19, a21, and a23 connected to node a = a24 via arcs in the pairwise interchange graph (Figure 4.7), the assignemnt vector corresponding to the minimum TC is { }19 5 11 13 19 21 23arg min ( ), ( ), ( ), ( ), ( ), ( )TC TC TC TC TC TC′ = =a a a a a a a a .

Step 2 (1st pass): Since TC(a ) = TC(a¢ 19) = 3,770 < TC(a) = TC(a24) = 4,450, interchange machines at sites 2 and 4 (a ← a ), let TC(a) ← TC(a ), and GOTO Step 1 (start 2nd pass). ¢ ¢

Step 1 (2nd pass): Of the nodes a20, a22, a24, a4, a10, and a18 connected to node a = a19 via arcs in the graph, { }19 20 22 24 4 10 18arg min ( ), ( ), ( ), ( ), ( ), ( )TC TC TC TC TC TC′ = =a a a a a a aa .

Step 2 (2nd pass): Since TC(a ) = TC(a¢ 18) = 3,670 < TC(a) = TC(a19) = 3,770, interchange machines at sites 1 and 2 (a ← a ), let TC(a) ← TC(a ), and GOTO Step 1 (start 3rd pass). ¢ ¢

Step 1 (3rd pass): Of the nodes a19, a5, a7, a13, a15, and a17 connected to node a = a18 via arcs in the graph, { }19 19 5 7 13 15 17arg min ( ), ( ), ( ), ( ), ( ), ( )TC TC TC TC TC TC′ = = a a a a a aa a .

Step 2 (3rd pass): Since TC(a ) = TC(a¢ 19) = 3,770 < TC(a) = TC(a18) = 3,670 , STOP, with

[ ] [ ](1), (2), (3), (4) 3, 4, 2,1a a a a= =a

as a locally optimal assignment vector, which corresponds to the final assignment of machines (squares) to sites (circles) shown in Figure 3.9, and to node a18 in the pairwise interchange graph (Figure 3.7).

0 10 35 50

13

24

32

41

Figure 4.11. Final machine–site assignment.

64


Inspection of the pairwise interchange graph (Figure 4.7) indicates that the node a18 found by the SDPI heuristic is the only local optima that correspond to the global optimum TC of 3,670. If a0 = a1 = [1, 2, 3, 4], then the local optima found by the heuristic would have been a2 = [1, 2, 3, 4], with a TC of 3,680, which is greater than the global optimum. Since the SDPI heuristic will not always find the global optimum, the heuristic should be applied to a sequence of several different (randomly generated) initial assignment vectors, picking the best solution found as the final assignment. As a rule of thumb, the best solution found using M2 different random assignment vectors can be used for an M-machine layout problem. Although 3-way interchanges could be used as a heuristic for the machine layout problem, the ease with which initial assignments can be generated reduces their utility.

Solving the Example 1 using MATLAB Using the same 4-machine SDPI example, the MATLAB function sdpi that implements the SDPI heuristic is used three times for three different initial assignments. Also, the built-in MATLAB function randperm(N) is used to construct random N-element assignment vectors. (Also, for this example the built-in function rand('state',1) is used to fix the random number sequence so that the same results can be duplicated, but, in practice, there is no need to do this.)

» help sdpi » D = dists(x,x)

D = (help screen for sdpi) 0 10 35 50 10 0 25 40 ______________ Create W _____________ 35 25 0 15

50 40 15 0

» help rte2W _________ First Run (specified a0) ________

Converts routings to W matrix W = rte2W(rte,f,h)

» a0 = [4 1 2 3] rte = routings; e.g., a0 = rte = {[1 2 3],[4 1]}, for 4 1 2 3 routing 1-2-3 and 4-1

f = flow h = handling cost » sdpi(W,D,a0) (or equivalence factor) Initial TC = 4450 Initial a = » rte={[1 2 3 4],[2 4 1 2 3], [3 4 1 2 4]};

4 1 2 3

Interchange 2 and 4: » f = [8 5 12]; Current TC = 3770

Current a = » h = [3 2 1]; 4 3 2 1

» W = rte2W(rte,f,h) Interchange 1 and 2: Current TC = 3670

W = Current a = 0 46 0 0 3 4 2 1 0 0 34 22 0 0 0 36

Final TC = 3670 22 0 0 0

Final a = _____________ Calculate D _____________ 3 4 2 1

» x = [0 10 35 50]’;

65


________ Second Run (random a0)________ Final TC = 3680

Final a = » rand('state',1) 1 2 4 3 » sdpi(W,D)

________ Best of M2 = 42 = 16 runs _______ Initial TC = 5300 Initial a = 4 2 1 3

» [TC,a] = sdpi(W,D,16) Interchange 1 and 3: TC = Current TC = 3680 3670 Current a = a = 1 2 4 3 3 4 2 1

Example 2 of SDPI heuristic: Four-different distance scanarios In this example, the same weight matrix from Example 1 is used, except that a “dummy” fifth machine is added to the matrix since there are five sites and only four machines. Four different distance scenarios are considered. In each scenario, sites are indicated as numbered circles. (You can assume that items can use any site as transit points along their paths.)

(a) Open spaces: Since there is unobstructed travel between all pairs of sites, Euclidean distances can be used.

(b) Rectangular grid: Since travel between all pairs of sites requires a series of 90° turns without any backtracking due to obstructions, rectilinear (a.k.a. city block or Manhattan) distances can be used.

(c) Circulating conveyor: Since travel between sites is in a counterclockwise direction along the conveyor, shortest path distances can be used.

(d) General network: Since travel between sites is obstructed, making Euclidean and rectangular distances inappropriate, shortest path distances can be used.

Solving the Example 2 using MATLAB In this example, a 5 × 5 matrix W2 is created by adding a fifth row and fifth column the 4 × 4 matrix W used in Example 1. The function dists is available to determine the (lp norm) distances between each pair of site locations, and the function dijk is available to determine the shortest paths between each pair of site locations. In the function dists, the variable p is used to specify the type of distance: p = 1, for rectilinear, and p = 2, for Euclidean distances. dists(S,S,1) translates an N × 2 matrix S of N total (x, y) site locations to the N × N matrix D of rectilinear distances between all pairs of sites. In the function dijk, given an N × N weighted adjacency matrix A, where each positive element a(i,j) represents the distance along a direct arc between Site i and Site j, dijk(A) determines the N × N matrix D of shortest distances between all pairs of sites.

66


(c) Circulating conveyor.

(b) Rectangular grid.

(a) Open space.

(d) General network.

1

5

4

3

2

40

5554

52

25

30

1 2 3

45

1217

9 18

16

2

4

1 3

5

(33,80)

(45,76)

(56,80)

(52,90)(35,90)

(x,y)

3 4

1 2

5

0 50

0

40

yx 90

Figure 4.12. Four machine layout scenarios used in Example 2.

56 80 ______________ Create W2 _____________ 52 90 35 90 W Da = dists(XYa,XYa,2) W = Da = 0 46 0 0 0 12.65 23.00 21.47 10.20 0 0 34 22 12.65 0 11.70 15.65 17.20 0 0 0 36 23.00 11.70 0 10.77 23.26 22 0 0 0 21.47 15.65 10.77 0 17.00 W2 = [W zeros(4,1); zeros(1,5)] 10.20 17.20 23.26 17.00 0 W2 = 0 46 0 0 0 XYb = [ 0 0 34 22 0 0 0 0 0 0 36 0 90 0 22 0 0 0 0 0 40 0 0 0 0 0 50 40

________ Create Distance Matrices _______ 90 40] XYb = 0 0 XYa = [ 90 0 33 80 0 40 45 76 50 40 56 80 90 40 52 90 Db = dists(XYb,XYb,1) 35 90] Db = XYa = 0 90 40 90 130 33 80 90 0 130 80 40 45 76

67


55 0 0 0 40 40 130 0 50 90 0 0 25 40 0 90 80 50 0 40 Dd = dijk(Ad) 130 40 90 40 0 Dd =

IJDc = [ 0 52 54 55 79 1 2 9 52 0 30 95 55 2 3 18 54 30 0 65 25 3 4 16 55 95 65 0 40 4 5 12 79 55 25 40 0 5 1 17] IJDc = _______ Run SDPI for Scenario (a) ______ 1 2 9 2 3 18 rand('state',100) 3 4 16 4 5 12 sdpi(W2,Da) 5 1 17 Ac = list2adj(IJDc) Initial TC = 2.2653e+003 Ac = Initial a = 0 9 0 0 0 1 2 4 3 5 0 0 18 0 0 Interchange 3 and 4: 0 0 0 16 0 Current TC = 2.1843e+003 0 0 0 0 12 Current a = 17 0 0 0 0 1 2 3 4 5 Dc = dijk(Ac) Final TC = 2.1843e+003 Dc = Final a = 0 9 27 43 55 1 2 3 4 5 63 0 18 34 46

_______ Run SDPI for Scenario (b) ______ 45 54 0 16 28 29 38 56 0 12 sdpi(W2,Db) 17 26 44 60 0 Initial TC = 11520 IJDd = [ Initial a = 1 2 52 3 4 2 1 5 1 3 54 Interchange 2 and 5: 1 4 55 Current TC = 11200 2 3 30 Current a = 3 5 25 3 5 2 1 4 4 5 40] Interchange 1 and 4: IJDd = Current TC = 9820 1 2 52 Current a = 1 3 54 1 5 2 3 4 1 4 55 Interchange 4 and 5: 2 3 30 Current TC = 9420 3 5 25 Current a = 4 5 40 1 5 2 4 3 Ad = list2adj(IJDd) Final TC = 9420 Ad = Final a = 0 52 54 55 0 1 5 2 4 3 0 0 30 0 0

0 0 0 0 25 _______ Run SDPI for Scenario (c) ______ 0 0 0 0 40 0 0 0 0 0 sdpi(W2,Dc) Ad = Ad + Ad' Ad = Initial TC = 6078 0 52 54 55 0 Initial a = 52 0 30 0 0 3 4 2 5 1 54 30 0 0 25

68


Initial TC = 7800 Interchange 3 and 5: Initial a = Current TC = 3158 5 4 1 3 2 Current a = Interchange 3 and 4: 3 4 1 5 2 Current TC = 7070 Interchange 3 and 4: Current a = Current TC = 2774 5 4 3 1 2 Current a = Interchange 2 and 3: 3 4 5 1 2 Current TC = 6770 Final TC = 2774 Current a = Final a = 5 3 4 1 2 3 4 5 1 2 Final TC = 6770

_______ Run SDPI for Scenario (d) ______ Final a =

5 3 4 1 2sdpi(W2,Dd)

4.2.5 QAP Model with Fixed Costs Up to now, the only costs used in the QAP model of the machine layout problem are the costs associated with the interactions between the machines. The QAP model can be extended to include additional fixed costs associated with assigning machines to particular sites. For each machine, a fixed cost is incurred that depends only on the site to which the machine is assigned; the additional cost is independent of the assignment of the other machines.

As before, the QAP with fixed costs is solved to find the minimum cost assignment of M machines to N sites.

QAP with Fixed Costs: Minimize (4.10) TC c x c x xik ikk

N

i

M

ijkl ik jll

N

j

M

k

N

i

M= ◊ + ◊

== ====ÂÂ ÂÂÂÂ

11 1111◊

N= 1, ,

i M

subject to xÂ (4.11) kiki

M=

=1

1, for all sites …

xikk

N=

=1

1, for all machines …= 1, ,Â (4.12)

x = l q (4.13) ik 0 1,

where xik and cijkl are as before and

cik = “fixed cost” of assigning machine i to site k.

The objective function (4.10) of the QAP with fixed costs is still quadratic because of the xik·xik terms. The constraints are the same as before.

If all of the cijkl’s are equal to zero or are identical, then the sum of the quadratic terms in the objective function is a nonnegative constant Constant and (4.10) reduces to

Minimize TC TC Constant c xik ikk

N

i

M¢ ◊

==ÂÂ

11= - = , (4.14)

69


which is a linear function. The objective function (4.14) together with the constraints (4.11)–(4.13) represent a Linear Assignment Problem (LAP). Computationally efficient procedures (e.g., the Hungarian Method) exists for finding (globally) optimal solutions for LAPs.

Likewise, if all of the cik’s are equal to zero or are identical, then the sum of the linear terms in the objective function (4.10) are either zero or some positive constant and (4.10) reduces to the original QAP objective function (4.4).

4.3 Department Layout In machine layout, each activity (i.e., machine or workstation) is assumed to have a fixed shape. In a department layout, since the shape of each activity (e.g., department, production area, office, etc.) is not necessarily fixed, both the arrangement and the shapes of the activities are determined.

A manufacturing department is a group of machines and/or workstations considered as a single activity for facility layout purposes—although each machine and workstation has a fixed shape, the overall shape of the department is not fixed. Nonmanufacturing departments include shipping/receiving areas, storage areas, offices, cafeterias, etc. In a facility, departments do not have to be separated by physical walls or barriers unless there is a need to isolate particular departments from adjacent activities.

4.3.1 Flow Patterns between Departments The flow between departments determines the overall flow pattern within a facility and typically consists of a combination of the following general flow patterns: straight line, U-shaped, S-shaped, and W-shaped. The beginning and end of the overall flow pattern correspond to the location of the principal receiving (entrance) and shipping (exit) docks, respectively, in the facility. Because of site restrictions, the location of the shipping (S) and receiving (R) docks are often fixed and become a constraint on the flow pattern within the facility.

The following possibilities exist for the location of the S/R docks along the perimeter of the facility:

1. Single dock for S/R—dock is used for both S and R (shared) since flow volume is too low to justify separate (dedicated) docks for S and R

2. Multiple S/R docks at same location—may increase dock utilization (compared to 3 and 4) since the same docks and equipment can be used for both S and R, and reduces service road requirements to/from the dock apron and truck waiting area (compared to 3 and 4)

3. Same side but separate locations for S and R docks—reduces service road requirements to/from the dock aprons and truck waiting areas (compared to 4) and may improve flow pattern within the facility (compared to 1 and 2)

70

SPRING 2003 4.3. DEPARTMENT LAYOUT

4. S and R docks on different sides—increases service road requirements to/from the dock aprons and truck waiting areas (compared to 1–3), but may improve flow pattern within the facility.

The use of single areas in a facility for shipping and receiving is often associated with “centralized storage.” It is becoming common in facilities using JIT-type production to have multiple docks around the perimeter of the facility, with docks located close to individual departments. This “decentralized storage” reduces unloading, storage, and travel times within the facility for the frequent deliveries associated with JIT (and may also reduce truck waiting area requirements), but at the possible cost of increases in the number of docks required and the service road requirements to/from the dock aprons. In some cases (termed “third-party logistics” or “3PL”), a logistics company will manage the S/R activities in a facility, up to and off of each production line—the owner of the facility only manages the line.

4.3.2 Block Layout Representations A block layout is an initial, macro-level representation of the basic arrangement, shape, and size of the departments in a facility. It can serve as the basis from which more detailed layouts of the facility can be developed. A more detailed layout (e.g., CAD layout) may include information concerning, for example, the aisles, support columns, doors, and windows in the facility.

Several different representations can be used for block layouts. Each representation places different restrictions on the shape of each department in the layout, which results in different shapes for the overall layout. The following layout representations (see Figure 4.13) form a hierarchy, starting from the least restrictive (map layout) to the most restrictive (grid and rectangular layouts):

A A A A A A A

B B A A C C C

B B B B C C C

B B B B C C C

A

B C

A

B C

(a) Map layout

(b) Polygonal layout

(c) Orthogonal layout

(d) Grid layout

(e) Rectangular layout

B

A

CB (L-Shaped)

A (T-Shaped)

C (Rect.)

Figure 4.13. Hierarchy of block layout representations.

(a) Map Layout—each department is a closed region whose boundary is a curve such that the resulting overall layout is a planar graph or “map” (a graph is planar if it can be drawn so that each edge intersects the other edges only at their endpoints); planar graphs and their

71


duals, which are also planar graphs, are useful for representing adjacency relationships between departments.

(b) Polygonal Layout—a map layout in which each department (and the resulting overall layout) is a simple polygon (i.e., a closed region whose boundary is composed of a series of straight lines).

(c) Orthogonal Layout—a polygonal layout in which the corners of each department (and the resulting overall layout) form either 90° or 270° angles.

(d) Grid Layout—an orthogonal layout in which each department (and the resulting overall layout) is composed of an integral number of equal-sized grid squares; grid layouts are used in CRAFT.

(e) Rectangular Layout—an orthogonal layout in which each department is a rectangle; the resulting overall shape of the facility need not be rectangular, although it must be an orthogonal polygon.

In practice, orthogonal layouts with simple-shaped (i.e., rectangular-, L-, or T-shaped) departments inside of a facility with an overall rectangular shape are usually preferred because they correspond to the type of facility that is least costly to build; they correspond closely to the final detailed building plans. Rectangular layouts limit the shape and proximity relationships of departments in the layout. The grid layouts produced by CRAFT are usually translated (by hand) into orthogonal layouts with simple-shaped departments and an overall rectangular shape.

4.3.3 CRAFT CRAFT (Computerized Relative Allocation of Facilities Technique) is one of the earliest (1963) and best known (it was available for free on mainframes in the 1960s) programs for department layout problems.

CRAFT is based on the SDPI heuristic used for machine layout, but does not require the use of fixed sites at which the activities can be located. CRAFT is not appropriate for machine layout because the shape of activities (i.e., machines) would be altered by the program. Layouts are specified in CRAFT as “grid layouts,” where the area and shape of each department is specified by the number and arrangement of unit-sized grid squares. Departments can be fixed in the layout so that their shape and location does not change, and dummy departments can be added to layouts to make the overall shape of the layout, for example, a rectangle with a desired aspect ratio.

In a similar manner as the SDPI heuristic, CRAFT uses the total cost of material flow (TCMF) between departments as its objective. Starting from an initial layout of the departments, interchanges are considered to try and reduce TCMF:

, (4.15) TC f h dij ij ijj

M

i

M

MF = ◊==ÂÂ

11◊

where M = number of departments

72

SPRING 2003 4.3. DEPARTMENT LAYOUT

fij = flow volume between departments i and j, measured in moves per time period

dij = distance between departments i and j, measured in grid-square units

hij = cost per move between departments i and j per unit distance.

Input Data Input data to run CRAFT includes the following:

1. Specification of parameter values (including the type of interchanges to perform and the list of department(s), if any, that are to remain fixed)

2. From-to chart of flow volumes (fij’s)

3. Move cost matrix (hij’s)

4. Initial grid layout, where the area and shape of each department is indicated by the number and arrangement of the grid squares used for the department.

Distance When fixed sites are used (as in machine layout), the distances (dij’s) can be calculated once; in CRAFT, the distances between departments are different for each different layout considered and must be continually recalculated. The distance between activities in the layout is calculated as the rectilinear distance between the centroids (i.e., centers of mass) of the departments.

Types of Interchanges Unlike the SDPI heuristic, where only pairwise or 2-way interchanges are made, CRAFT allows the user to specify five different combinations of 2- and 3-way interchanges: 2-way, 3-way, 2-way followed by 3-way, 3-way followed by 2-way, and best of 2- and 3-way.

Allowed Interchanges Departments can be interchanged if they are not fixed and either

1. they have equal areas (i.e., an equal number of grid squares), or

2. they are adjacent (i.e., they share a common border of positive length, not just meeting at a single point at the corners of two grid squares) and can be interchanged without causing either department to become split.

0 1 2 3 4 5 6 7 8 0 1 A A A E E C C C 0 2 A A E E C C C 0 3 A A E E D D D 0 4 A A A E E D D 0 5 B B B E E D D 0 6 B B B E E D D D

Figure 4.14. Grid layout representation in CRAFT.

73


4.3.4 Activity Relationships The layout of activities (e.g., machines in a department or departments in a facility) should be based on the relationships between activities. Activity relationships can be based on quantitative and/or qualitative relationships. In facilities planning, activity relationships are often translated into proximity requirements. A positive relationship between two activities corresponds to the desire that the activities be as close as possible, if not adjacent, in the layout, while a negative relationship corresponds to having the activities as far apart, or at least not adjacent, in the layout. Proximity requirements can often be satisfied by other means than physical proximity; for example, communication networks, walls, or other barriers, etc.

Quantitative Relationships For manufacturing departments, the principal quantitative measure of activity relationships is usually based on the flow of material between or within the departments. For nonmanufacturing departments, measures of other types of flow may be used; for example, the flow of people or information between activities.

Flow relationships are typically specified in from-to charts. Given M activities, a from-to chart is an M × M table or (square) matrix that represents the M2 – M relationships from each activity to each of another activities. The matrix need not be symmetric and the diagonal of the matrix is usually blank or zero. The equivalent flow volume matrix W is a from-to chart.

Qualitative Relationships Qualitative activity relationships correspond to relationships that can not be directly measured. Examples of possible qualitative relationships between activities include:

• Material Flow: flow volumes that are not convenient to directly measure, or, if measured, enables, after conversion to qualitative values, quantitative flow volumes to be combined with other qualitative measures.

• Personnel Flow: usually not necessary to determine quantitative measure.

• Same Resource: e.g., same support service used by two or more activities (e.g., spare parts).

• Same Personnel: e.g., one operator works on two machines.

• Communication: e.g., two activities need to be within shouting distance of each other.

• Safety: usually want to make sure activities are not located close together, e.g., fumes from one activity may ignite another activity.

• Noise: usually want to make sure activities are not located close together, e.g., a machine should not be located close to an office.

• Structural: e.g., two activities need to be in a refrigerated area of the facility, but otherwise they do not interact with each other.

74

SPRING 2003 4.4. SPACE AND PERSONNEL REQUIREMENTS

Closeness Relationship Values Closeness relationship values can be used to indicate physical proximity requirements between activities that have qualitative and/or quantitative relationships. The values A, E, I, O, U, and X are used to indicate the importance of locating two activities close together in a layout:

A: Absolutely necessary

E: Especially important

I: Important

O: Ordinary closeness

U: Unimportant (don’t care)

X: Not desirable

While flow volumes are “cardinal numbers,” closeness relationship values are only “ordinal numbers” (e.g., an A, as compared to an E, value only represents the fact that closeness is more important, but not how much more important). Closeness values can be converted to (arbitrary) cardinal numbers to allow their comparison in algorithmic procedures. Quantitative relationship measures (e.g., flow) can be converted to closeness relationship values in order to allow consideration of both quantitative and qualitative relationships.

Relationship Chart Closeness relationship values are specified in a relationship chart. Given M activities, a relationship chart is a triangular matrix that represents the (M2 – M)/2 relationships between each pair of activities. A relationship chart can only represent symmetric relationships between activities, as compared to from-to charts, which can represent asymmetric relationships (e.g., wij ≠ wji).

A relationship diagram is a graph that provides a spatial representation of a relationship chart. Each activity is a node in the graph and arcs are used to represent activity relationships. Typically, U (unimportant) closeness relationship values are not represented in the graph, and each of A, E, I, O, and X values are represented by arcs of different color, line style, and/or line thickness.

There may be up to (M2 – M)/2 arcs in a relationship diagram. For M ≥ 2, the 3M – 6 highest valued arcs (relationships) can be selected to form a “planar graph” that enables each relationship to be satisfied in a layout through adjacency (i.e., activities with a high-valued relationship will be adjacent in the layout).

4.4 Space and Personnel Requirements Once PP&S design is completed, the number and type of each machine and workstation is known and the number operators is known. From this information, initial estimates of the space

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and personnel requirements for each manufacturing department in a facility can be determined and used to develop a more detailed machine layout and an initial material handling system design for the department. Additional analysis is required to estimate the space and personnel requirements for the nonmanufacturing departments in the facility. The initial estimates of the space and personnel requirements of each department can then be used in developing an initial department layout for the facility and the site plan for the facility.

4.4.1 Personnel Requirements The personnel requirements for each manufacturing department includes all machine/workstation operators and all support personnel dedicated to the department (e.g., supervisors, material handling operators, etc.). The personnel requirements for the entire facility includes the personnel requirements for each manufacturing department together with all support personnel not dedicated to manufacturing departments (e.g., administrative staff, maintenance workers, etc.). Machine/workstation operator requirements are directly available from PP&S design; only estimates can be made of the number of additional support personnel required.

An estimate of the personnel requirements for the entire facility is needed in order to determine a number of aspects of the facility and site plan:

• Number of parking spaces needed for employees.

• Number and type of restrooms needed in the facility.

• Capacity of food service areas.

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Personnel Requirements

PP&S Design

Machine/ Workstation 1

Machine/ Workstation N

Mfg. Department 1 Mfg. Department i Non-Mfg. Departments (e.g., Service Areas)

Aisle/MHE Requirements or Allowance

Total Facility

Total Site

Aisle/MHE Requirements or Allowance

• • •

• • •

Parking Lot

S/R Dock Access

Other Outside Areas

Figure 4.15. Elements of facility and site space requirements.

4.4.2 Space Requirements The total space requirements for the site on which the facility is located is the sum of the space requirements “under-roof” (the facility building) and “outside” (everything except the facility building), as shown in Figure 4.15. The space requirements for a facility can be developed in two ways:

1. Calculate: Starting “from the ground up,” calculate the space requirements for each machine/workstation, which leads to the space requirements for each manufacturing department, which, together with the space requirements of the non-manufacturing departments and main aisles, leads to the total space requirements for the entire facility.

2. Template: Arrange scaled templates of the major equipment to be used in the facility (e.g., machines, etc.) into a drawing and then design the remainder of the facility “around” the templates. Traditionally, paper cutouts were used as templates; now, software packages like FactoryCAD provide large libraries of templates.

In practice, a combination of both approaches can be used.

Machines/workstations In product layouts, production is typically organized around a series of individual machines and/or assembly workstations that may be connected by material handling equipment (e.g., conveyors) that provide fixed-path material flow and the small amount of WIP storage needed.

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In process layouts, production is typically organized around individual fabrication and/or assembly workstations, with variable-path material flow between the workstations occurring along aisles and high WIP storage requirements at each workstation; each fabrication workstation may include one or more machines together with additional support equipment and storage space for WIP.

The space requirements of a machine/workstation can include the following:

1. Static machine dimensions—static width, depth, and height at maximum points.

2. Machine travel—maximum travel to the left and right and toward and away from the operator.

3. Personnel area—operator at machine together with ingress and egress.

4. Storage area—WIP, raw materials, waste and scrap, tools, fixtures, jigs, dies, and maintenance materials.

5. Support equipment—bench, tool locker, and maintenance/setup equipment.

The fabrication workstations in a process layout may include 1–5, while the machines and assembly workstations in a product layout may only include 1–3. Machine dimensions and travel are typically available from data sheets.

Manufacturing departments The total space requirements for a manufacturing department can be estimated as the sum of the space requirements of each machine/workstation together with the space required for departmental aisles and department-wide fixed material handling equipment (MHE). In a process layout, departmental aisles are typically used for both material transport and personnel movement, with little fixed MHE outside of each workstation; in a product layout, departmental aisles may only be used for personnel movement, with fixed MHE connecting each machine/workstation.

Until the material handling system has been designed for the department, an accurate machine layout can not be determined because material handling costs are not known (e.g., the hij’s); thus, the actual aisle and MHE space requirements will not be known. Instead, in order to allow an initial department layout to be determined, an aisle/MHE allowance (expressed as a percentage of the total machine/workstation space requirements) can be used. Once the material handling system design is completed, the aisle/MHE allowance can be replaced by their actual space requirements.

Nonmanufacturing departments The total space requirements for the nonmanufacturing departments in a facility can be estimated once (1) the personnel requirements for the entire facility and (2) the storage and shipping/receiving requirements for materials have been determined.

The types of nonmanufacturing departments in a facility can include the following:

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• Offices—offices for administrative, support, and engineering staff; meeting/conference rooms; etc.

• Storage/warehousing—dedicated areas outside of each manufacturing department for the storage of raw materials, in-process inventories, and finished goods.

• Shipping/receiving—dockboard area, maneuvering area for MHE used for loading/unloading, buffer/staging areas, container and trash storage, offices, and trucker’s lounge.

• Restrooms—located within 200 feet of every permanent workstation.

• Food services—located within 1,000 feet of every permanent workstation; possibilities include off-premises dining or a cafeteria with either vending machines, a serving line (over 200 employees), or a full kitchen (over 400 employees); a cafeteria can also be used as a meeting room.

• Health services, locker rooms, and washrooms.

• Plant services—HVAC, pumps, generators, etc.

• Emergency exits—an exit must be within 150 ft of any point in a building without sprinklers and within 200 ft of any point in a building without sprinklers (Tompkins et al., 1996, p. 520).

The space requirements for many of the types of service areas (types 4–7) may be small and should not be included as separate departments when determining an initial block layout, although they should be included in the final detailed facility layout. The requirements of many of the service areas and other aspects a facility are specified in OSHA (Occupational Safety and Health Act) standards.

Total facility The total space requirements for the entire facility can be estimated as the sum of the space requirements of each department together with the space required for the main interdepartmental aisles and any facility-wide fixed MHE connecting different departments. Until the material handling system for interdepartmental material flow has been designed, an accurate department layout can not be determined; thus, the actual main aisle and MHE space requirements will not be known. Instead, in order to allow an initial block layout to be determined, an aisle/MHE allowance (expressed as a percentage of the total department space requirements) can be used. Once the material handling system design for interdepartmental material flow is completed, the aisle/MHE allowance can be replaced by their actual space requirements.

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Storage Dept.

Service Areas

Mfg. Dept. 1 Mfg. Dept. 2

Main Aisles

S/R Dock Apron &

Truck Waiting

Employee & Visitor Parking

Lot

Facility

Unused Site

Space

Site

Figure 4.16. Example of facility and site space requirements.

Total site The total space requirements for the site on which the facility is to be located can be estimated as the sum of the space requirements under-roof and outside. The total space under-roof is the sum of the space requirements (or “footprint”) of each separate building (facility) located on the site (see Figure 4.16). The total space outside is the site’s total land area minus the space under-roof. Outside (or yard) areas can include the following areas.

Employee and visitor parking lots Employee parking lot design requires estimates of the total personnel requirements for each shift; the employee parking lot should accommodate the maximum number of employee vehicles on site at any one time (including shift changes); every employee parking space should be located within 500 feet of an entrance to the facility, and local authorities may regulate the number of parking spaces per employee and the number of handicapped parking spaces; parking lot design involves issues concerning the tradeoffs between accessibility, turnover, and space utilization associated with different parking angles and aisle configurations and the use of random versus dedicated parking space assignment (the issues in parking lot design are similar to those faced in warehouse design).

Dock aprons Outside space required to access truck docks, including truck turning areas (drive-in docks, where trucks enter the facility, are usually not economical); apron depth and dock bay width depend on the angle of the dock: 90° docks are preferred to “finger docks” (less than 90°) because, even though they maximize apron depth, they minimize bay width (which reduces facility costs).

Truck waiting area Should be located adjacent to the dock apron and provide space to hold the maximum number of trucks waiting at any one time; blocking in the waiting area makes it difficult to sequence trucks

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at the docks; trailers parked in the waiting area can be used for short-term storage, subject to “demurrage” (a penalty charge assesses by carriers for detention of their trailers beyond a specified free time (e.g., 30 days)).

Service roads and driveways Allows access to/from public roads and a site’s outside areas (e.g., truck waiting areas, dock aprons, and parking lots); access should be planned so that trucks to not need to back onto the site; two-way service roads should be 24 feet wide and one-way roads should be 12 feet wide; if possible, all truck traffic should circulate counterclockwise because left turns are easier and safer to make than right turns (assuming a left-side steering wheel).

Railroad spur Allows access to/from off-site rail line and on-site rail docks.

Yard storage Outside storage of raw materials, finished goods, and waste (can include cooling ponds and waste treatment areas).

Unused site space Site’s total land area minus the space under-roof and outside areas 1–6; the amount of unused space for a site can be influenced by several factors: future expansion possibilities, and minimum land-to-building ratios and minimum building–to–site-border distances decreed by local authorities.

4.5 Problems 4.1. Products A and B are to be produced using four different machines, Machines 1–4. The

routings for the products are A: 1–2–3–4–1 and B: 1–3–4–1. The material handling effort for each unit of each product is expected to be proportional to each unit’s overall volume. Each unit of Product A has dimensions of 2 by 3 by 2, and each unit of Product B has dimensions of 3 by 4 by 2. Assuming that there is no scrap, that a unit’s volume does not change during production, and that 10 and 15 units of A and B, respectively, are to be produced, determine equivalent flow volumes between the machines.

4.2. Products A, B, and C are to be produced using three different machines, Machines 1–3. The routings for the products are A: 1–2–3–1–3, B: 2–1–3–1, and C: 3–1–2. The material handling effort for each unit of each product is expected to be inversely proportional to the number of units that can be placed on a pallet. Two units of Product A, one unit of Product B, and four units of Product C can be placed on a pallet. Assuming there is no scrap and that 64, 44, and 80 units of A, B and C, respectively, are to be produced, determine equivalent flow volumes between the machines.

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4.3. Products A, B, and C are to be produced using four different machines, Machines 1–4. The routings for the products are A: 1–4–3–2–1, B: 2–4–3–1, and C: 2–1–4–3–2. Since the rectangular-shaped products will transported on pallets and the units will not be stacked on the pallet, the material handling effort for each unit of each product is expected to be proportional to the area of the bottom face of each unit. The bottom face is the side of a unit that touches the pallet and, to maximize a pallet’s carrying capacity, should be one of the unit’s smallest faces. Each unit of Product A has dimensions of 6 by 18 by 5, each unit of Product B has dimensions of 5 by 4 by 12, and each unit of Product C has dimensions of 4 by 15 by 18. Assuming there is no scrap, that a unit’s volume does not change during production, and that 120, 68, and 55 units of A, B and C, respectively, are to be produced, determine equivalent flow volumes between the machines.

4.4. Each node a1 to a24 of the pairwise interchange graph shown in Figure 4.7 represents one of the 4! = 24 possible machine-to-site assignment vectors for a 4-machine–4-site machine layout problem. The nodes of the graph are labeled with the total cost of material flow associated with each assignment. Use the SDPI heuristic to determine a (locally) optimal layout for each of the following three different initial assignment vectors (please list the intermediate nodes used at each iteration):

(a) a = a1 = [1,2,3,4]; (b) a = a17 = [3,4,1,2]; and (c) a = a23 = [4,1,3,2].

4.5. Under what conditions is the linear assignment problem an appropriate model for a machine layout problem?

4.6. Under what conditions is a fixed product layout likely to be the most appropriate type of machine layout?

4.7. Describe one advantage and one disadvantage of a U-shaped material flow pattern as compared to a straight-line material flow pattern.

4.8. What is another term used to describe a job shop layout?

4.9. Explain the differences between a polygonal layout and an orthogonal layout. Why is the latter usually the preferred representation for a facility layout?

4.10. Shown below is a CRAFT initial layout. Given departments A–F, with department F fixed, list all of the 2-way interchanges that will be considered by the program during its first iteration.

A A A A A F F F D D D A A A A F F D D A A C C F F F D D D A A A C C F F E E E E B B B C C E E E E B B C C C E E E E E E

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4.11. Explain the difference in the type of relationships between activities that can be represented in a from-to chart as opposed to a relationship chart.

4.12. Why might a facility planner want to convert quantitative equivalent flow volume values to qualitative closeness relationship values when constructing a layout?

4.13. Describe a qualitative relationship that could result in two activities having an A closeness relationship value between them, and a qualitative relationship that could result in two activities having an X closeness relationship value between them.

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5. Material Handling

5.1 Introduction

5.1.1 Definitions of Material Handling The following are some definitions of material handling (MH):

1. MH is handling material (where handling refers to the moving, lifting, transferring, and storing of goods and materials) [Apple].

2. The art and science of moving, packaging, and storing substances in any form [BMH, MHI].

3. The art of implementing movement—economically and safely [Apple].

4. The processes and systems that transfer and manage the transfer of goods from one place to another [IE Terminology].

5. Efficient short-distance movement that usually takes place within the confines of a building such as a plant or a warehouse and between a building and a transportation agency [Management of Business Logistics, 5th ed., West, 1992].

6. MH embraces all of the basic operations involved in the movement of bulk, packages, and individual products in a semisolid or solid state by means of machinery, and within the limits of a place of business [Sule].

7. MH uses the right method to provide the right amount of the right material at the right place, at the right time, in the right sequence, in the right position, in the right condition, and at the right cost [T&W].

8. MH is the act of creating “time and place utility” through the handling, storage, and control of material, as distinct from manufacturing (i.e., fabrication and assembly operations), which creates “form utility” by changing the shape, form, and makeup of material [Apple].

9. MH is the movement, storage, control, and protection of materials, goods, and products throughout the process of manufacturing, distribution, consumption, and disposal. The focus is on the methods, mechanical equipment, systems, and related controls used to achieve these functions [MHIA, Keyword Glossary].

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5. MATERIAL HANDLING LECTURE NOTES FOR FACILITIES DESIGN

10. The movement of raw goods from their native site to the point of use in manufacturing, their subsequent manipulation in production processes, and the transfer of finished products from factories and their distribution to users or sales outlets [Britannica].

5.1.2 Scope of Material Handling Scope of MH with respect the distance: As shown in Figure 5.1, MH fills the gap between the study of workplace design (ergonomics), where movement takes place within arm’s reach, and the study of transportation science, where moves take place over miles.

Industrial logistics is concerned with total flow of materials: from the acquisition of raw materials to the delivery of finished products to their ultimate users. Both MH and transportation science are important areas of study within industrial logistics.

Scope of MH with respect to time: the design MH systems, as part of the facilities planning process, fits within the long range (years) strategy of the corporation; the actual operation of an automated MH system utilizes many aspects of real-time control.

Figure 5.1. Scope of material handling.

Can MH Add Value to a Product? It is often said that MH only adds to the cost of a product, it does not add to the value of a product. Although MH does not provide a product with form utility (cf. Def. 8, above), the time and place utility provided by MH can add real value to a product, i.e., the value of a product can increase after MH has taken place; for example:

• The value (to the customer) added by the overnight delivery of a package (e.g., Federal Express) is greater than or equal to the additional cost of the service as compared to regular mail service—otherwise regular mail would have been used.

• The value added by having parts stored next to a bottleneck machine is the savings associated with the increase in machine utilization minus the cost of storing the parts at the machine.

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SPRING 2003 5.1. INTRODUCTION

5.1.3 Design of MH Systems A common approach to the design of MH systems (MHSs) is to consider MH as a cost to be minimized (e.g., the hij’s in the total cost of material flow defined in Chapter 2). This approach may be the most appropriate in many situations because, while MH can add real value to a product, it is usually difficult to identify and quantify the benefits associated with MH; it is much easier to identify and quantify the costs of MH (e.g., the cost of MH equipment, the cost of indirect MH labor, etc.). Once the design of a production process (exclusive of MH considerations) is completed, alternate MHS designs are generated, each of which satisfy the MH requirements of the production process. The least cost MHS design is then selected.

The appropriateness of the use of MHS cost as the sole criterion to select a MHS design depends on the degree to which the other aspects of the production process are able be changed. If a completely new facility and production process is being designed, then the total cost of production is the most appropriate criterion to use in selecting a MHS—the lowest cost MHS may not result in the lowest total cost of production. If it is too costly to even consider changing the basic layout of a facility and the production process, then MHS cost is the only criterion that need be considered. In practice, it is difficult to consider all of the components of total production cost simultaneously, even if a new facility and production process is being designed. Aspects of the design that have the largest impact on total cost are at some point fixed and become constraints with respect to the remaining aspects of the design.

Figure 5.2. Material handling system equation.

Material flow refers to the combination of the physical characteristics of material together with its move or flow requirements. As shown in Figure 5.2, material flow requirements are determined once it has been decided that each move is necessary (why), what is being moved, and where and when it is being moved. Data from product, process, and schedule (PP&S) design and the initial facility layout are two of the primary sources of information that can be used to determine the material flow requirements. Material flow requirements are transformed to material handling system (MHS) alternatives by selecting methods of handling, storing, and controlling the material that satisfy the requirements. From among the MHS alternatives

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generated, the “best” MHS is selected. The selected MHS can then either be directly implemented or, if the goal is to minimize the total cost of material flow, used to provide an estimate of the hij’s in subsequent layout procedures and flow requirements adjustments.

5.1.4 Principles of Material Handling Although there are no definite “rules” that can be followed when designing an effective MHS, the following “Ten Principles of Material Handling” as defined by the Material Handling Institute (MHI) and the College-Industry Council on Material Handling Education (CIC-MHE) represent the distillation of many years of accumulated experience and knowledge of many practitioners and students of material handling [MHI]:

1. Planning Principle. All MH should be the result of a deliberate plan where the needs, performance objectives, and functional specification of the proposed methods are completely defined at the outset.

2. Standardization Principle. MH methods, equipment, controls and software should be standardized within the limits of achieving overall performance objectives and without sacrificing needed flexibility, modularity, and throughput.

3. Work Principle. MH work (defined as material flow multiplied by the distance moved) should be minimized without sacrificing productivity or the level of service required of the operation.

4. Ergonomic Principle. Human capabilities and limitations must be recognized and respected in the design of MH tasks and equipment to ensure safe and effective operations.

5. Unit Load Principle. Unit loads shall be appropriately sized and configured in a way that achieves the material flow and inventory objectives at each stage in the supply chain.

6. Space Utilization Principle. Effective and efficient use must be made of all available (cubic) space.

7. System Principle. Material movement and storage activities should be fully integrated to form a coordinated, operational system which spans receiving, inspection, storage, production, assembly, packaging, unitizing, order selection, shipping, and transportation, and the handling of returns.

8. Automation Principle. MH operations should be mechanized and/or automated where feasible to improve operational efficiency, increase responsiveness, improve consistency and predictability, decrease operating costs, and to eliminate repetitive or potentially unsafe manual labor.

9. Environmental Principle. Environmental impact and energy consumption should be considered as criteria when designing or selecting alternative equipment and MHS.

10. Life Cycle Cost Principle. A thorough economic analysis should account for the entire life cycle of all MHE and resulting systems.

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5.1.5 Characteristics of Materials The characteristics of materials affecting handling include the following: size (length, width, height); weight (weight per item, or per unit volume); shape (round, square, long, rectangular, irregular); and other (slippery, fragile, sticky, explosive, frozen).

Table 5.1. Material Categories

Physical State

Material Category Solid Liquid Gas

Individual units Part, subassembly — —

Containerized items Carton, bag, tote, box, pallet, bin

Barrel Cylinder

Bulk materials Sand, cement, coal, granular products

Liquid chemicals, solvents, gasoline

Oxygen, nitrogen, carbon dioxide

Figure 5.3. Unit vs. bulk handling of material [BMH, MHI].

Impact of material category on MH equipment:

• Individual units and containerized items ⇒ discrete material flow ⇒ unit loads ⇒ unit handling equipment

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• Bulk materials ⇒ continuous material flow ⇒ bulk handling equipment

Figure 5.3 shows an example of alternate ways of handling a dry bulk material: as containerized (bagged) items on pallets handled using unit handling equipment (boxcar, pallet, fork truck), or as bulk material handled using bulk handling equipment (hopper car, pneumatic conveyor, bulk storage bin).

5.1.6 Material Handling Equipment Old adage (that applies to a lack of MH equipment knowledge): “If the only tool you have is a hammer, it’s amazing how quickly all your problems seem to look like nails.”

The different types of MH equipment listed in Table 5.2 can be classified into the following five major categories [Chu]:

I. Transport Equipment. Equipment used to move material from one location to another (e.g., between workplaces, between a loading dock and a storage area, etc.). The major subcategories of transport equipment are conveyors, cranes, and industrial trucks. Material can also be transported manually using no equipment.

II. Positioning Equipment. Equipment used to handle material at a single location (e.g., to feed and/or manipulate materials so that are in the correct position for subsequent handling, machining, transport, or storage). Unlike transport equipment, positioning equipment is usually used for handling at a single workplace. Material can also be positioned manually using no equipment.

III. Unit Load Formation Equipment. Equipment used to restrict materials so that they maintain their integrity when handled a single load during transport and for storage. If materials are self-restraining (e.g., a single part or interlocking parts), then they can be formed into a unit load with no equipment.

IV. Storage Equipment. Equipment used for holding or buffering materials over a period of time. Some storage equipment may include the transport of materials (e.g., the S/R machines of an AS/RS, or storage carousels). If materials are block stacked directly on the floor, then no storage equipment is required.

V. Identification and Control Equipment. Equipment used to collect and communicate the information that is used to coordinate the flow of materials within a facility and between a facility and its suppliers and customers. The identification of materials and associated control can be performed manually with no specialized equipment.

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Table 5.2. Material Handling Equipment

I. Transport Equipment

A. Conveyors B. Cranes C. Industrial Trucks D. No Equipment

1. Chute conveyor 2. Wheel conveyor 3. Roller conveyor 4. Chain conveyor 5. Slat conveyor 6. Flat belt conveyor 7. Magnetic belt conveyor 8. Troughed belt conveyor 9. Bucket conveyor

10. Vibrating conveyor 11. Screw conveyor 12. Pneumatic conveyor 13. Vertical conveyor 14. Cart-on-track conveyor 15. Tow conveyor 16. Trolley conveyor 17. Power-and-free conveyor 18. Monorail 19. Sortation conveyor

1. Jib crane 2. Bridge crane 3. Gantry crane 4. Stacker crane

1. Hand truck 2. Pallet jack 3. Walkie stacker 4. Pallet truck 5. Platform truck 6. Counterbalanced lift truck 7. Narrow-aisle straddle truck 8. Narrow-aisle reach truck 9. Turret truck

10. Order picker 11. Sideloader 12. Tractor-trailer 13. Personnel and burden carrier 14. Automatic guided vehicle

1. Manual

II. Positioning

Equipment III. Unit Load Formation

Equipment

IV. Storage Equipment V. Identification and Control Equipment

1. Manual (no equipment)

2. Lift/tilt/turn table 3. Dock leveler 4. Ball transfer table 5. Rotary index

table 6. Parts feeder 7. Air film device 8. Hoist 9. Balancer

10. Manipulator 11. Industrial robot

1. Self-restraining (no equipment)

2. Pallets 3. Skids 4. Slipsheets 5. Tote pans 6. Pallet/skid boxes 7. Bins/baskets/racks 8. Cartons 9. Bags

10. Bulk load containers 11. Crates 12. Intermodal containers 13. Strapping/tape/glue 14. Shrink-wrap/

stretch-wrap 15. Palletizers

1. Block stacking (no equipment)

2. Selective pallet rack 3. Drive-through rack 4. Drive-in rack 5. Flow-through rack 6. Push-back rack 7. Sliding rack 8. Cantilever rack 9. Stacking frame

10. Shelves/bins/drawers 11. Storage carousel 12. Automatic storage/

retrieval system 13. Split-case order picking

system 14. Mezzanine


2. Bar codes 3. Radio frequency

identification tags 4. Magnetic stripes 5. Machine vision 6. Portable data terminals 7. EDI/XML

communication protocols8. Warehouse management

systems

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Transport equipment (see Table 5.2) is used to move material from one location to another, while positioning equipment is used to manipulate material at a single location. The major subcategories of transport equipment are conveyors, cranes, and industrial trucks. Material can also be transported manually using no equipment.

The following general equipment characteristics can be used to describe the functional differences between conveyors, cranes, and industrial trucks (see Figure 5.4 and Table 5.3):

Path: Fixed—move between two specific points

Variable—move between a large variety of points

Area: Restricted—move restricted to a limited area

Unrestricted—unlimited area of movement

Move frequency: Low—low number of moves per period, or intermittent moves

High—high number of moves per period

Adjacent move: Yes—move is between adjacent activities

No—move is between activities that are not adjacent

Variable Path + Restricted Area (Cranes)

Fixed Path (Conveyors)

Variable Path + Unrestricted Area (Industrial Trucks)

Figure 5.4. Path and area characteristics of transport equipment.

Table 5.3. Transport Equipment Characteristics

Path Fixed Variable

Area Restricted Restricted Unrestricted

Frequency High Low High Low —

Adjacent — Yes No — — —

Equipment Category

Conveyor Conveyor Industrial Truck/Crane

Industrial Truck

Crane Industrial Truck

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SPRING 2003 5.2. THE UNIT LOAD CONCEPT

5.2 The Unit Load Concept A unit load is one or more individual units or containerized items so arranged or restricted that it can be handled as a single item and maintain its integrity.

Advantages of unit loads:

1. More items can be handled at the same time, thereby reducing the number of trips required and, potentially, reducing handling costs, loading and unloading times, and product damage.

2. Enables the use of standardized material handling equipment.

Disadvantages of unit loads:

1. Time spent forming and breaking down the unit load.

2. Cost of containers/pallets and other load restraining materials used in the unit load

3. Empty containers/pallets may need to be returned to their point of origin.

Basic ways of restraining a unit load:

• Self-restraining—one or more items that can maintain their integrity when handled as a single item (e.g., a single part or interlocking parts)

• Platforms—pallets (paper, wood, plastic, metal), skids (metal, plastic)

• Sheets—slipsheets (plastic, cardboard, plywood)

• Reusable containers—tote pans, pallet boxes, skid boxes, bins, baskets, bulk containers (e.g., barrels), intermodal containers

• Disposable containers—cartons, bags, crates

• Racks—racks

• Load stabilization—strapping, shrink-wrapping, stretch-wrapping, glue, tape, wire, rubber bands

Basic ways of moving a unit load:

• Use of a lifting device under the mass of the load (e.g., a pallet and fork truck)

• Inserting a lifting element into the body of the load (e.g., a coil of steel)

• Squeezing the load between two lifting surfaces (e.g., lifting a light carton between your hands, or the use of carton clamps on a lift truck)

• Suspending the load (e.g., hoist and crane)

5.2.1 Unit Load Design Unit loads can be used both for in-process handling and for distribution (receiving, storing, and shipping).

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Unit load design involves determining the:

1. Type, size, weight, and configuration of the load

2. Equipment and method used to handle the load

3. Methods of forming (or building) and breaking down the load.

Selecting unit load size for in-process handling:

• Unit loads should not be larger than the production batch size of parts in process—if the unit load size is larger, then a delay would occur if the load is forced to wait until the next batch of the part is scheduled to start production (which might be days or weeks) before it can be transported.

• Large production batches (used to increase the utilization of bottleneck operations) can be split into smaller transfer batches for handling purposes, where each transfer batches contains one or more unit loads, and small unit loads can be combined into a larger transfer batch to allow more efficient transport (e.g., several cartons at a time can be transported on a hand truck, although each carton is itself a unit load and could be transported separately); thus:

Single part ≤ Unit load size ≤ Transfer batch size ≤ Production batch size

• When parts are transferred between adjacent operations, the unit load may be a single part.

• When operations are not adjacent, short distance moves ⇒ smaller unit load sizes, and long distance moves ⇒ larger unit load sizes.

• The practical size of a unit load (cf. the Unit Load Principle) may be limited by the equipment and aisle space available and the need for safe material handling (in accord with the Safety Principle).

Selecting unit load size for distribution (see Figure 5.5):

• Containers/pallets are usually available only in standard sizes and configurations.

• Truck trailers, rail boxcars, and airplane cargo bays are limited in width, length, and height.

• The existing warehouse layout and storage rack configuration may limit the number of feasible container/pallet sizes for a load.

• Customer package/carton sizes and retail store shelf restrictions can limit the number of feasible container/pallet sizes for a load.

94

SPRING 2003 5.3. UNIT LOAD FORMATION EQUIPMENT

Figure 5.5. Unit load size for distribution [BMH, MHI].

5.3 Unit Load Formation Equipment Unit load formation equipment is used to restrict materials so that they maintain their integrity when handled a single load during transport and for storage. If materials are self-restraining (e.g., a single part or interlocking parts), then they can be formed into a unit load with no equipment.

Table 5.4. Unit Load Formation Equipment

1. Self-restraining (no equipment) 2. Pallets 3. Skids 4. Slipsheets 5. Tote pans 6. Pallet boxes/skid boxes 7. Bins/baskets/racks 8. Cartons 9. Bags

10. Bulk load containers 11. Crates 12. Intermodal containers 13. Strapping/tape/glue 14. Shrink-wrap/stretch-wrap 15. Palletizers (a) Manual palletizing (b) Robotic pick and place palletizers (c) Conventional stripper plate palletizers

1. Self-restraining (no equipment)

One or more items that can maintain their integrity when handled as a single item (e.g., a single part or interlocking parts)

95


96

2. Pallets

Platform with enough clearance beneath its top surface (or face) to enable the insertion of forks for subsequent lifting purposes

Materials: Wood (most common), paper, plastic, rubber, and metal

Size of pallet is specified by its depth (i.e., length of its stringers or stringer boards) and its width (i.e., length its deckboards)—pallet height (typically 5 in.) is usually not specified

Orientation of stringers relative to deckboards of pallet is specified by always listing its depth first and width last: Depth (stringer length) × Width (deckboard length)

48 × 40 in. pallet is most popular in the US (27% of all pallets—no other size over 5%) because its compatibility with railcar and truck trailer dimensions; e.g., the GMA (Grocery Manufacturers of America) pallet is four-way and made of hardwood

1200 × 800 mm “Euro-Pallet” is the standard pallet in Europe

Single-face pallets are sometimes referred to as “skids”

3. Skids

Platform (typically metal) with enough clearance beneath its top surface to enable a platform truck to move underneath for subsequent lifting purposes

Forks can also be used to handle skids since the clearance of a skid is greater than that of a pallet

Compared to a pallet, a skid is usually used for heavier loads and when stacking is not required

A metal skid can lift heavier loads than an equal-weight metal pallet because it enables a platform truck to be used for the lifting, with the platform providing a greater lifting surface to support the skid as compared to the forks used to support the pallet

Handling methpush/pull lift truck attachment

30% of pallet costs and their weight and volume is 1–5% o

special lift truck attachment reduces the vehicle’s load capacity

4. Slipsheets

Thick piece of paper, corrugated fiber, or plastic upon which a load is placed

od: tabs on the sheet are grabbed by a special

Advantages: usually used in place of a pallet for long-distance shipping because their cost is 10–f a pallet

Disadvantages: slower handling as compared to pallets; greater load damage within the facility;


97

R

for in-process handling

not in use

5. Tote pans

eusable container used to unitize and protect loose discrete items

Typically used

Returnable totes provide alternative to cartons for distribution

Can be nested for compact storage when 6. Pallet/skid boxes

eusable containers used to unitize and or fork/platform

truck handling

Pa in

Rprotect loose items f

llet box sometimes referred to as a “bpallet”

8. Cartons

Disposable container used to unitize and protect loose discrete

D ns always specified as sequence: Length × Width × ger, and width is the smaller, of the two dimension of the open

face of the carton, and depth is the distance perpendicular to the length and width

L il

items

Typically used for distribution

imensioDepth, where length is the lar

arge quantities of finished carton blanks or knocked-down cartons can be stored on pallets untneeded

9. Bags

Disposable container used to unitize and protect bulk materials

Typically used for distribution

Polymerized plastic (“poly”) bags available from light weight (1 mil.) to heavy weight (6 mil.) in flat and gusseted styles

Dimensions of bag specified as: Width × Length, for flat bags, and × Depth (half gusset) × Length, for gusseted bags Width

Pallet box Skid box

5. MATERIAL HANDLING L ES FOR FACILITIES DESIGNECTURE NOT

98

etc.

10. Bulk load containers

eusable container used to unitize and protect bulk materiaR ls

Includes barrels, cylinders,

Used for both distribution and in-process handling

11. Crates

Disposable container used to protect discrete items

ed for distribution Typically us

Rdiscrete items

Enables a load to be handled as a single unit when it is transferred

from a cargo ship and loaded onto a truck as a single unit

is not as common to use intermodal containers for airfreigh

andard outside dimensions of intermodal containers are: 20 or 40

length, 5 in. of width, and 9.5 in. of heighdetermine the inside dimensions

ypical sea transport costs per 40-ft. container acoast, $4000–5000 from Singapo

[Global Supply Management, D. Locke]

12. Intermodal containers

eusable container used to unitize and protect loose

between road, rail, and sea modes of transport; e.g., the container can be unloaded

Itt transport because of aircraft shape

and weight restrictions

Stft. in length; 8 ft. in

width; and 8, 8.5, or 9.5 ft. in height; less 8 in. of t to

T re: $3000–4000 from Japan to the US west re to the US west coast, and $2500–3500 from Europe to the

US east coast; transport costs for a 20-ft. container is 70% of the costs of a 40-ft. container


99

13. Strapping/tape/glue

Used for load stabilization

Straps are either steel or plastic

Plastic strapping that shrinks is used to keep loads from becoming loose during shipment

14. Shrink-wrap/stretch-wrap

Used for load stabilization

Allows irregular loads to be stabilized

In shrink-wrapping, a film or bag is placed over the load and then heat is applied to shrink the film or bag; manual or automatic; most shrink-wrap applications are being replaced by stretch-wrapping

In stretch-wrapping, a film is wound around the load while the film is stretched; as compared to shrink-wrapping, stretch-wrapping has lower material, labor, and energy costs

Stretch-wrap machine

15. Palletizers

Used for load formation

Three general methods of building (or “palletizing”) unit loads

15(a) Manual palletizing

Operators arrange items into the desired pattern used to form the unit load

Since the ergonomics of loading and unloading are important (e.g., vertically, the prime working zone is between the knees and the chest; horizontally, reaches of more than 24 in. with a load should be avoided), lift and turn tables are often used

Semi-mechanized palletizers use operators to arrange items into the desired pattern for each layer of the unit load and a powered device is used to transfer layers onto a pallet and then lower the load for the next layer

5. MATERIAL HANDLING L OTES FOR FACILITIES DESIGNECTURE N

100

15(b) Robotic pick and place palletizers

Fully automated device to build unit loads

Used when flexibility is required (e.g., the “Distributor’s Pallet Loading Problem”)

Greatest limitation is capacity, typically 6 cycles per minute; capacity is determined by the number of items handled with each pick operation

15(c) Conventional stripper plate palletizers

Fully automated device to build unit loads

Used when high throughput of identical loads is required (e.g., the “Manufacturer’s Pallet Loading Problem”)

Capacity is typically greater (30–180 items per minute) than pick and place because an entire layer is placed on the load at one time; not as flexible as pick and place

Preformed layer of items (cases) are indexed onto the stripper plate (or apron); when properly positioned over the pallet, the apron is pulled out from underneath the layer to deposit the layer onto the pallet

“Right angle” pattern formation—very flexible patterns are possible; can handle a wide variety of case sizes and types; limited capacity (up to 80 items per minute); compact design

“In-line” pattern formation—flexible patterns are not possible; ideal for high speed operation (up to 180 items per minute); takes up more room (larger machine) than right angle

Right-angle pattern formation

In-line pattern formation


5.3.1 Pallets

Pallet vs. Skid As compared to a pallet, a skid is usually used for heavier loads and when stacking is not required. A metal skid can lift heavier loads than an equal-weight metal pallet because it enables a platform truck to be used for the lifting, with the platform providing a greater lifting surface to support the skid as compared to the forks used to support the pallet.

Pallet Characteristics

Material and cost: • Paper—$3–10; expendable, low cost; usually used in shipping.

• Wood—$3–25; most common type of pallet; economical, reusable pallet; repair cost typically two-thirds the cost of a new pallet.

• Plastic—$20–100; becoming more common (as lumber and repair costs of wood pallets increase); product protection, provide uniform “tare weight” (i.e., gross weight of the load less the weight of the product); can be steam cleaned for sanitary applications; durable.

• Rubber—used in spark-free environments.

• Metal—used for heavy loads.

Elements of wooden pallets: • Deckboards—boards that make up the top and bottom surfaces (or faces) of the pallet.

• Stringers—boards (typically three per pallet), to which the deckboards are fastened, used to provide clearance for fork insertion; can be notched to allow four-way entry.

• Block legs—wooden blocks fastened to a stringer board, used in place of notched stringers.

(Stringer length) Depth Width (Deckboard length)

x

Deckboards Stringer

Notch

Figure 5.6. Elements of a wooden pallet.

Dimensions: • The size of a pallet is specified by its depth (i.e., the length of its stringers or stringer

boards) and its width (i.e., the length its deckboards)—pallet height (typically 5 in.) is

101


usually not specified; the orientation of the stringers relative to the deckboards of the pallet is specified by always listing its depth first and width last:

Depth (stringer length) × Width (deckboard length)

• Most popular standard ANSI pallet sizes:

32 × 40 in. 36 × 48 in. 40 × 48 in.

42 × 42 in. 48 × 40 in. 48 × 48 in.

• Other standard ANSI pallet sizes:

24 × 32 in. 32 × 48 in. 36 × 36 in.

36 × 42 in. 48 × 60 in. 48 × 72 in.

• 48 × 40 in. pallet is the most popular (27% of all pallets—no other size over 5%) because it can be placed two abreast across the 48 in. dimension in railroad freight cars and two abreast across the 40 in. dimension in most trucks. (Note: the 48 × 40 in. pallet is not the same as a 40 × 48 in. pallet.)

• Maximum depth of standard pallets is 48 in., which is why the rated load capacity of counterbalanced lift trucks is specified with respect to a 24 in. load center.

Design features: 1. Two-way vs. four-way entry—four-way entry enables the forks of a lift truck to be inserted

into, and strapping to be run through, any of the four sides of the pallet, increasing the pallet’s flexibility; four-way pallets are of either a notched or block-leg design.

Notched vs. block-leg designs—the notched-stringer design is less costly, but it allows only two-way entry for pallet jacks and pallet trucks because their forks cannot be inserted into the notches; the block-leg design allows four-way entry for all fork trucks and, if nonreversible, requires less space for empty pallet storage as compared to a double-faced nonreversible notched-stringer design since the pallets can be nested inside of each other.

2. Single face vs. double face—the single-face design has only a single deckboard surface similar to a skid (although it cannot be handled like a skid due to its lower stringer height and the presence of a center stringer); the single-face design is less costly and requires less space for empty pallet storage since the pallets can be nested inside of each other; the additional bottom deckboard surface of the double-face design adds strength and stability, and provides more surface area for support when loaded pallets are stacked on top of each other. Most disposable wooden pallets are single-face designs due to their low cost, while most reusable wooden pallets are double-face designs due to their durability.

3. Reversible vs. nonreversible—the reversible design allows either face of the pallet to be used for load support, but pallet jacks and pallet trucks cannot be used because the front wheels mounted inside the end of their forks cannot extend to the floor; the nonreversible

102


design can be handled by all fork trucks since its bottom face does not have deckboards at the positions needed for front-wheel extension.

4. Flush stringer vs. single wing vs. double wing—single- and double-wing designs have their stringers recessed so that the ends of their deckboards overhang, forming “wings”; the flush stringer design has greater long-term structural integrity than either of the wing designs, the wings typically being the first point of pallet failure; the single-wing design allows pallets to be placed side-by-side on the floor while still providing the clearance required for the outriggers of a narrow-aisle straddle truck; the double-wing design (termed a “stevedore’s pallet”) allows bar slings to be placed in the space between the wings, thus allowing a crane to be used for handling.

Table 5.5. Types of Wooden Pallets

Two way

Single face Nonreversible Flush stringer

Two way Single face

Nonreversible Single wing

Two way Double face Reversible

Flush stringer

Two way

Double face Reversible

Double wing

Two way Double face

Nonreversible Flush stringer

Two way Double face

Nonreversible Single wing

Two way

Double face Nonreversible Double wing

Four-way notched Double face


Four-way block leg Double face


Pallet type: • Each pallet type is a combination of design features. Some of the design-feature

combinations correspond to pallet types are either not feasible (e.g., a single-face reversible pallet) or, if feasible, very uncommon due to their inherent structural weakness (e.g., a four-way-block-leg single-face flush-stringer pallet, or a four-way-notched double-face reversible flush-stringer pallet).

• The most common types of wooden pallets are listed in Table 5.5.

103


• The most popular type of pallet is the two-way double-face nonreversible flush pallet.

Figure 5.7. Basic pallet patterns.

Special-purpose pallets: The following terms are used to distinguish pallets used for specific purposes [Glossary of Terms, National Wooden Pallet & Container Assoc., http://www.nwpca.com]:

• Take-it-or-leave-it pallet—pallet fitted with fixed cleats on the top deckboards to permit forks to pass beneath the unit load and remove it from the.

• Slave pallet—pallet or platform used as a support base for palletized loads in a rack or conveyor system.

• Captive pallet—pallet intended for use within a facility and not exchanged.

• Exchange pallet—pallet exchanged among a group of shippers and where ownership of the pallet is transferred with the ownership of the load.

• Shipping pallet—pallet used for a single one-way trip from shipping to receiving, after which it is disposed.

The Pallet Loading Problem The pallet loading (or packing) problem refers to determining the “optimal” patterns (or layouts) of the items to be loaded onto pallets.

There are, at least, two different problems that can be identified as “the Pallet Loading Problem”:

• The Manufacturer’s Pallet Loading Problem—loading identical items onto a pallet so that the number of items per pallet is maximized.

• The Distributor’s Pallet Loading Problem(s)—(single pallet) loading various size items onto a pallet so that the volume of items loaded onto the pallet is maximized; (multiple

104

SPRING 2003 5.4. POSITIONING EQUIPMENT

pallets) loading various size items onto identical pallets so that the number of pallets required to load all of the items is minimized.

Unlike the Manufacturer’s Problem, the Distributor’s Problem is nonrepetitive (i.e., it requires a unique solution for each pallet loaded) ⇒ one should be willing to spend more time and effort to find a good solution to the Manufacturer’s Problem as compared to the Distributor’s Problem.

Manufacturer’s Problem ⇒ use of automatic stripper plate palletizer possible

Distributor’s Problem ⇒ manual or robotic (pick and place) palletization

Both problems are difficult optimization problems to solve (they are, in fact, both “NP-hard”), even with the following restrictions that are usually assumed:

1. All items and pallets are rectangular.

2. Items are placed orthogonally on a pallet (i.e., all item edges are parallel to pallet edges).

5.4 Positioning Equipment Positioning equipment (see Table 5.2) is used to handle material at a single location. It can be used at a workplace to feed, orient, load/unload, or otherwise manipulate materials so that are in the correct position for subsequent handling, machining, transport, or storage. In many cases, positioning equipment is required for and can be justified by the ergonomic requirements of a task. As compared to manual handling, the use of positioning equipment can provide the following benefits [MMH, Sept 1993]:

• raise the productivity of each worker when the frequency of handling is high,

• improve product quality and limit damage to materials and equipment when the item handled is heavy or awkward to hold and damage is likely through human error or inattention, and

• reduce fatigue and injuries when the environment is hazardous or inaccessible.

Table 5.6. Positioning Equipment

1. Manual (no equipment) 2. Lift/tilt/turn table 3. Dock leveler 4. Ball transfer table 5. Rotary index table 6. Parts feeder 7. Air film device

8. Hoist 9. Balancer 10. Manipulator (a) Rigid-link manipulator (b) Articulated jib crane manipulator (c) Vacuum manipulator 11. Industrial robot


Under ideal circumstances, maximum recommended weight for manual lifting to avoid back

105

5. MATERIAL HANDLING L NOTES FOR FACILITIES DESIGNECTURE

106

injuries is 51 lbs.

Recommendation based on NIOSH (National Institute for Occupational Safety and Health) 1991 Lifting Equation, which uses six multipliers to reduce maximum recommended weight for less than ideal lifting tasks

2. Lift/tilt/turn table

Used when positioning involves the lifting, tilting, or turning of a load.

Can be used to reduce or limit a worker’s lifting and/or reaching motions.

Pallet load levelers are lift and turn tables used in manual palletizing to reduce the amount of bending and stooping involved with manually loading a pallet by combining a lifting and turning mechanism with a device that lowers the table as each layer is completed so that loading always takes place at the optimal height of 30 in.

3. Dock leveler

Used at loading docks to compensate for height differences between a truck bed and the dock

4. Ball transfer table

Used in conveyor systems to permit manual transfer to and from machines and conveyors and between different sections of conveyors

Since loads are pushed on the table, ball friction limits the maximum load weight to 600 lbs.

5. Rotary index table

Used for the synchronous transfer of small parts from station to station in a single workcenter

Circular table rotates in discrete intermittent steps to advance parts between stations located along its perimeter

Since each part moves between stations at the same time, it is


107

difficult to put buffers between stations

Different from conveyors used as in-line indexing machines, where linear transfers can take place between multiple workcenters separated by long distances, since a rotary index table is restricted to circular transfers with a single compact workcenter

6. Parts feeder

Used for feeding and orienting small identical parts, particularly in automatic assembly operations [Boothroyd]

Motion of parts in a random pile channeled so that each part automatically assumes a specified orientation, where the symmetries of a part define its possible orientations

Motion can be imparted through vibration, gravity, centrifugal force, tumbling, or air pressure

In a vibratory bowl feeder, the most versatile type of parts feeder, parts are dumped into a bowl and then move vibrate uphill along a track towards an outlet, where rejected parts fall off the track and are recycled

Parts feeders can be used to provide inspection capabilities with respect to the shape and weight of parts (e.g., the coin feeder of a vending machine)

7. Air film device

Used to enable precision positioning of heavy loads

Sometimes referred to as “air pallets”

Can be used in place of cranes and hoists

Thin film of compressed (10–50 psi) air used to float loads of up to 300,000 lbs. so that a horizontal push of 1 lb. can move 1000 lb. load; floating action enables load to rotated or translated in any direction in the horizontal plane

Requires a smooth floor surface against which air streams underneath the device can push

Can be used in warehousing as the mechanism to convert stationary racks into sliding racks


108

8. Hoist

Used for vertical translation (i.e., lifting and lowering) of loads

Frequently attached to cranes and monorails to provide vertical translation capability

Can be operated manually, electrically, or pneumatically

Uses chain or wire rope as its lifting medium

Hoists are categorized into duty classes: H1—infrequent, standby duty use (1 or 2 lifts per month); H2—light duty (avg. 75 start/stops per hour); H3—medium (max. 250 start/stops per hour); H4—heavy, and H5—severe duty

9. Balancer

Mechanism used to support and control loads so that an operator need only guide a balanced (“weightless”) load, thus providing precision positioning

Can be use to support hand tools to reduce changeover time

Can also be attached to hoists and manipulators

10. Manipulator

Used for vertical and horizontal translation and rotation of loads

Acting as “muscle multipliers,” manipulators counterbalance the weight of a load so that an operator lifts a small portion (1%) of the load’s weight

Can be powered manually, electrically, or pneumatically

Manipulator’s end-effector can be equipped with mechanical grippers, vacuum grippers, electromechanical grippers, or other tooling

Manipulators fill the gap between hoists and industrial robots: they can be used for a wider range of positioning tasks than hoists and are more flexible than industrial robots due to their use of manual control

10(a) Rigid-link manipulator

Although similar in construction, a rigid-link manipulator is distinguished from an industrial robot by the use of an operator for control as opposed to automatic computer control


109

10(b) Articulated jib crane manipulator

Extends a jib crane’s reaching capability in a work area through the use of additional links or “arms”

10(c) Vacuum manipulator

Provides increased flexibility because rigid links are not used (vacuum, rigid-link, and articulated jib crane manipulators can all use vacuum gripper end-effectors)

11. Industrial robot

Used in positioning to provide variable programmed motions of loads

“Intelligent” industrial robots utilize sensory information for complex control actions, as opposed to simple repetitive “pick-and-place” motions

Industrial robots also used for parts fabrication, inspection, and assembly tasks

Consists of a chain of several rigid links connected in series by revolute or prismatic joints with one end of the chain attached to a supporting base and the other end free and equipped with an end-effector

Robot’s end-effector can be equipped with mechanical grippers, vacuum grippers, electromechanical grippers, welding heads, paint spray heads, or any other tooling

Although similar in construction, an industrial robot is distinguished from a manipulator by the use of programmed control logic as opposed manual control

Pick-and-place industrial robots can be used as automatic palletizers

Mobile robots similar in construction to free-ranging AGVs

Can be powered manually, electrically, or pneumatically ____________________________________________________________________________________________________________________________________________________________

5. MATERIAL HANDLING ECTURE NOT

1. Chute conveyor

Unit/Bulk + On-Floor + Accumulate

Inexpensive

Used to link two handling devices

Used to provide accumulation in shipping areas

Used to convey items between floors

Difficult to control position of the items

L ES FOR FACILITIES DESIGN

110

5.5 Conveyors Conveyors are used:

• When material is to be moved frequently between specific points

• To move materials over a fixed path

• When there is a sufficient flow volume to justify the fixed conveyor investment

Conveyors can be classified in different ways:

• Type of product being handled: unit load or bulk load

• Location of the conveyor: in-floor, on-floor, or overhead

• Whether loads can accumulate on the conveyor or no accumulation is possible

Table 5.7. Conveyors

1. Chute conveyor 2. Wheel conveyor 3. Roller conveyor (a) Gravity roller conveyor (b) Live (powered) roller conveyor 4. Chain conveyor 5. Slat conveyor 6. Flat belt conveyor 7. Magnetic belt conveyor 8. Troughed belt conveyor 9. Bucket conveyor 10. Vibrating conveyor 11. Screw conveyor 12. Pneumatic conveyor (a) Dilute-phase pneumatic conveyor (b) Carrier-system pneumatic conveyor

13. Vertical conveyor (a) Vertical lift conveyor (b) Reciprocating vertical conveyor 14. Cart-on-track conveyor 15. Tow conveyor 16. Trolley conveyor 17. Power-and-free conveyor 18. Monorail 19. Sortation conveyor (a) Diverters (b) Pop-up devices (c) Sliding shoe device (d) Tilting device (e) Cross-belt transfer device

20.

SPRING 2003 5. CONVEYO5. RS

111

2. Wheel conveyor

Unit + On-Floor + Accumulate

Uses a series of skatewheels mounted on a shaft (or axle)

Spacing of the wheels is dependent on the load being transported

Slope for gravity movement depends on load weight

More economical than the roller conveyor

For light-duty applications

Flexible, expandable mobile versions available

Mobile

3. Roller conveyor

Unit + On-Floor + Accumulate

May be powered (or live) or nonpowered (or gravity)

Materials must have a rigid riding surface

Minimum of three rollers must support smallest loads at all times

Tapered rollers on curves used to maintain load orientation

Parallel roller configuration can be used as a (roller) pallet conveyor (more flexible than a chain pallet conveyor because rollers can be used to accommodate are greater variation of pallet widths)

3(a) Gravity roller conveyor

Alternative to wheel conveyor

For heavy-duty applications

Slope (i.e., decline) for gravity movement depends on load weight

For accumulating loads

3(b) Live (powered) roller conveyor

Belt or chain driven

Force-sensitive transmission can be used to disengage rollers for accumulation

For accumulating loads and merging/sorting operations

Provides limited incline movement capabilities

5. MATERIAL HANDLING L ES FOR FACILITIES DESIGNECTURE NOT

112

4. Chain conveyor

Unit + In-/On-Floor + No Accumulation

Uses one or more endless chains on which loads are carried directly

Parallel chain configuration used as (chain) pallet conveyor or as a pop-up device for sortation (see Sortation conveyor: Pop-up devices)

Vertical chain conveyor used for continuous high-frequency vertical transfers, where material on horizontal platforms attached to chain link (cf. vertical conveyor used for low-frequency intermittent transfers)

5. Slat conveyor

Unit + In-/On-Floor + No Accumulation

Uses discretely spaced slats connected to a chain

Unit being transported retains its position (like a belt conveyor)

Orientation and placement of the load is controlled

Used for heavy loads or loads that might damage a belt

Bottling and canning plants use flat chain or slat conveyors because of wet conditions, temperature, and cleanliness requirements

Tilt slat conveyor used for sortation

6. Flat belt conveyor

Unit + On-Floor + No Accumulation

For transporting light- and medium-weight loads between operations, departments, levels, and buildings

When an incline or decline is required

Provides considerable control over the orientation and placement of load

No smooth accumulation, merging, and sorting on the belt

The belt is roller or slider bed supported; the slider bed is used for small and irregularly shaped items

In 1957, B.F. Goodrich, Co. patented the Möbius strip for conveying hot or abrasive substances in order to have “both” sides wear equally [M. Gardner, New Math. Diversions]

SPRING 2003 5. CONVEYORS

and unloading, and can include v55, n12, 2000, p. 35]

5.

113

ments are available for trailer loadinginto the trailer [MMH,

B

bed or a magnetic pulley is

To transport ferrous materials vertically, upside down, and around

Telescopic boom attachventilation to pump conditioned air

7. Magnetic belt conveyor

ulk + On-Floor

A steel belt and either a magnetic sliderused

corners

8. Troughed belt conveyor

ulk + On-Floor B

When loaded, the belt conforms to the shape of the troughed rollers

Used to transport bulk materials

and idlers

Bulk + On-Floor

B

Buckets are automatically un

10. Vibrating conveyor

Bulk + On-Floor

Consists of a trough, bed, or tube

Vibrates at a relatively high frequency and small amplitude in order to convey individual units of

9. Bucket conveyor

Used to move bulk materials in a vertical or inclined path

uckets are attached to a cable, chain, or belt

loaded at the end of the conveyor run

5. MATERIAL HANDLING L NOTES FOR

ates at a lower frequency and larger

ECTURE FACILITIES DESIGN

114

terial

vey almost all granular, free-flowing materials

rlarger objects such as hot castings

Bulk + On-Floor

Consists of a tube or U-shaped stationary trough through which a shaft-mounted helix revolves to push loose material forward in a horizontal or inclined direction

ne of the most widely used conveyors in the processing industry, with many applications in al processing

conveyor sometimes referred to as an “auger feed”

C by Archimedes

products or bulk ma

Can be used to con

An Oscillating Conveyor is similar in construction, but vibamplitude (not as gentle) in order to convey

11. Screw conveyor

Oagricultural and chemic

Straight-tube screw

Water screw developed circa 250 B

12. Pneumatic conveyor

ulk/Unit + Overhead B

M es

12(a) Dilute-phase pneumatic conveyor

Moves a mixture of air and solid

Push (positive pressure) systems push material from one entry point to several discharge points

) systems move material from ints to one discharge point

ions with multiple entry and

Can be used for both bulk and unit movement of materials

Air pressure is used to convey materials through a system of vertical and horizontal tubes

aterial is completely enclosed and it is easy to implement turns and vertical mov

Pull (negative pressure or vacuumseveral entry po

Push-pull systems are combinatdischarge points

SPRING 2003 5.5. CONVEYORS

12(b) Carrier-system pneumatic conveyor

Carriers are used to transport items or paperwork

ks and Examples: transporting money to/from drive-in stalls at bandocuments between floors of a skyscraper

. Vertical conveyor 13

U ransfers (cf.

vertical transfers

13(a) Vertical lift conveyor

Carrier used to raise or lower a load to different levels of

Differs from a freight elevator in that it is not designed or certified to carry people

Can be manually or automatically loaded and/or controlled and can interface with horizontal conveyors

Unit + On-Floor + No Accumulation

sed for low-frequency intermittent vertical tvertical chain conveyor can be used for continuous high-frequency

a facility (e.g., different floors and/or mezzanines)

1

Utilizes gravity-actuatethe load overcomes the magnitude o

Can only be used to lower a load

lternative to a chute conveyor for vertical “drops” whload is fragile and/or space is limited

Can be manually or automaticcontrolled and can interface with horizontal conveyors

3(b) Reciprocating vertical conveyor

d carrier to lowering loads, where f a counterweight

A en

ally loaded and/or

115


116

U

tube

arying angle of

C

Accumulation can be achieved by maintaining the drive wheel parallel to the tube

14. Cart-on-track conveyor

Unit + In-Floor + Accumulate

sed to transport carts along a track

Carts are transported by a rotating

Drive wheel connected to each cart rests on tube and is used to vary the speed of the cart (by vcontact between drive wheel and the tube)

arts are independently controlled

15. Tow conveyor

nit + In-Floor + Accumulate

to wheeled carriers such as trucks, dollies, or carts that move along the floor

Used for fixed-path travel of carriers (each has variable from towline)

e can be located

Se tomatic switching (power or spur lines)

Generally used when long distance and high frequency moves are required

U

Uses towline to provide power

path capabilities when disengaged

Although usually in the floor, the towlinoverhead or flush with the floor

lector-pin or pusher-dog arrangements used to allow au

16. Trolley conveyor

Unit + Overhead + No Accumulation

Uses a series of trolleys supported from or within an

Does not provide for accumulation

Commonly used in processing, assembly, packaging, and storage operations

overhead track

Trolleys are equally spaced in a closed loop path and are suspended from a chain

Carriers are used to carry multiple units of product

SPRING 2003 5. CONVEYORS5.

117

nveyor

ransported by an overhead chain;

r nonpowered (or free)

d lated or switched onto spurs

Inverted Power-and-Free Conveyor when

17. Power-and-free co

Unit + Overhead/On-Floor + Accumulate

Similar to trolley conveyor due to use of discretely spaced carriers thowever, power-and-free conveyor uses two tracks: one powered and the othe

Carriers can be disengaged from the power chain anaccumu

Termed an tracks are located on the floor

8. Monorail

ack network on which one or more carriers ride

C

C

Si ilar to bridge

M rail similar to both a trolley conveyor, except that the carriers operate

y and the track need not be in a closed loop, and a fixed-path automatic guided vehicle (AGV) system, except that it operates overhead

(AEM) system when it has similar control

1

Unit + Overhead + Accumulate

Overhead single track (i.e., mono-rail) or tr

arriers: powered (electrically or pneumatically) or nonpowered

arrier can range from a simple hook to a hoist to anintelligent-vehicle-like device

ngle-carrier, single-track monorail simor gantry crane

ulti-carrier, track network mono

independentl

Termed an Automated Electrified Monorailcharacteristics as an AGV system


19. Sortation conveyor

nit + On-Floor/Overhead U

ts to be Sortation conveyors are used for merging, identifying, inducting, and separating producconveyed to specific destinations

Typical sortation system

19(a) Sortation conveyor: Diverters

Stationary or movable arms that deflect, push, or pull a product to desired destination

Since they do not come in contact with the conveyor, they can be used with almost any flat surface conveyor

Usually hydraulically or pneumatically operated, but also can be motor driven

Simple and low cost

Deflector diverter Push diverter

19(b) Sortation conveyor: Pop-up devices

One or more rows of powered rollers or wheels or chains that pop up above surface of conveyor to lift product and guide it off conveyor at an angle; wheels are lowered when products not required to be diverted

Only capable of sorting flat-bottomed items

118

SPRING 2003 5.5. CONVEYORS

Pop-up rollers (not shown) are generally faster than pop-up wheels

Pop-up wheel device

Pop-up chain device

19(c) Sortation conveyor: Sliding shoe sorter

Sliding shoe sorter (a.k.a. moving slat sorter) uses series of diverter slats that slide across the horizontal surface to engage product and guide it off convey

o either side

Gentle and gradual handling of products

or

Slats move from side to side as product flows in order to divert the product t

119

( ) S i i i i

5. MATERIAL HANDLING

Either continuous loop, wherlinked together to form an (asynchronous), where a small numtogether with potential for several tr

LECTURE NOTES FOR F

e individual carriages are endless loop, or train style

ber of carriers tied ains running track

ACILITIES DESIGN

120

simultaneously

Each carriage equipped with small belt conveyor, called the cell, that is mounted perpendicular to direction of travel of loop and discharges product at appropriate destina

Automatically separates single line of products into multiple in-line discharge lines

19(e) Sortation conveyor: Cross-belt transfer device

tion

G

tal

nt than conv

• Provide less flexibility in movement than industrial trucks

• Loads handled are more varied with respect to their shape and weight than those handled by a conveyor

• Most cranes utilize hoists for vertical movement, although manipulators can be used if precise positioning of the load is required

5.6 Cranes eneral characteristics of cranes:

• Used to move loads over variable (horizon and vertical) paths within a restricted area

volume such that the use of a

eyors

• Used when there is insufficient (or intermittent) flowconveyor cannot be justified

• Provide more flexibility in moveme

SPRING 2003 5. CRANES6.

121

Table 5.8. Cranes

1. Jib crane 2. Bridge crane

3. Gantry crane 4. Stacker crane

1. Jib crane

Horizontal boom (jib) supported from a stationary vertical support

Hoist can move along the jib and can be used for lifting

Operates like an arm in a work area, where it can function as ks

r

a manipulator for positioning tas

Jib can also be mounted on the wall

A m can rotate up to 360° 2. Bridge crane

Bridge mounted on tracks that are located on opposite w

Top riding (heavier loads) or underhung (more v

Underhung crane can transfer loads and interface with other MHS (e.g., monorail systems)

alls of the facility

Enables three-dimensional handling

ersatile) versions of the crane

3. Gantry crane

Single leg, double leg, and mobile types of gantry cranes

Similar to a bridge crane except that it is floor supported at one or both ends instead of overhead (wall) supported

Used to span a smaller portion of the work area as compared to a bridge crane


4. Stacker crane

milar to ait uses a mast with forks or a platform to handle unit loads

onsidered “fork trucks on a rail”

Used for storing and retrieving unit loracks, especially in high-

Can be controlledon the mast

5.7 Industrial Trucks el on public roads—“commercial trucks”

ar dustrial trucks are:

e materials over variable (horizontal) paths with no restrictions on the area , unrestricted area)

pabilities

ot be justified

Industrial trucks are trucks that are not licensed to trave licensed to travel on public roads. In

• Used to movcovered (i.e.

• Provide vertical movement if the truck has lifting ca

• Used when there is insufficient (or intermittent) flow volume such that the use of a conveyor cann

• Provide more flexibility in movement than conveyors and cranes

122

The supports can be fixed in position or they can travel on runways

oors when “fCan be used outd loor” supported at both ends

Double-leg gantry

Single-leg gantry Mobile gantry

Si bridge crane except that, instead of a hoist,

C

ads in storage rise applications in which

the racks are more than 50 feet high

remotely or by an operator in a cab

Can be rack supported

SPRING 2003 5.7. INDUSTRIAL TRUCKS

1. Pallet/Non-Pallet

Non-Pallet ⇒

2. Manual/Powered:horizontal (travel) m

Manual ⇒ walk ⇒ the vehicle

123

Powered ⇒ on-board power source (e.g., batteries) used for lifting and/or travel

3. Walk/Ride: For non-automated trucks, can the operator ride on the truck (in either a standing or sitting position) or is the operator required to walk with the truck during travel.

R d ⇒ travel speed can be faster than a walk

Walk ⇒ manual or powered travel possible ⇒ powered travel speed limited to a normal

for stacking purposes.

xpensive to add stacking capability

No Stack may lift a load a few inches to clear the floor for subsequent travel (e.g., pallet stacked on top of each other or on shelves

a small turning radius or does it not have to

Narrow Aisle ⇒ greater cost and (usually) standing operator ⇒ less aisle space required

alance and/or straddle used for load support

us ⇒ load support via straddle or reaching capabilities

No turning required ⇒ even narrower aisle ⇒ only one-side loading (sideloaders) or the capability to rotate the load (turret truck)

6. Automated: Is the truck au ds without requiring an

far the largest cost to operate a non-

sed to control loading/unloading, but automated transport

her

Characteristics: : Does the truck have forks for handli

(usually) other means required to load truck

Does the truck have manual or powovement capabilities.

operator provides the force needed

ng pallets, or does the truck have a

ered vertical (lifting) and/or

for lifting loads and/or pushing

flat surface on which to place loads.

ide ⇒ powere ing pace

walking pace

4. Stack/No Stack: Can the truck be used to lift loads

Stack ⇒ can also be used as no stack ⇒ more e

jack), but the loads cannot be

5. Narrow Aisle: Is the lift truck designed to have turn at all in an aisle when loading/unloading.

Counterb

Small turning radi

tomated so that it can transport loaoperator.

Non-Automated ⇒ direct labor cost of operator is byautomated truck

Semi-Automated ⇒ operator ucontrol (e.g., the S/R machine of a Man-on-board AS/RS)

Automated ⇒ Automated Guided Vehicle (AGV) ⇒ no direct labor cost, but higequipment costs


Table 5.9. Industrial Trucks

1. Hand truck (a) Two-wheeled hand truck

7. Narrow-aisle straddle truck

2. (a) Manual pallet jack

3.

5.

6. ck (a) Sit-down counterbalanced lift truck

8. Narrow-aisle reach truck

(b) Operator-up turret truck 10. Order picker

12. Tractor-trailer

(e) Fork AGV

(b) Dolly 9. Turret truck (c) Floor hand truck

Pallet jack (a) Operator-down turret truck

(b) Powered pallet jack Walkie stacker

11. Sideloader

(a) Manual walkie stacker 13. Personnel and burden carrier (b) Powered walkie stacker 4. Pallet truck

Platform truck

14. Automatic guided vehicle (AGV) (a) Tow AGV (b) Unit load AGV

(a) Walkie platform truck (c) Assembly AGV (b) Rider platform truck

Counterbalanced lift tru (d) Light load AGV

(b) Stand-up counterbalanced lift truck

1. Hand truck

Pallet + Manual + No Stack Non-

1(a) T

st

Simplest type of industrial truck

wo-wheeled hand truck

Load tilted during travel

Good for moving a load up or down airways

1(b) Dolly

or more wheeled hand truck with a flat plThree atform in which, since it has no handles, the load is used for pushing

1(c) Floor hand truck

with handles for pushing or

Some

Four or more wheeled hand truck

hitches for pulling

times referred to as a “cart” or Tilt floor hand truck

“(manual) platform truck” Wire floor hand truck

124


2. Pallet jack

Pallet + Walk + No Stack

d inside the e floor as the pallet is only for vel

reversible pallets cannot be use , doubwheels extendallet because

ck

/or travel

Front wheels are mounte rks and extend to thlifted enough to clear the floor ra

Pallet restrictions: d le-faced nonreversible pahave deckboards where the front to the floor, and eninto a four-way notched-stringer p the forks cannot b

2(a) Manual pallet ja

Pallet + Walk + No Stack + Manual

Manual lifting and

2(b) Powered pallet jack

P Walk + No Stack + Powered

end of the fo subsequent t

llets cannot ables only two-way entry

e inserted into the notches

Powered lifting

Powered pallet jack is sometimes truck”

3. Walkie stacker

Pallet + Walk + Stack

milar to a cSi ounterbalanced lift truck except the operator cannot ride on the truck

l walkie stacker

M

3(a) Manua

Pallet + Walk + Stack + Manual

anual lifting and/or travel (and straddle load support)

allet +

and/or travel

referred to as a “(walkie) pallet

125


3(b) Powered walkie stacker

wered Pallet + Walk + Stack + Po

Powered lifting and/or travel (and either counterbalance or straddle load support)

Same pallet restrictions as a pallet jack

Control handle typically tilts to allow operator to walk during loading/unloading

times referred to as a “(walkie)

4. Pallet truck

Pallet + Ride + No Stack

Powered pallet jack is somepallet truck”

Used for skid handl

Greater lifting capacitysurface to support a l

5(a) Walkie platform truck

Non-Pallet + Powered + No St

Operator walks next to truck

Floor hand truck is sometimes referred to as a “(manual

5. Platform truck

Non-Pallet + Powered + No Stack

Platform used to provide support for nonpalletized loads

ing; platform can lift skid several inches to allow it to clear the floor

compared to fork trucks because the platform provides a greater lifting oad

ack + Walk

) platform truck”

5(b) Rider platform truck

Non-Pallet + Powered + No Stack + Ride

Operator can ride on truck

126

SPRING 2003 5. INDUSTRIAL T

s forks can be used)

counterbalances weight of th

7.

127

ruck

Weight of vehicle (and operator) behind the front wheels of truck load (and weight of vehicle beyond front wheels); front wheels act as fu

Rated capacity reduced for load centers greater than 24 in. and lift heigh

Workhorses of material handling because of their flexibility: indoor/variety of different surfaces; variety of load capacities available; and v

clamps) or enhance the capabilities of the forks (e.g., blad

6(a) Sit-down counterbalanced

12–13 ft. minimum aisle width

RUCKS

6. Counterbalanced (CB) lift t

Pallet + Ride + Stack

Sometimes referred to as a “fork truck” (but other attachments beside

e lcrum or pivot point

ts greater than 13 ft.

outdoor operation over a ariety of attachments

available—fork attachments can replace the forks (e.g., cartones for slipsheets)

lift truck

Operator sits down

requirement

6(b) Stand-up counterbalanced lift truck

Operator stands up, giving vehicle narrow-aisle capability

9–11 ft. minimum aisle width requirement

Faster loading/unloading time compared to NA straddle and reach trucks

7. Narrow-aisle (NA) stradd

Similar to stand-up CB lift truck, except ouare used to support the load instead of the

7–8 ft. minimum aisle width r

Less expensive than stand-up CB lift truck and NA reach truck

be provided for the outrigg

Arm clearance typically provided throughstorage or single-wing pa

le truck

trigger arms straddle a load and counterbalance of the truck

equirement

Since the load is straddled during stacking, clearance between loads must er arms

the use of load-on-beam rack llets for load-on-floor storage

5. MATERIAL HANDLING ECTURE

k and NA straddle truck

L ES FOR FACILITIES DESIGNNOT

128

CB lift truc

C

ires slightly wider aisles thoutrigger arms do not enter a rack during storage, it does not require arm

ce is still required when the truck must enter a storstacking or drive-in or -through racks are used)

le to enable deep-reach storage

8. Narrow-aisle (NA) reach truck

Similar to both stand-up


Load rests on the outrigger arms during transport, but a pantograph (scissors) mechanism is used for reaching, thereby eliminating the need to straddle the load during stacking

Reaching capability enables the use of shorter outrigger arms (arms > ½ load depth) as compared to NA straddle truck (arms = load depth)

ounterbalance of the truck used to support the load when it extends beyond the outrigger arms

Although the NA reach truck requ an a NA straddle truck since its clearance between

age lane when block loads (arm clearan

Extended reaching mechanisms are availab

9. Turret truck

Greater stacking height compared to other narrow-aisle trucks (40 ft. vs. 25 ft

does not rotate during stacking, the e its counterbalance capability and to allow the

an function like a sideloader for transporting greater-than-pallet-size load

.), but greater investment cost

Forks rotate to allow for side loading and, since truck itself body of the truck can be longer to increasoperator to sit

C

9(a) Operator-down turret truck

Operator not lifted with the load


Termed a swingmast truck when, instead of just the forks, the entire mast rotates (thus can store on only one side of a aisle while in aisle)

SPRING 2003 5. INDUSTRIAL TRUCKS7.

129

king

9(b) Operator-up turret truck

Operator lifted with the load to allow precise stacking and pic


S

and to support a pallet during less-than-pallet-load picking

ed for operator safety during picking

10. Order picker

imilar to NA straddle truck, except operator lifted with the load to allow for less-than-unit-load picking

Typically has forks to allow the truck to be used for pallet stacking

“Belly switch” us

. Sideloader

orks mounted pside loading and straddle load support

5–6 ft. minimum aisle width require

Can be used to handle greater-thastock)

11

F erpendicular to direction of travel to allow for

ment

n-pallet-size loads (e.g., bar

12. Tractor-trailer

Non-load-carrying tractor used to pull a train of trailers (i.e., dollies or floor hand trucks)

Advantage: Enables a single operator to transport multiple floor hand trucks in a single move

Disadvantage: Requires wide aisles or open spaces to operate

Tractor sometimes termed a “tugger”


130

Non-load-carrying vehicle used to transport personnel within a facility (e.g., golf cart, bicycle, etc.)

Manual version of a tow AGV

Typically used at airports for baggage handling

13. Personnel and burden carrier

Good for high labo

Also termed “automated guided vehicle”

GVs good for low-to-medium volume operations (e.g., transport between work cells in a flexible manufaenvironment)

Two means of guidance can be used for AGV systems:

14(a) Tow AGV

Used to pull a train of trailers

utomated version of a tractor trailer

Trailers usually loaded manually (early typnot much used today)

14(b) Unit load AGV

be loaded manually or automatically

sm for automatic

ds

Typically less than 10 vehicles in AGV system

Have decks that can

Deck can include conveyor or lift/lower mechaniloading

Typically 4 by 4 feet and can carry 1–2,000 lb. loa

14. Automatic guided vehicle (AGV)

AGVs do not require an operator

r cost, hazardous, or environmentally sensitive conditions (e.g., clean-room)

A medium-to-long distance random material flow cturing system (FMS)

Fixed path: Physical guidepath (e.g., wire, tape, paint) on the floor used for guidance

Free-ranging: No physical guidepath, thus easier to change vehicle path (in software), but absolute position estimates (from, e.g., lasers) are needed to correct dead-reckoning error

A

e of AGV,


131

gines, appliances)

the 1980s (alternative

T

14(c) Assembly AGV

Used as assembly platforms (e.g., car chassis, en

Greatest development activity duringto AEMs)

ypically 50–100 vehicles in AGV system

14(d) Light load AGV

Used for small loads (< 500 lbs.), e.g., components, tools

Typically used in electronics assembly and office environments (as mail and snack carriers)

14

Counterbalanced, narrow-aisle straddle, and sideloading

(e) Fork AGV

versions available

Typically have sensors on forks (e.g., infrared sensors) for pallet interfacing

• Varie

truck counterbalances the weight of the load (and the weight of the vehicle beyond the front

5.7.1 Counterbalanced Lift Trucks Counterbalanced lift trucks (a.k.a. fork trucks) are the workhorses of material handling because of their flexibility:

• Indoor/outdoor operation over a variety of different surfaces

• Variety of load capacities available

ty of attachments available; for example, fork attachments can replace the forks (e.g., carton clamps) or enhance the capabilities of the forks (e.g., blades for slipsheets)

Principle of Operation: the weight of the vehicle (and operator) behind the front wheels of the

wheels); the front wheels of the truck act as a fulcrum or pivot point (see Figure 5.8(a)).


ve degrees of freedom (DOF) in its

132

any as fimovement (see Figure 5.8):

l translation (drive wheels).

lift (forks along mast).

ding and backward tilt fo

5. Fork translation (to handle different size loads).

ce of th height of up to 13 ft; attachments and loads with a center of grav

Degrees of Freedom: a lift truck can have as m

1. Horizonta

2. Horizontal rotation (turning wheels).

3. Vertical

4. Mast tilt (forward tilt for loading/unloa r travel).

rated load capacity is specified e forks of the trucks and a lift

ter than 24 inches reduce

Rated Load Capacity: 1,000–100,000 lbs available; a truck’s assuming a standard load center of 24 inches from the fa

ity grea a 3,000 lb lift truck. the load capacity of the truck. Figure 5.9 shows the specification sheet for

Load Capacity: A truck’s approximate allowable load capacity W (see Figure 5.8(a)) is given by

Figure 5.8. Sit-down counterbalanced lift truck.

( )0 00 W F LGB M += = =

+ + +, (5.1) Load capacity: W

F L F L F L

e wher

F = front-axle to fork-face distance (in.)

G = empty truck weight (lbs)

B = front-axle to truck-load-center distance (in.)


L0 = 24 in. = standard load center

L = actual load center, distance from fork face to load center of gravity (in.)

= ULD if constant-density rectangular-shaped load

specify a truck’s rated load moment (M0),

2

M0 = rated load moment (in·lbs)

W0 = rated load capacity (lbs).

Although it might seem preferable, in light of (5.1), toits W0 is specified instead because it is easier to relate to the truck’s maximum allowable load weight.

Two different adjustments can be made with respect to the load capacity of the truck:

• Derating — determing the maximum permissible load weight given that the load’s center of gravity exceeds the standard load center (L0 = 24 in.).

• Rerating — modifying the truck’s rated load capacity due to changes to the truck; e.g., adding extra counterbalance weight, a fork attachment, or an extended mast.

Derating Example: Assuming a constant density rectangular-shaped load, ULD = 60, F = 12, and W0 = 3,000 lbs, the derated load capacity is reduced to

( ) ( )0 0 3,000 12 24 108,000 2,57160 42122

W F LW

F L+ +

= = = =+ +

lbs.

Rerating Example: Assuming F = 12 and W0 = 3,000 lbs, if a 500 lb. counterbalance weight isattached to the back of the truck at a distance of 72 in. from the front axle, then the new rated load capacity of the truck is

0 00

500 72 500 723,000 3,000 1,000 4,00012 24

W WF L

⋅ ⋅′ = + = + = + =+ +

lbs.

Lift Height: up to 40 feet using single-, double-, triple-, and quad-stage masts; for multiple-stage trucks, the free lift is the length of fork movement before the mast starts to move (important when traveling through d

(M0) should be reduced by 4,800 in·lbs for ev

ower Sources: detertruck (i.e., how steep an incline the truck can climb).

mbustion Engine: gradability of 15%

ore

oorways and inside trailers).

In determining a truck’s approximate allowable load capacity using (5.1), its rated load moment ery foot of lift greater than 13 ft.

ck can operate (inside/outside) anP mines where tru d the gradability of the

1. Internal Co

(a) Gasoline—no one makes anym

(b) Diesel—only for outside operation

133


(c) Liquid Petroleum Gas (LPG)—outside and ventilated inside operation (80% of

1. Electric Motor: gradability of 10%

(a) Battery Powered—inside operation; requires battery recharge station

the truck can operate over

ain)

rk the height of shelves

e used)

(c) Rotators—

(d) Push/Pull—

used together with Push/Pull for slipsheet handling

(b)

Replacem

6. Trailer Hitch

7. Radio/RF Data Modem—for communication with the truck operator

8. Extra Counter Balance—to increase the load capacity of the truck

9. TV—mounted between the forks

trucks)

Tires: determines what type of terrain

1. Pneumatic—outside (rough terr

2. Cushion—inside and outside (smooth terrain)

3. Solid—inside

Attachments: determines the functionality of the truck

1. Mast: attachments to the mask of the truck

(a) Shelf Guides—e.g., masking tape on the mast to ma

2. Carriage: attachments to the carriage that moves on the mask

(a) Sideshifter—shifts the forks without repositioning the truck

(b) Fork Positioner (spreader)—each fork can move independently (aids load stabilization when a variety of pallet sizes ar

mps enable dumping of a load when used with barrel cla

grips/pushes/pulls slipsheet (used together with blades)

5. Forks: attachment can be either an enhancement or replacement for the forks

Enhancements:

(a) Blades (platens)—

Length—shorten, lengthen, or extendable

ents:

(a) Blades for slipsheets—can replace forks for slipsheet handling

(b) Clamps—carton, bale, roll, or barrel

(c) Ram—used for coils

(d) Shovel

(e) Block Forks—more than two forks for handling nonpalletized loads (e.g., bricks)

134


Figure 5.9. Specification sheet for the Caterpillar Model EC15 3000 lb. lift truck

ument No. CECB0162 1/93, 1993). (Caterpillar, Doc

135


5.7.2 Narrow-Aisle Lift Trucks Narrow-aisle lift trucks are designed to have a small turning radius when loading/unloading in an aisle or, in the case of turret trucks and sideloaders, not to have to turn at all. The major types of narrow-aisle trucks listed in Table 5.9 are the following:

6(a). Stand-up counterbalanced (CB) lift truck

7. Narrow-aisle (NA) straddle truck

8. Narrow-aisle (NA) reach truck

9. Turret truck

10. Order picker (less-than-unit load)

11. Sideloader

Except for order pickers, all the trucks handle unit loads. Three closely related narrow-aisle trucks are compared in Figure 5.10.

9 - 11 ft 7 - 8 ft 8 - 10 ft

Stand-Up CB NA Straddle NA Reach Figure 5.10. Narrow-aisle lift truck comparison.

136


5.7.3 Automatic (or Automated) Guided Vehicle (AGV) Systems

ing and loading capabilities at each pickup and

uidepath (e.g., wire, tape, paint) on the floor used for guidance

cannot pass each other on a path (typically

AGVs good for low-to-medium volume medium-to-long distance random material flow operations (e.g., transport between work cells in a flexible manufacturing system (FMS) environment).

In a FMS, AGVs usually have automatic dockdelivery (P/D) station.

First AGVs appeared in the 1950s.

Guidance

Fixed-Path • A physical g

• Changing the guidepath can be expensive

• Can have congestion problems because vehiclesuse one-way paths to reduce congestion)

• Can be considered “on-the-floor” version of an AEM (automated electrified monorail)

Free-Ranging • No physical guidepath used ⇒ easier to change vehicle path (in software)

• Can maneuver to avoid congestion

• Dead-reckoning (e.g., odometers), laser, and/or optical sensors used for guidance

• Position error increases over time using just dead reckoning, so most free-ranging vehicles use some type of other sensor to obtain estimates of absolute position to correct dead-reckoning error

• RF (radio frequency) or infrared modems typically used for communication

137


5.8 MH Equipment Selection Given the material flow requirements for one or moves, MHS alternatives can be determined by

e classification level from which the MH equipment is selected:

ipment, e.g., conveyors, cranes, industrial trucks, positioning equipment

Intermediate Level—equipment types within categories, e.g., chute or roller conveyors, ck or pallet truck industrial trucks

del X diesel-ated lift capacity of 5,000 lbs.

startin umber of possible choices enough; starting from s of

selecting appropriate MH equipment that, in some way, “satisfies” the requirements.

An important issue is th

• High Level—categories of equ

•pallet ja

• Low Level—equipment models within an equipment type, e.g., an Acme Mopowered counterbalanced lift truck with a r

Selection Problem: Starting from a low level can result in too many possible choices, while g from a high level does not narrow the n

the intermediate level reduces the selection problem to choosing from 15–50 possible typeMH equipment.

Figure 5.11. MHE selection.

The process of MH equipment selection can be decomposed into two stages (see Figure 5.11):

1. Determine Technical Feasibility—select MH equipment types that can satisfy the material flow requirements from a technological perspective;

e.g., a pallet jack is not technically feasible for stacking pallets onto storage racks

2. Determine Economic Feasibility—from among the technically feasible equipment types, select the equipment type that is most cost effective given the material handling requirements;

138


e.g., while both a pallet jack and pallet truck are technically feasible for long-distance moves, the pallet truck, while costing more initially, would be more cost effective because it can travel faster due the operator’s ability to ride on the truck

5.9 Problems .1. With respect to the scope of material handling, what are some of the differences and

similaritie5

s between industrial logistics and material handling?

5 an

5

two factors that should be considered when determining the unit load size for in-process handling.

.2. Can material handling add value to a product? Explain your answer (good arguments cbe made for or against).

.3. Under what circumstances would the minimization of material handling system cost not be appropriate as the sole criterion with which to select a system design?

5.4. State and briefly describe one of the Principles of Material Handling.

5.5. Describe

5.6. Describe one advantage and one disadvantage of unit loads.

5.7. Why should the size of a unit load not be larger than the production batch (or lot) size?

5.8. Describe, with respect to the four design features, the pallet shown below

5.9. Describe one advantage and single-face pallet as compared

5

5.1 le pallet

5.12 advantage and one disadvantage of using a pick-and-place palletizer as opposed to a stripper-plate palletizer. Which is more likely to be used for the Distributor’s Pallet Loading Problem?

one disadvantage of using ato a double-face pallet of the same dimensions.

.10. Describe one advantage and one disadvantage of using a slipsheet as opposed to a pallet to support a unit load.

1. Describe one advantage of using a nonreversible pallet as compared to a reversibof the same dimensions.

. Describe one

139


3. Why would one typically be willing to spend more time and effort to find a good soluto the Manufacturer’s Pallet Loading Problem as compared to the Distributor’s Problem?

5.1 tion

5.14. Identify each of the five different types of material handling equipment shown below.

List five different types of bulk handling conveyors. 5.15.

5 r is located overhead, on-floor, or in-floor: Towline, Inverted Power-and-Free, Trolley, Roller, and

5.17. Describe one advantage and one disadvantage of using a power-and-free conveyor as

5

5 lic is very likely to have used when visiting a bank.

5.20. Given two operations with random es, explain an advantage or disadvantage of using a flat belt conveyor as opposed to a roller conveyor to connect the operations.

5 to a process layout.

5.23. Describe why, as compared to a pallet jack or counterbalanced lift truck, a walkie stacker

from a loading dock to pallet racks.

a

.16. For each of the following types of conveyors, list whether the conveyo

Pneumatic.

opposed to a monorail to transport material.

.18. Explain two differences between a trolley conveyor and a monorail.

.19. Describe one example of a pneumatic conveyor carrier system that the pub

processing tim

.21. Explain why it is more likely that conveyors would be appropriate for inter-machine material handling in a product layout as opposed

5.22. Describe a principal difference between a pallet jack and a pallet truck.

is likely to be the most economical and/or technically feasible for infrequent, short-distance moves of pallets

5.24. Describe one advantage and one disadvantage of using a NA reach truck as opposed tostand-up CB lift truck.

140

SPRING 2003 5. PROBLEMS

k while transporting loads?

e rated lo

s of material handling equipm

The use of narrow-aisle lift trucks demmaterial handling?

Describe two things that will reduce thtruck.

List two different typebundles of 20-foot-long bar stock within

onstrates the application of which principle of

ad capacity of

ent that are suitable fo

9.

141

operator to ride on the truc

5.27.

5.28. a counterbalanced lift

5.29. r moving a facility with narrow aisles.

conomical for facilities located in high labor cost areas?

5.31. a loading dock to pallet racks?

the llets are to be used, what is maximum

uniform density load weight that the truck can handle?

5.33. Although the rated load capacity of a lift truck is 2,500 lbs, a 750 lb counterbalance ce

. and the distance from the front axle to the back of the truck is 6 ft, what is the truck’s load capacity with the extra counterbalance?

5.34. he truck operator, Jim, weighs at least 450 lbs and likes to remain seated on

the truck throughout an entire shift, even when not handling material (i.e., Jim doesn’t do d

nder the seat of the truck) is 48 in., what is the actual rated load capacity of the truck when Jim’s

load capacity

lbs, has uniform density, and is 12 in. wide (so that, with the attachment, the distance from the front axle to the front of the attachment will be 24 in.).

5.25. Describe one advantage and one disadvantage of using a stacker crane as opposed to a sideloader.

5.26. What type of industrial truck cannot handle pallets or stack loads, but does allow the

5.30. What type of industrial truck is likely to be the most e

What type of industrial truck is likely to be the most economical for infrequent, short-distance moves of pallets from

5.32. The rated load capacity of a lift truck is 2500 lbs. If the distance from the front axle to fork face is 18 in. and 52 × 42 in. two-way pa

weight will be placed at the back of the truck to increase its load capacity. If the distanfrom the front axle to the fork face is 15 in

Although the rated load capacity of the lift truck used at the shipping dock of Sumo, Ltd. is 2500 lbs, t

other productive work). If the distance from the front axle to the fork face is 18 in. anthe distance from the front axle to the truck load center (located directly u

onboard?

5.35. The rated load capacity of a lift truck is 3000 lbs and the distance from the front axle to the fork face is 12 in. If a push/pull carriage attachment for handling slipsheets is mounted on the front of the fork face, what will be the truck’s actual ratedassuming a standard load center of 24 in. from the front of the attachment? The attachment weighs 750


5.36. Why might it be necessary to use other types of sensory information, in addition to deadreckoning, t

o control the movement of a free-ranging AGV?

er bers (200+) of small (2 × 2 × 1 ft)

lightweight (< 20 lbs) cartons?

5.38. al handling equipment is likely to be the most economical for frequent (60–100 per hour), short-distance (< 50 ft), fixed-path, horizontal (i.e., no

5.39. After performing an economic analysis to select between two technically feasible MHE

referred?

rolley conveyor and a monorail. 10 carriers would be used for the move. The cost of each trolley carrier is $100 and the cost of each monorail carrier is

ll cost (i.e., carriers plus

nce er overall cost.

the same for each type and are $5 per hour. Assuming each equipment type will only be

t

5.42. r

having a salvage value of $1,000 after 10 years, will require 4 minutes per pallet; and (3) automatically, using a pick and place palletizer purchased for $25,000 and

ermine

5.43. per

away: a pallet truck (PT) and a fork AGV. The PT and AGV have investment costs of

5.37. What type of industrial truck is likely to be the most economical for infrequent (3–4 p8-hr shift), long-distance (500+ ft) moves of large num

What type of materi

stacking required) moves of identical-sized pallet loads?

alternatives, it was found that a pallet truck was slightly less costly than a counterbalanced lift truck. Why might the lift truck be the equipment p

5.40. Two types of material handling equipment have been identified as being technically feasible for a move: a t

$250. The track cost per foot for the trolley is $20 and the track cost per foot for the monorail is $5. The trolley conveyor would have a lower overatrack) if the length of the track is 25 feet. Determine the length of track at which the overall cost of the trolley and the monorail would be the same (i.e., the cost indifferepoint) and beyond which the monorail would have a low

5.41. Two types of material handling equipment have been identified as being technically feasible for a move: a pallet truck and an AGV. Each equipment type would require 6 hours to perform the move. The investment costs per shift for the pallet truck and AGVare $25 and $85, respectively. The operating costs per shift, exclusive of labor costs, are

used for this move during a shift and that the operator will be used for other productive tasks when not operating the equipment, determine the labor rate at which the overall cosof the pallet truck and the AGV would be the same.

Three methods of palletization are being considered: (1) manually, with no equipment, will require 6 minutes per pallet; (2) manually, using a lift-turn table purchased fo$3,000 and

having a salvage value of $5,000 after 5 years, will require 2 minutes per pallet. If the labor rate is $10 per hour and the cost of capital is 15% compounded annually, detthe range of annual pallet demands for which each method would be preferred.

Two different types of industrial trucks are being considered to move 150 pallet loadsshift between the loading dock and the first machine of a production line located 75 ft

142


$5,000 and $150,000, respectively, and will have salvage values of $1,000 and $10,000, respectively, at the end of ten years. For both the PT and AGV, each move requires two minutes and fuel costs are $2.00 per hour of operation. The fully burdened labor rate of a

ual compounding, determine which truck would be preferred.

5.44. per production line located 50 ft

away: a manual pallet jack (MPJ) and a pallet truck (PT). The MPJ and PT have

0 is 50

hour

e of

truck operator is $15 per hour, and s/he can perform other productive tasks when not transporting the pallet loads. If there are 500 eight-hour shifts per year and the cost of capital is 15% per year with ann

Two different types of industrial trucks are being considered to move 50 pallet loadsshift between the loading dock and the first machine of a

investment costs of $500 and $5,000, respectively, and will have salvage values of 0 and$1,000, respectively, at the end of five years. Manual lift/lower time for the MPJ is 3sec, and powered lift/lower time for the PT is 15 sec. Walking speed for the MPJft/min, and riding speed for the PT is 100 ft/min. The PT has a fuel cost of $2.00 per of operation. Assuming there are 250 8-hr shifts per year, the cost of capital is 15% per year with annual compounding, and that the truck operator will be performing other productive tasks when not operating the truck, determine the fully burdened labor ratthe operator at which the cost of using the MPJ or the PT would be the same.

143

6. Storage and Warehousing

6.1 Introduction

6.1.1 The Need for Storage and Warehousing In production, ideally, raw material should arrive at a manufacturing facility just when it is needed and then immediately processed, the resulting products should be fabricated and assembled without delay, and the final finished products should be immediately shipped to their customers; in this situation (what could be termed pure “Just-In-Time” or JIT) there is little need for buffering or storing materials. In practice (including real-world JIT), there usually are economic benefits associated with the buffering and/or storage of raw materials, work in process (WIP), and/or finished goods.

In distribution, the ideal of no storage can sometimes be realized using cross docking, where there is a direct flow of material from trucks at the receiving docks to the shipping docks without buffering or storage in-between, but cross docking requires detailed planning and coordination (e.g., implemented using EDI) that in many cases may not be feasible.

In most cases, the benefits associated with buffering and storage are due to the fixed costs associated with the other elements of production and the impact of variability pooling on achieving a target service level. Storing a product allows the other elements of production to operate more efficiently on a per-unit basis because the fixed costs associated with utilizing the element can be spread over more products; e.g.,

• Storing up to a truckload of product in a facility reduces the per-unit costs of shipping.

• The buffering or storage of WIP enables batch production which reduces the per-unit setup costs.

Benefits of storage In addition to the use of storage to reduce the per-unit costs of production, other potential benefits associated with storage include the following:

• Time bridging—allows product to be available when it is needed (e.g., storing spare machine parts at the facility)

145

6. STORAGE AND WAREHOUSING LECTURE NOTES FOR FACILITIES DESIGN

• Material flow—allows product to be collected, sorted, and distributed efficiently

• Processing—for some products (e.g., wine), storage can be considered as a processing operation because the product undergoes a required change during storage

• Securing—e.g., nuclear waste storage

Storage versus Warehousing The two terms are used to describe similar activities, the only difference being where the storage takes place:

• Storage function—storing or buffering raw materials, supplies, and WIP (at the production facility)

• Warehousing function—storing finished goods (either at the production facility or at separate “warehouse” facilities)

Decentralized versus Centralized Storage In a facility, the location of storage/warehousing activities can be centralized at one site or decentralized among several sites. Decentralized storage can range from all storage and receipt of materials taking place close to their point of use (termed “focused storage” in JIT-type manufacturing), to having all storage except in-process storage take place at a central site. It is common to have shipping/receiving docks located close to each storage site.

Centralized storage can reduce the overall storage-space requirements and can increase control (e.g., security) over the materials stored, while decentralized storage can reduce the overall material flow requirements to/from storage, give workcenters more direct control over inventory levels, and can reduce the number of dedicated material handling personnel required.

6.1.2 Storage/Warehousing Functions and Elements

Functions The basic storage and/or warehousing functions are traditionally considered to be the following:

1. Receiving

2. Identification and sorting

3. Dispatching to storage

4. Placing in storage

5. Storing

6. Removing (or “picking”) from storage

7. Order accumulation

8. Packaging

9. Shipping

10. Record keeping

Elements The storage/warehousing function is composed of the following elements:

146

1. Building Shell—materials can be stored in a portion of the manufacturing facility or in a separate structure.


A separate structure (up to 80 ft high, in some cases) can be used for centralized storage as part of an automated storage and retrieval system (AS/RS).

In some cases, the separate structure consists only of a lightweight shell that is supported by the storage rack structure ⇒ reduced building costs (and allows the structure to be depreciated at the faster equipment rate for tax purposes).

2. Storage Medium—used to provide support and protection of materials and/or to allow materials to be accessible.

Common storage media are storage racks, shelving, storage bins, and rotating carousels.

No storage medium is used for bulk storage.

3. Transport Mechanism—the mechanism (either automated, semiautomatic, or manual) used to transport loads between input/output (I/O) locations and storage locations.

The most common mechanism used for storage racks is some type of lift truck, although a dedicated storage/retrieval (S/R) machine is used in an AS/RS.

In a storage carousel, the storage medium is itself the transport mechanism.

4. Storage/Retrieval Policies—the means used to assign storage locations to each type of load.

The storage policy determines, in large part, the layout of the warehouse.

5. Controls—the means used to direct the transport mechanism during storage and retrieval operations (e.g., order picking).

Sophisticated information processing systems are used for AS/RS control.

147


6.1.3 Sortation Systems Sortation is the act of merging, identifying, inducting, and separating products to be conveyed to specific destinations. Sortation is used for batch picking, where an entire batch is picked and then sorted into individual orders; this can reduce the cost to assemble each order as compared to discrete order picking.

Figure 6.1. Typical sortation system [MHI].

Sortation system throughput is expressed in cartons per minute (CPM). A sortation system is composed of four subsystems (see Figure 6.1):

1. Merge subsystem—items transported from picking (storage) or receiving areas on conveyors and consolidated for proper presentation at the induct area.

2. Induct subsystem—destination of each item identified by visual inspection or automatic identification system (e.g., bar code scanner), then a proper gap between items is generated using short variable speed conveyors as they are released to the sort subsystem.

3. Sort subsystem—items are diverted to outbound conveyors of the post-sort subsystem.

4. Post-sort subsystem—conveyors move items to shipping, palletizing, staging, and/or secondary sort subsystems.

There is a trend towards more use of mixed-item loads that eliminate the need for sortation: instead of a producer sending pallet loads of a single item to a distribution center for subsequent sortation or consolidation into multi-item customer loads, single pallets can be loaded at a producer with a different mix of items for each customer. This also can enable greater use of cross-docking.

148

SPRING 2003 6.2. STORAGE SYSTEM DESIGN

6.2 Storage System Design Each distinct type of load is termed a stock-keeping unit (or SKU); e.g., each different style, size, and color of a garment would be assigned a unique SKU. An item is one or more units of a SKU. Each item is stored in a slot (short for storage location). A slot is a generic term for any of a variety of different types of identifiable storage locations (e.g., racks, bins, am even marked-off floor areas for block storage).

The handling costs for the items within a SKU can usually be minimized by always storing and retrieving an item at the nearest (i.e., least handling effort or cost) available location, or what can be termed a nearest-in, nearest-out (or NINO) policy. As long as the inventory levels of each SKU are controlled, a NINO will result in an approximate uniform rotation of the items; but, if inventory is not controlled, using a NINO policy can result in items remaining at far away slots for a long time. If a strict uniform rotation of the items is required (e.g., due to the items being perishable), then a first-in, first-out (or FIFO) policy can be used. In addition, a last-in, first-out (or LIFO) policy can be used.

FIFO Policy:

⇒ oldest item must be accessible

⇒ (multilayer) block stacking is not feasible

⇒ possible increased demands on storage/retrieval control to assure oldest item can be identified

In practice, a “semi-FIFO” retrieval can be achieved using multilayer block stacking by always picking the oldest accessible item (e.g., the item on the top of the oldest accessible stack).

Leve

l

Lane

Stack

Down Aisl

e

(acce

ss fo

r I/O)

Cross Aisle

(no access)

1

23

4

5

6

Y (depth) X (leng

th)zxy

Z (h

eigt

h)

Row

8 1 = Slot

1 + 2 + 3 + 4 = Lane

1 + 5 + 2 + 6 = Row

2 + 6 + 4 + 8 = Levels (or tiers)

1 + 2 = Stack (or column)

Figure 6.2. Stacking terminology.

149


6.2.1 Storage Terminology Terminology for stacking is illustrated in Figure 6.2. Eight slots numbered 1 to 8 are shown in cross section. Down aisles (or storage aisles) are aisles that provide access to the slots; cross aisles are aisles in which access to the slots is not possible because of the presence of, for

150

inventory level at the same time, randomized storage will require a lesser number of slots as compared to dedicated storage:

example, rack structures. In the figure, slots 1 through 4 would not be accessible if a storage rack were being used because of the beams and braces of the rack would block access.

6.2.2 Storage Policies For multiple SKUs, four types of storage policies can be used to select storage locations (or slots):

1. Dedicated (or Fixed Slot) Storage—each SKU has a predetermined number of lanes assigned to it.

The minimum number of slots in the lanes assigned to each SKU must equal the maximum inventory level of each individual SKU, where the actual number of slots might exceed the maximum level due to “honeycomb loss” (see Section 6.2.3 below).

Control is not difficult because each lane can be identified with a permanent label.

2. Randomized (or Open Slot or Floating Slot) Storage—each SKU can be stored in any (usually the closest) available lane.

The minimum total number of slots in the lanes must equal the maximum aggregate inventory level of all of the SKUs, where the actual number of slots might exceed the maximum level due to honeycomb loss.

Control is more difficult than dedicated storage because the identity of SKU stored at each slot needs to be recorded for retrieval purposes.

3. Class-based Storage—a combination of dedicated and randomized storage, where each SKU is assigned to one of several different storage classes.

Randomized storage is used for each SKU within a class, and dedicated storage is used between classes.

Classes can be formed from SKUs that have negatively correlated (or, at least, uncorrelated) individual inventory levels.

4. Supermarket Storage—a combination of dedicated and randomized storage, where randomized storage is used for reserve stock and dedicated is used for forward stock.

“Supermarket” storage is commonly used in orderpicking operations, where cartons are picked from forward stock (in flow-through racks), and full pallet loads of cartons are taken from reserve stock (in bulk storage) and used to replenish the forward stock.

In the example shown in Figure 6.3 and Table 6.1, as long as each SKU is not at its maximum


Dedicated ⇒ sum of max SKU levels = MA + MB + MC = 3 + 5 + 4 = 12 ⇒ min 12 slots

Randomized ⇒ max Aggregate level = M = MABC = 9 slots ⇒ min 9 slots required

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10

Time

A

B

C

ABC

Figure 6.3. Inventory profiles for dedicated and randomized storage policies.

Table 6.1. Inventory and Storage Requirements for Different Storage Policies

Dedicated Random Class-Based

Time A B C ABC AB AC BC

1 4 1 0 5 5 4 1 2 1 2 3 6 3 4 5 3 4 3 1 8 7 5 4 4 2 4 0 6 6 2 4 5 0 5 3 8 5 3 8 6 2 5 0 7 7 2 5 7 0 5 3 8 5 3 8 8 3 4 1 8 7 4 5 9 0 3 0 3 3 0 3

10 4 2 3 9 6 7 5

Mi 4 5 3 9 7 7 8

fi 24 7 21 52 31 45 28

151


6.2.3 Cube Utilization and Honeycomb Loss In both deep-lane and multilevel block storage, full utilization of all of the available space is not desirable because it could result in some items not being accessible. Honeycomb loss, the price paid for accessibility, is the unusable empty storage space in a lane or stack that cannot be utilized because either:

• storing items from a different SKU in the lane or stack would block access, or

• storing items from the same SKU in the lane or stack would make FIFO retrieval difficult.

Cube utilization is percentage of the total space (or “cube”) required for storage actually occupied by items being stored. There is usually a trade-off between cube utilization and material accessibility:

increasing cube utilization ⇒ decreased accessibility, and

increasing accessibility ⇒ decreased cube utilization.

Bulk storage using block stacking can result in the minimum cost of storage since cube utilization is high and no storage medium is required, but material accessibility is low since only the top of the front stack is accessible and loads at bottom of a stack must not require support. Storage racks are used when support and/or material accessibility is required.

Given a contiguous region where several different SKUs are to be stored, the principal decision variable for deep-lane storage is D, the number of rows of storage for the region. Given a slot depth of y, the resulting lane depth is Y = yD. Different row values for the region will result in different cube utilizations. Since the space occupied by the items is assumed to be known, cube utilization can be determined once the total space is determined, where the total space is the item space plus honeycomb loss and the space used for access (e.g., down aisles). Given D and assuming identical size slots for all items, the cube utilization for dedicated and randomized storage can estimated as follows:

( ) ( )1

item space item spaceCube utilizationhoneycomb down aisletotal space item space loss space

, dedicated( )

, randomized( )

Niix y z M

TS Dx y z M

TS D

=

= =+ +

⋅ ⋅ ⋅=

⋅ ⋅ ⋅

∑ (6.1)

where

x = lane/slot width

y = slot depth

z = slot height

152


Mi = maximum number of slots needed for SKU i

M = maximum number of slots needed for all SKUs

N = number of different SKUs

D = number of rows

TS = total space.

Defining the effective lane depth as the depth of the lane plus half of the width of the down aisle in front of the lane, the total space required, as a function of lane depth, is

Eff. lane depth

Total space (3-D): ( ) ( )2 2A ATS D X Y Z xL D yD zH = ⋅ + ⋅ = ⋅ + ⋅

, (6.2)

where

X = length of storage region (row length)

Y = depth of storage region (lane depth)

Z = height of storage region (stack height)

A = down aisle width (in units of slot depth)

L = number of lanes

H = number of levels.

To convert the total 3-D space to 2-D area:

( )Total area (2-D) TS DZ

= (6.3)

Given D, the total number of lanes required for storage in the region can be estimated as follows:

1

, dedicated

Number of lanes: ( ) 1 1, randomized ( 1)2 2

Ni

i

MDH

L D D HM NH N NDH

=

= − − + + >

∑, (6.4)

For dedicated storage, the honeycomb loss can be directly determined for each item via the ceiling operation in (6.4), which then determines the corresponding number of lanes required; for randomized storage, since only the total maximum number of items, M, is known and not the specific the number of each SKU that comprise this total at the exact time that the total reaches its maximum (unless the SKU’s inventory levels are not perfectly correlated), the honeycomb loss can only be estimated by assuming that, at the maximum inventory level, the number of items in the partially filled lane and/or stack for each SKU is equally likely. The honeycomb loss is estimated as follows:

•

153


( )1

Partial lane loss Partial stack loss

, dedicated

1 1Honeycomb loss, randomized2 2

Niixyz LDH M

D HHN x yz

= − − − = +

∑. (6.5)

Given the number of lanes of storage, the corresponding down aisle space is

Down aisle space2AxL zH= ⋅ ⋅ . (6.6)

Optimal Lane Depth The lane depth that maximizes cube utilization corresponds to best compromise between honeycomb loss (6.5) and down-aisle space loss (6.6) (see, also, Figure 6.4). The optimal value for dedicated storage can be determined by calculating the utilization associated with each stack using for D ranging from 1 to { }max iM ′ . The optimal value for randomized storage can be determined either thorough direct calculation using a range of D values or by using the following analytical approximation. Since th space is constant in (6.1), cube utilization can be maximized by minimi izing (6.2) (ignoring the ceiling operation in (6.4)) by solving for D in

e itemzing total space. Minim

( )dTS D dD*

= 0 results in the following expression that can be rounded to the nearest integer to determine D , the lane depth (in rows) that maximizes cube utilization. (Note: Rounding (6.7) provides only an approximation of the optimal lane depth because the ceiling operation is ignored; to calculate the optimal depth, actual TS(D) values should be directly calculated for several D values close to D*.)

( )* 2

Optimal lane depth for randomized storage (in rows):2

A M ND

NyH

−= . (6.7)

154


0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

Lane Depth (in Rows)

Item Space 24,000 24,000 24,000 24,000 24,000 24,000 24,000 24,000 24,000 24,000

Honeycomb Loss 1,536 3,648 5,376 7,488 9,600 11,712 13,632 15,936 17,472 20,160

Aisle Space 38,304 20,736 14,688 11,808 10,080 8,928 8,064 7,488 6,912 6,624

Total Space 63,840 48,384 44,064 43,296 43,680 44,640 45,696 47,424 48,384 50,784

1 2 3 4 5 6 7 8 9 10

Figure 6.4. Total space associated with different lane depths

for deep-lane randomized storage.

Example In this example, x = 4, y = 4, z = 3, M = 500, N = 20, A = 12, H = 4, and D* = 4.29. Figure 6.4 shows the total space associated with D ranging from 1 to 10. Also shown are the components of total space: item space, honeycomb loss, and down-aisle space. Rounding D* to 4 results in the same optimal lane depth as found through direct calculation. The corresponding maximum cube utilization is as follows:

item space 4 4 3 500Max cube utilization 0.5543 55.43%total space ( = 4) (4) 43,296

x y z MD TS

⋅ ⋅ ⋅ ⋅ ⋅ ⋅= = = = = .

6.2.4 Dedicated Storage Assignment Problem (DSAP) In this section, the items of each SKU are assigned to the slots in empty lanes so that the total cost of material flow (TCMF) is minimized.

Given a layout with 1N

iiM M=

≥ ∑ slots and N SKUs, the following Dedicated Storage

Assignment Problem (DSAP) can be used to determine slot assignments:

155


DSAP SOLUTION PROCEDURE

1. Order Slots: Compute the expected cost cj for each slot j and then put into nondecreasing order

2. Order Items: Put the flow per slot for each SKU i (

c c c M[1] [ ] [ ]£ £ £2

i if M ) into nonincreasing order

[1] [2] [ ]

[1] [2] [ ]

N

N

f f fM M M

≥ ≥ ≥

3. Assign Items to Slots: For i = 1, …, N, assign item [i] to the first M[i] slots still available in empty lanes in the layout.

Given a total of P I/O ports in the layout,

TCMF = [ ][ ]

[ ]1

Mi

iii

fcM=

⋅∑ = total cost of material flow to/from all I/O ports and slots

cj = 1

P

jk jkk

p c=

⋅∑ = expected cost of utilizing slot j for moves to/from all I/O ports

pjk = percent of S/R moves of a item stored at slot j to/from I/O port k

cjk = cost of utilizing slot j for moves to/from I/O port k

fi = flow (i.e., moves per period) of SKU i

Mi = maximum number of slots needed for SKU i

If N1 ii M M

=<∑

1 1Ni

, then an extra “dummy SKU,” N + 1, can be added to fill the

N iM M M+ == − ∑

identical for all m

empty slots at a cost of c(N+1), j = 0, j = 1, …, M. If the handling costs are

oves between slots and I/O ports, then cj can be viewed as the expected distance traveled between slot j and all of the I/O ports, and TCMF becomes the total distance traveled.

Assumptions The following assumptions must be satified in order to be able to use the DSAP procedure:

1. All storage/retrieval (S/R) operations are performed as single-command cycles.

2. For SKU i, the probability of a move to/from slot j is 1 iM .

3. The factoring assumption:

(a) Handling costs and distances (or times) are identical for all items

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(b) The percent of S/R moves of a item stored at slot j to/from I/O port k is identical for all SKUs.

If any of these assumptions are not satisifed, then the DSAP can be solved as a Transportation Problem, where each of the N SKUs is a source, each source i must ship Mi units, and each of the M slots is required to receive one unit. Transportation problems can be solved relatively easily using commercial software packages.

Due to Assumptions 1 and 2, the slots do not interact with each other; if some of the S/R operations were dual command, then the cost of assigning a slot to a item would depend on what items were assigned to the other slots. If the probabilities of using slots for a SKU were not all equal (e.g., if the slots that are nearer an I/O port had a higher probability of being used), then the cost for a slot would depend on what other slots are assigned to the SKU.

Assumption 2 would be valid if, for example, both a FIFO retrieval policy is used for all items, and the slot assigned to SKU i that has remained empty the longest is always the next slot used for storage. In practice, these conditions would be approximately satisfied if all storages (retrievals) took place in a short time period (e.g., receiving (shipping) of truck loads of material) and the slots were emptied (filled) before the next storages (retrievals) took place.

Assumption 3 is termed the factoring assumption because it allows TCMF to be factored into the product of two terms, one based only on the slot j (cj) and one based only on the flow per slot ( i if M ). In practice, Assumption 3(a) would be satisfied if, for example, the same MHE is used for all items and the handling characteristics (including loading/unloading times) are the same for all items. Assumption 3(b) would be valid if, for example, there is only one I/O port, or there are two ports and one is used only for input and the other port is used only for output and the ratio of flow into a slot to flow out of a slot is identical for all items; the assumption would need to be verified in other situations.

6.2.5 Warehouse Design Two situations can occur in planning a storage layout: either a storage layout is required to fit into an existing facility, or the facility will be designed to accommodate the storage layout. In the first case, the existing facility provides constraints on the types of layouts that are feasible (e.g., the existing ceiling height constrains the maximum number of possible rack tiers); in the second case, the only constraints on the layout are those imposed by the unit load design, and everything else about the layout is variable.

In both cases, the objectives for the layouts can be, for example, to maximize cube utilization, minimize total storage costs (including building, equipment, and labor costs), achieve the required storage throughput, and enable efficient order picking.

The design of a new warehouse includes the following elements:

1. Determining the layout of the storage locations (i.e., the warehouse layout).

2. Determining the number and location of the I/O ports (e.g., the shipping/receiving docks).

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3. Assigning SKUs to storage locations if dedicated storage is being used.

A typical objective in warehouse design is to minimize the overall storage cost while providing the required levels of service.

Storage cost includes both the building cost and the total cost of material flow. The objective of minimizing storage cost involves a trade-off between maximizing cube utilization (to reduce building costs) and minimizing the total cost of material flow.

Minimizing Total Material Flow Costs Several factors associated with the objective of minimizing building costs can result in increased material flow costs:

• Travel Distance—the layout that maximized “cube” utilization results in long travel distances to/from locations in the center of the layout.

• Aisle Width—the use of narrow-aisle lift trucks to reduce aisle space requirements can increase equipment costs and the time required for storage/retrieval (S/R) operations (e.g., aisles that do not allow passing).

• Storage Racks—storage racks that increase cube utilization can also increase equipment costs and S/R time.

• Number of I/O Ports—I/O ports add to building costs, both inside and outside the building.

• Location of I/O Ports—the layout that maximized “cube” utilization had its I/O port at the end; if it had been located in the middle, a cross-aisle would have been required (decreasing cube utilization), but the average travel distances would have been reduced in half; the cross-aisle added to a layout to reduce perimeter length will also reduce travel distances.

I/O Port Location For a given layout of storage locations, the problem of I/O port location can be formulated as a facilities location problem, where:

• I/O ports are the “new facilities” to be located and storage locations are the “existing facilities”

• rectilinear distances are used to approximate aisle travel

• the objective is to minimize the total cost of material flow (TC).

To simplify, the discrete storage locations are often approximated as a single continuous equal-density 2-D surface.

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I/O I/O

I/O

Euclidean RectilinearL = 2W

W

Figure 6.5. Single I/O port locations to minimize travel distance.

Given no restrictions on the location of the single I/O port used in a warehouse, a location in the center of the warehouse minimizes TC; even if a center I/O location is not feasible, a conveyor, e.g., can be used to transport loads from a central lift truck drop-off point to the side of the warehouse.

When the single I/O port is restricted to being located on a side of the warehouse, TC is minimized when the port is at the midpoint of the length of the warehouse (L) and L is twice its width (W).

159


terials over a period of time. Some storage achines of an AS/RS, or storage

160

6.3 Storage Equipment Storage equipment is used for holding or buffering maequipment may include the transport of materials (e.g., the S/R mcarousels). If materials are block stacked directly on the floor, then no storage equipment is required. Storage racks are used to provide support to a load and/or to make the load accessible.

Table 6.2. Storage Equipment

1. Block stacking (no equipment) 2. Selective pallet rack 3. Drive-through rack 4. Drive-in rack 5. Flow-through rack 6. Push-back rack 7. Sliding rack 8. Cantilever rack 9. Stacking frame

10. Shelves/bins/drawers Storage carousel 12. Automatic storage/retrieval system (AS/RS) (a) Unit load AS/RS (b) Miniload AS/RS (c) Man-on-board AS/RS (d) Deep-lane AS/RS 13. Split-case order picking system 14. Mezzanine

11.

1. Block stacking (no equipment)

Bulk storage using block stacking can result in the minimum cost of storage since cube utilization is high and no storage medium is required, but material accessibility is low since only the top of the front stack is accessible and loads at bottom of a stack must not require support

Storage racks are used when support and/or material accessibility is required

2. Selective pallet rack

Most popular type of storage rack

Pallets are supported between load-supporting beams

Special attachments and decking can be used to make the racks capable of supporting other types of unit loads besides pallets (e.g., coils, drums, skids)

Selective racks used for following types of storage:

Standard—single-deep storage using a counterbalanced lift truck

Narrow-Aisle—storage using a narrow-aisle lift truck

Deep-Reach—greater than single-deep storage (typically double-deep storage)

SPRING 2003 6.3. STORAGE EQUIPMENT

ide clearance for straddles; load-on-floor racks can be used dles.

161

Load-on-beam racks are used to provwhen it is not necessary to use strad

3. Drive-in rack

Used to provide high density pallet storage

Loads are supported by rails attached to the upright beams

Lift trucks are driven between the uprights beams

Requires similar-width loads

Closed at one end, allowing entry from one end (LIFO)

4. Drive-through rack

Similar to drive-in rack, except open at both ends, allowing access from both ends (FIFO)


162

5. Push-back rack

Used to provide highly accessible carton or pallet storage

Loads are supported on an incline to enable gravity-based movement of the loads within the rack (via, e.g., a gravity roller conveyor)

Loaded and unloaded at the lower end and closed at the higher end (LIFO)

Push-back pallet racks can be used to enable deep-reach storage without the need for extended reach mechanisms for loading/unloading

6. Flow-through rack

Similar to push-back rack, except loaded at the higher end and unloaded at the lower end (FIFO)

Termed pallet-flow rack when pallets are used

Typically used in orderpicking operations so that replenishment does not interfere with picking

Can have WMS-controlled LED displays attached to shelf beam (see figure) for “pick-to-light” operations

SPRING 2003 6. STORAGE EQUIPMEN3. T

163

7. Sliding rack

Used when only single-deep storage is possible and space is very limited or expensive

Sometimes referred to as a “mobile rack” or “movable aisle” rack

Expensive compared to other storage racks

Only one mobile aisle is used to access several rows of racks

Location of the aisle is changed by sliding rows of racks along guide rails in floor

Provides increased security for items compared to other racks

Typically found in library stacks, vaults, and climate-controlled (e.g., refrigerated) storage rooms

8. Cantilever rack

Loads are supported by two or more cantilevered “arms” (i.e., horizontal beams supported at only one end)

Similar to pallet racks, except the front upright and front shelf beams are eliminated

Used when there is a need for a full clear shelf that can be loaded from the front without obstruction from rack support uprights

Typically used to store long loads (e.g., bar stock, pipes, lumber)

9. Stacking frame

Interlocking units that enable stacking of a load so that crushing does not occur

Can be disassembled and stored compactly when not in used

Pallet frames can be used to enable multilevel block stacking


s

164

10. Shelves/bins/drawers

Alternative to racks to store small, loose, nonpalletized item

Difficult to automate picking

Space is frequently underutilized

11. Storage carousel

Carousel consists of a set of vertically or horizontally revolving storage baskets or bins.

Materials (and the storage medium) move to the operator, “part-to-man,” for end-of-aisle picking

Each level of the carousel can rotate independently in a clockwise or counter-clockwise direction

Control ranges from manually activated push buttons to automated computer controlled systems

Provides an alternative to typical “man-to-part” AS/RS, where the S/R machine moves to part

Similar to a trolley conveyor with storage baskets

12. Automatic storage/retrieval systems (AS/RS)

Consists of integrated computer-controlled system that combines storage medium, transport mechanism, and controls with various levels of automation for fast and accurate random storage of products and materials

Storage/retrieval (S/R) machine in an AS/RS operates in narrow aisle, serving rack slots on both sides of aisle; can travel in horizontal (along the aisle) and vertical (up and down a rack) directions at same time


165

Advantages: fewer material handlers, better material control (including security), and more efficient use of storage space

Disadvantages: high capital and maintenance costs, and difficult to modify

12(a) Unit load AS/RS

Used to store/retrieve loads that are palletized or unitized and weigh over 500 lbs.

Stacking heights up to 130 ft. high, with most ranging from 60 to 85 ft. high; 5 to 6 ft. wide aisles; single- or double-deep storage racks

12(b) Miniload AS/RS

Used to store/retrieve small parts and tools that can be stored in a storage bin or drawer

End-of-aisle order picking and replenishment

Stacking heights range from 12 to 20 ft.; bin capacities range from 100 to 750 lbs.

Termed a “microload AS/RS” when capacity is less than 100 lbs (used in assembly, kitting, and testing operations to deliver small containers of parts to individual workstations)

Workstations are typically located on the sides of a pair of racks and the S/R machine operates between the racks to min the racks (storage lanes) located next to each station

12(c) Man-on-board AS/RS

Used for in-aisle picking; operator picks from shelves, bins, or drawers within the storage structure

Manual or automatic control

S/R machine is similar to an order picker or turret truck and can sometimes operate as an industrial truck when outside an aisle, except the S/R is guided along a rail when operating in an aisle

12(d) Deep-lane AS/RS

Similar to unit load AS/RS, except loads can be stored to greater depths in the storage rack

A rack-entry vehicle is used to carry loads into the racks from

ove containers to openings

6. STORAGE AND WAREHOUSING

the S/R machine

” when al items or

tic picking from the

LECTURE NOTES FOR FACILITIES DESIGN

166

the S/R machine, and is controlled by

Termed an “automated item retrieval systemused to automatically retrieve individucases, with replenishment (storage) taking place manually from the rear of a flow-through storage lane and items are pushed forward with a rear-mounted pusher bar for automafront of the storage lane

13. Split-case order picking system

Unlike an AS/RS, a split-case order picking system enables fully auto-mated picking of individual items

Two general categories of split-case order picking system are robotic based systems and magazine/ dispenser based systems

Robotic based systems are similar in construction to robotic pick and place palletizers

Magazine/dispenser based systems are similar to vending machines, but larger in scale

“A-Frame” dispenser system (pictured) is popular within pharmaceutical distribution centers; items are dispensed onto a belt conveyor that carries them into a container


167

14. Mezzanine

Stand-alone structure constructed within an existing building

Inexpensive means of providing additional storage or office space

Makes use of clear space over activities not requiring much headroom (e.g., restrooms, block storage, etc.)

At least 14 ft of clear space is needed for a mezzanine

Table 6.3. Storage Rack Comparison

Type of Rack

Storage Pattern

All Loads Accessible

FIFO Retrieval

Principal Advantage

Principal Disadvantage

Standard single deep yes yes — ↓ cube util.

Narrow Aisle single deep yes yes ↑ cube util. ↓ truck cost

Deep Reach > 1 deep no no ↑ cube util. ↑ truck cost

Drive In > 1 deep no no ↑ cube util. ↑ honeycomb loss potential

Drive Through > 1 deep no yes ↑ cube util. ↑ honeycomb loss potential

Flow Through > 1 deep no yes ↑ cube util. ↑ rack cost

Push Back > 1 deep no no ↑ cube util. ↑ rack cost

Sliding Racks single deep yes yes ↑ cube util. ↑ rack cost + ↑ S/R time


6.4 Automated Storage/Retrieval Systems An automated storage/retrieval system (AS/RS) consists of an integrated computer-controlled system that implements the storage/warehousing elements (e.g., storage medium, transport mechanism, and controls) with various levels of automation for fast and accurate random storage of products and materials.

Although AS/RS were originally developed for warehousing and distribution operations, they are now also being used for in-process storage as part of an automated job shop. In an automated job-shop, an AS/RS can be combined with an automatic identification system and an automatic transportation system (e.g., automatic conveyors and/or an AGV system) to provide real-time material control capabilities. The material stored in the AS/RS can include both finished goods and work in process and even production tools and jigs.

• Advantages of an AS/RS include: fewer material handlers, better material control (including security), and more efficient use of storage space.

• Disadvantages of an AS/RS include: high capital and maintenance costs, and difficult to modify.

6.4.1 Components of an AS/RS Racks: A typical AS/RS utilizes high-rise storage racks, ranging in height between 40 and 80 feet or higher, for random storage. High-rise racks require tight rack tolerances and level floors, all of which increase the cost of the racks as compared to a basic storage rack. The racks in an AS/RS can be free-standing or uses to support the building (RSS—rack-supported structure).

S/R Machine: An S/R machine in an AS/RS operates in a narrow aisle, serving rack slots on both sides of the aisle. The machine can travel in the horizontal (along the aisle) and vertical (up and down a rack) directions at the same time. Often the machine is captive to one aisle, although, if throughput requirements do not justify dedicating a machine to each aisle, a transfer car can be provided to move the machine from the end of one aisle to another, thus enabling the machine to operate in more than one aisle. The machine is a structural single- or multiple-mast frame which rides on one or two floor-mounted wheel rails. A carriage carrying a load-supporting mechanism (or shuttle) operates within the frame. The shuttle is used to store/retrieve loads at the racks and, at the end of the aisle, to transfer loads onto or away from conveyors, vehicles, or pick-up and delivery (P/D) stations or transfer stations.

Control: The operation of an AS/RS can be controlled by an operator working from a console, but in many cases, the control system is under complete computer control. Typically, distributed control, where each S/R machine is controlled by a dedicated computer with interfaces with a central computer, is used to increase system reliability.

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SPRING 2003 6.4. AUTOMATED STORAGE/RETRIEVAL SYSTEMS

6.4.2 AS/RS Design One of the unique aspects of an AS/RS with respect to its design is the mode of operation of the S/R machines. In the design of most storage systems, rectilinear distances can be used to represent the movement of the transport mechanisms; in an AS/RS, the S/R machines can move a load in the horizontal direction along an aisle and lift the load in the vertical direction simultaneously (and, typically, at different speeds), so that the use of rectilinear distances would overestimate the distance (or time) the load travels.

Movement Time Letting vx and vz be the horizontal (X) and vertical (Z) speeds, respectively, of an S/R machine, then the time required for the machine to move from (x0, z0) to (x, z), assuming instantaneous acceleration, can be represented by the Chebychev “distance”:

max ( ) , ( )abs absx xv

z zvx z

- -RSTUVW

0 0 . (6.8)

For each aisle of an AS/RS, the I/O port for the aisle is typically at the end the aisle and at the bottom level of the racks in the aisle; thus, assuming (x0, z0) = (0, 0) as the location of the I/O port (and ignoring the horizontal movement (Y) of the S/R machine’s shuttle into the racks), the time required to travel from the I/O port to location (x, z) is

max ,xv

zvx z

RSTUVW. (6.9)

Travel Path Assuming that a load starts moving in the horizontal and vertical immediately upon leaving the I/O port, the travel path taken by the load to reach a location (x, z) depends ratio of the horizontal and vertical travel speeds of the S/R machine. For example, the paths taken to reach a location equal distance from the port in the X and Z directions (i.e., x = z) are shown in Figure 6.6 for three cases: vx < vz (or v vx z < 1), vx = vz (or v vx z = 1), and vx > vz (or v vx z > 1).

I/O

Z

X

x = z

Vx = Vz

Vx <

Vz

Vx > Vz

Figure 6.6. Effect of speed ratio on travel paths.

169


Contour Lines For a given aisle of an AS/RS, let X and Z represent the maximum travel distances in the horizontal and vertical directions, respectively; then let Tx = X vx and Tz = Z vz

ar shaped and are “square-in-

represent the time it takes to reach X and Z, respectively. Given X, Z, vx, and vz, a set of equal-time contour lines can be drawn. The regions enclosed by the lines are rectangultime” for times up to . The shape of the equal-distance contour lines that correspond to the equal-time lines are not unique: they depend on X, Z, vx, and vz. In Figure 6.7, two different sets of equal-distance contour lines could correspond to the same set of equal-time contour lines.

min ,T Tx zl q

Tz (= 2Tx)

Tx X

Z (= 2X)

X

Z (= X)

OR⇒

(a) Equal-time contours (b) Equal-distance contour for (c) Equal-distance contour for for Tz = 2Tx Z = 2X and vx = vz Z = X and vx = 2vz

Figure 6.7. Equal-time and equal-distance contours.

Cycle Times For single-command S/R operations, assume that the cycle time (TSC) for each complete storage or retrieval operation is equal to

T E TSC L U= ◊ + ◊2 2( ) /one-way-travel-time , (6.10)

where TL/U = time required to perform either a loading or unloading operation.

Given Tx = X vx and Tz = Z vz and letting tx = x vx and tz = z vz , the expected one-way travel time for randomized storage in an aisle is

1

1

100

00 0

00 0

T Tt t dt dt

T Tt dt dt t dt dt T T

T Tt dt dt t dt dt T T

x zx z

TT

x zx z

z

tT

x z xt

TT

x z x z

x zx

tT

z x zt

TT

z x x z

xz

zz

z

xz

xx

x

zxmax ,

,

, .l qzz

zz zzzz zz

=

+LNMM

OQPP ≥

+LNMM

OQPP <

R

S||

T||

if

if

(6.11)

170

SPRING 2003 6.4. AUTOMATED STORAGE/RETRIEVAL SYSTEMS

In (6.11), the regions over which the integration is performed depends on whether or not Tx ≥ Tz. The case where Tx ≥ Tz is shown in Figure 6.8, where max tx , tz{ }

and to = tz in the region above the

diagonal line tx = tz, and = tx in the region below the right of the diagonal. max tx , tz{ }

Tz

Tx0

tx = t

ztz > tx

tx > tz

Figure 6.8. Case Tx ≥ Tz.

Completing the above integrations for each case yields

E

TT

T T T

TT

T T T

z

x

xx z

x

z

zx z

one-way-travel-timeif

if b g =

+ ≥

+ <

RS||

T||

2

26 2

6 2

,

, . (6.12)

In order to combine both cases into a single expression, let

T = max Tx ,Tz{ } and Q = min

Tx

Tz,Tz

Tx

so that

E

QT T T T

QT T T T

Q T Tz

x z

xx z

one-way-travel-timeif

if b g =

+ ≥

+ <

RS|

T|

UV|

W|= +6 2

6 26 2

2,

,, (6.13)

where use is made of the fact that Tz = QT, if Tx ≥ Tz, and Tx = QT, if Tx < Tz. Using this result, the single-command cycle time is

T Q T T T T Q TSC L U L U= +FHG

IKJ + = +

FHGIKJ +2

6 22

31 2

2 2

/ / . (6.14)

A similar analysis can be used to determine the following expression for dual-command cycle time:

T E E T

T Q Q T

DC L U

L U

= +

= + - +

2 4

3040 15 42 3

( ) (

,

/

/

one-way-travel-time travel-time- +)between

d i (6.15)

where the travel time out represents the time taken to reach the slot of the load to be retrieved, the travel time in represents the time to return from this slot, and four loading/unloading

171


operations occur in each dual-command cycle. In general, the travel time out is greater than the travel time in and the expected travel time in is equal to the expected on-way travel time of a single-command operation.

Square-In-Time Design It can be shown that an AS/RS rack design that is square in time (i.e., Tx = Tz ⇒ Q = 1) minimizes the cycle time for randomized storage along an aisle. When a rack is square-in-time, the horizontal and vertical movement of the S/R machine is completed just as it reaches the end of the aisle and the top of the rack (i.e., the location furthest from the I/O port).

Given N items, each with dimensions x and z, Tx = Tz ⇒ X vx = Z vz ⇒ X = Z vx vz( ) and N = X x( ) Z z( ); thus, ignoring the issue of rounding,

X vv

Nxz Z vv

Nxzx

z

z

x= =and ,

since

N Xx

Zz

ZX Nxz

ZZ vv

Nxz

Z vv

Nxz

Z vv

Nxz

x

z

z

x

z

x

= fi

=

=

=

=

2

and

X v

vZ v

vvv

Nxz

vv

vv

Nxz vv

Nxz

x

z

x

z

z

x

x

z

z

x

x

z

= =

= =2

2

.

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SPRING 2003 6.5. IDENTIFICATION AND CONTROL EQUIPMENT

6.5 Identification and Control Equipment Identification and control equipment is used to collect and communicate the information that is used to coordinate the flow of materials within a facility and between a facility and its suppliers and customers. The identification of materials and associated control can be performed manually with no specialized equipment.

Table 6.4. Identification and Control Equipment

1. Manual (no equipment) 2. Bar codes 3. Radio frequency identification (RFID) tags 4. Magnetic stripes

5. Machine vision 6. Portable data terminals 7. EDI/XML communication protocols 8. Warehouse management systems (WMS)

9.


Although it is sometimes possible to manually coordinate the operation of a material handling system, it becomes more difficult to due so as the speed, size, and complexity of the system increases

2. Bar codes

Unique bar/space patterns represent various alphanumeric characters

Bar code system consists of bar code label, bar code scanner, and bar code printer

Contact bar code scanners use pen or wand to read labels

Noncontact bar code scanners include fixed beam, moving beam, and omnidirectional

1-D codes are most common; 2-D codes enable much greater data storage capability

3. Radio frequency identification (RFID) tags

Data encoded on chip encased in a tag

Noncontact: can be read when the tag is within 30 ft. of an antenna

Tags can either be attached to a container, or permanently or temporarily to an item

RF tags have greater data storage capability than bar codes

4. Magnetic stripes

Data encoded on a magnetic stripe that is readable in almost any environment

Requires contact with a reader

173

Greater storage capability and more expensive than bar codes


5. Machine vision

Does not require explicit encoding of data since objects can be identified by their physical appearance

Noncontact, but typically requires structured lighting

More flexible than other identification equipment, but less robust

6. Portable data terminals

Used for real-time data communication with warehouse management systems (WMSs)

Handheld, arm-mounted, or vehicle-mounted data storage and communication device

Communicates with a host computer via a radio frequency or infrared link

Variety of input devices available: keyboard, bar code scanner, voice headset

7. EDI/XML communication protocols

EDI (Electronic Data Interchange) provides standards for inter-corporate transfer of purchase orders, invoices, shipping notices, and other frequently used business documents

Prior to the Internet, EDI required expensive dedicated value added networks (VANs)

EDI is critical for implementing JIT manufacturing

XML (Extensible Markup Language) provides a means for specifying meaning of data available and transmitted on the Internet

The XML protocal is more general than EDI (in fact, EDI could/will be implemented using XML)

8. Warehouse management systems (WMS)

Computerized information system that automates the control of warehouse or storage area operations

WMS together with identification (e.g., bar codes) needed to implement large-scale randomized storage

Most WMSs support real-time data communication ____________________________________________________________________________________________________________________________________________________________

174


6.6 Problems

175

32, respectively?

6.1. How can the storage of a product during its manufacture reduce the overall cost of producing the product?

6.2. Why, in general, is the use of centralized storage likely to reduce overall storage-space requirements as compared to the use of decentralized storage?

6.3. List the type(s) of pallet racks that will never result in honeycomb loss.

6.4. Explain why drive-in and drive-through storage racks might have greater potential for honeycomb loss as compared to other types of racks.

6.5. Why is a deep-reach pallet rack not appropriate when a FIFO retrieval policy is required?

6.6. What type of rack would likely be the most appropriate for the storage of 20-foot-long bar stock? Assuming that a unit load of bar stock is too heavy for manual handling, what type of material handling equipment would be appropriate to transport a single unit load of the bar stock?

6.7. What storage alternative is both the storage medium and the transport mechanism?

6.8. How can a product be stored so that FIFO retrieval is possible even though every load is not always accessible?

6.9. What type of rack would likely be the most appropriate for the temporary outdoor storage of pallet loads of eggs?

6.10. What type rack can be used to enable deep-reach storage without the need for extended reaching mechanisms for loading/unloading?

6.11. What type of storage medium would likely be the most appropriate if each item in storage needs to be accessible at all times and space for storage is very expensive due to high land costs?

6.12. What type of storage medium would likely be the most appropriate to store a very large number of identical pallet loads of a single type of fragile and perishable item?

6.13. What is the cube utilization associated with three-deep, four-high dedicated block stacking of 42 × 48 × 36 in. pallet loads of products A, B, and C along a 10-foot-wide down aisle assuming that the maximum inventory levels of the products are 10, 18, and


6.14. Determine the approximate minimum floor area (in ft2) needed for the randomized block stacking of 2,800 different SKUs along 10-ft-wide down aisles, assuming 15% of the space will be used for cross aisles. A maximum of 250,000 total units of product are to be stacked five-high on identical 40 × 36 × 48 in. two-way pallets.

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17.5 moves per hour.

6.15. What is the decrease in cube utilization associated with using two-deep storage as compared the depth that maximizes cube utilization for the randomized block stacking of 600 different SKUs along 8-foot-wide down aisles? A maximum of 25,000 total units of product are to be stacked four-high on identical 42 × 36 × 42 in. two-way pallets.

6.16. Although randomized storage will require a lesser number of slots as compared to dedicated storage (as long as each SKU does not have its maximum inventory level at the same time), why is dedicated storage still sometimes used?

6.17. Why is it likely that class-based storage will result in storage space requirements less than dedicated storage but greater than randomized storage, and average cycle times less than randomized storage but greater than dedicated storage?

6.18. Why is it unlikely that it will be possible to perform all storage and retrieval operations as dual-command cycles?

6.19. Two different types of industrial trucks are being considered to move pallet loads of raw material between a 900,000 ft3 triangular storage region and the first machine of a production line located 50 ft away from the corner of the region: a powered walkie stacker (PWS) and a standup counterbalanced lift truck (UCB). All of the slots in the region are equally likely to be used, items are stacked 18 ft-high, the down aisles are 10-ft-wide, and the triangular storage region has a shape that minimizes the expected travel distance to the machine. The PWS and UCB have investment costs of $10,000 and $24,500, respectively, and will have salvage values equal to 30% of their original cost at the end of 10 years. Riding and walking speeds are 7 and 3 mph (5,280 ft/mile), respectively, and each will require 30 seconds for loading or unloading. The fully burdened labor rate of a truck operator is $6.25 per hour, and s/he can perform other productive tasks when not transporting the pallet loads. Fuel costs can be ignored.

(a) If there are 250 eight-hour shifts per year and the cost of capital is 20% per year with annual compounding, determine the minimum number and type of truck that would be preferred to serve an expected annual demand of 35,000 single-command moves, with enough trucks to handle a peak demand of 50 single-command moves per hour. The trucks will not be used for any other moves in the facility and, in order to minimize maintenance and training costs, only a single type of truck should be selected.

(b) Explain the potential advantages and potential disadvantages of using the peak demand to determine the number of trucks instead of using the average demand of


6.20. The inventory levels of the products A, B, and C are listed in the table below. How many storage locations are required if a dedicated storage policy is used? How many locations are required if a randomized policy is used? How many are required if a class-based policy is used where Products A and C together form Class I and Product B forms Class II?

Product

Period A B C

1 10 12 7 2 8 9 8 3 9 20 7 4 15 8 3 5 11 5 2 6 8 2 18

Consider the storage area shown below. The I/O port is used for all S/R operations. Products A, B, and C each require 8, 4, and 12 slots, respectively, and have throughput requirements of 25, 13, and 38. Use the DSAP to determine the slot assignments for each product that minimizes the total distance traveled (label the product assigned to each slot). You can assume Assumptions 1–4 of DSAP are satisfied and that the same material handling equipment is used for all S/R operations. Rectilinear travel is used and is measured between the centroids of the slots and the I/O port.

6.21.

I/0

6.22. Consider the storage area shown below. A total of 8 slots, each 10 × 10, are available for the storage of three different products: Products A, B, and C. Two I/O ports are used for all S/R operations: I/O 1, which serves the painting department, and I/O 2, which serves the assembly department. 25% of the S/R operations for each product are to/from the painting department, and 75% are to/from the assembly department. Products A, B, and C each require 2, 3, and 2 slots, respectively, and have throughput requirements of 40, 30, and 36 S/R operations per week, respectively. Use the DSAP to determine the slot assignments for each product. You can assume Assumptions 1–4 of DSAP are satisfied and that the same material handling equipment is used for all S/R operations. Rectilinear travel is used and is measured between the centroids of the slots and the I/O ports.

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I/O 1

I/O 2 6.23. Determine which, if any, assumption(s) of DSAP is(are) likely not to be true if a different

type of material handling equipment is to be used for S/R operations for each different product to be stored in a warehouse. Explain your answer.

6.24. Dedicated storage is used for two products, A and B. Storage is to/from an I/O port located at one end of a one-dimensional rack and each slot in the rack requires 1 ft. Randomized storage is used within the slots dedicated to each product, and the slots can be approximated as a continuous length of rack. Product A has a maximum inventory level of 10 and a throughput requirement of 100 during the period under consideration, and product B has a maximum inventory level of 20 and a throughput requirement of 50 during the period under consideration. Assuming that the total cost of material flow are proportional to the total distance traveled and all S/R cycles are single command, what can the maximum aggregate inventory level for the products be during the period under consideration so that the total cost of material flow does not increase if randomized storage is used for both products instead of dedicated storage?

6.25. What is the average time required for each S/R cycle along a one-dimensional rack 50 ft long if the transport vehicle travels at 100 ft per min., loading or unloading each take 30 sec., one-quarter of the S/R cycles are dual command, and a single I/O port is located 25 ft beyond one of the ends of the rack (i.e., the vehicle must travel 25 ft to reach the rack)?

6.26. Determine the length (X) and width (Y) of the rectangular-shaped storage area that results in the minimum expected travel time given that a maximum of 900 1 × 2 ft loads are to be randomly stored single-deep in the area, a total of 450 single-command S/R cycles take place each 8 hr. shift, the I/O port is located half way along one side of the storage area, aisles and loading/unloading times can be ignored, and all transport vehicles used are identical and travel at 100 ft per min.

6.27. Determine the single-command S/R cycle time of an AS/RS given a storage rack 50 ft long by 30 ft high, with the I/O port located at the bottom end of the rack. The S/R machine travels 10 ft/sec in the horizontal direction and 5 ft/sec in the vertical direction. Loading/unloading takes 30 seconds.

6.28. Determine the maximum number of slots along one side of an aisle in an AS/RS, given that all S/R cycles are single command; the maximum possible average cycle time is 18; the time required to perform either a loading or unloading operation is 1; the horizontal and vertical dimensions of each slot are 9 and 8, respectively; the S/R machine travels at

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horizontal and vertical speeds of 3 and 2, respectively; and the I/O port is located at the bottom end of the rack.

6.29. Determine the maximum number of dual-command S/R cycles that can be completed per hour for an AS/RS. The AS/RS storage rack is 48 ft long by 27 ft high, the I/O port is located at the bottom end of the rack, the S/R machine travels 2 ft/sec in the horizontal direction and 1 ft/sec in the vertical direction, and each loading/unloading takes 5 seconds.

6.30. At the start of the peak hour of operation of an AS/RS, 100 items arrive at the AS/RS’s I/O point. During the hour, the S/R machine is only used to store these items into the racks (i.e., there is no storage or retrieval of other items). The AS/RS storage rack is 54 feet long by 36 feet high, the I/O port is located at the bottom end of the rack, the S/R machine travels 3 ft/sec in the horizontal direction and 2 ft/sec in the vertical direction, and each loading/unloading takes 8 seconds. Determine the number of items that will still be at the I/O point (i.e., not stored) at the end of the peak hour.

6.31. Acme Fine China Corp. receives large bags of powdered bone that it uses to produce its bone china and unassembled boxes to package the finished china. The bags of bone are placed on pallets. Several pallet loads are used each day, but they arrive in large lots because they are shipped from Argentina. The boxes are also placed on pallets and they come in a large variety of different types. Acme produces large batches of each type of china, and the type of china produced varies randomly. Each batch requires several pallet loads of boxes. For the bags of bone and the unassembled boxes, recommend, for each material, a viable material handling equipment alternative to move the material from receiving to storage and at least one storage alternative to store the material. For each alternative, explain why it is preferred to other viable alternatives.

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