ATHENS – SOCRATES Michal Kavan

The Goals of Managers and OrganizationsManagement is the accomplishment of an organization’s goals by the defining

of goals, organization of work, motivation of others, staffing of the positions, the control of the labor, material and evaluation of completed effort. Management is working with and through other people to accomplish the objectives of both the organization and its members.

1.1 Which are the excellent companies?Eight characteristics of excellent enterprises: Were oriented toward action Learned about the needs of their customers Promoted managerial autonomy and entrepreneurship Achieved productivity by paying close attention to the needs of their people Were driven by a company philosophy often based on the values of their leaders Focused on the business they knew best Had a simple organization structure with a lean staff Were centralized as well as decentralized, depending on appropriateness.

1.2 Productivity, Effectiveness, and EfficiencyAnother way to view the aim of all managers is to say that they must be productive.

Definition of productivity: The output-input ratio within a time period with due consideration for quality. Productivity = outputs / inputs (within a time period, quality considered)Companies use several kinds of inputs, such as labor, materials, and capital.

Peter F. Drucker: one of the most prolific writers in management, observed, “The greatest opportunity for increasing productivity is surely to be found in knowledge work itself, and especially in management”. Productivity implies effectiveness and efficiency in individual and organizational performance.

Effectiveness is the achievement of objectives.Efficiency is the achievement of the ends with the least amount of resources.

1.3 Innovation and EntrepreneurshipThe essence of entrepreneurship is innovation, goal-oriented change to utilize

the enterprise’s potential. As entrepreneurs, managers try to improve the situation. Entrepreneurs have creative ideas; they use their management skills and resources to meet identifiable needs in the marketplace. If successful, an entrepreneur can become wealthy.

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Peter Drucker suggests that innovation applies not only to high-tech companies but equally to low-tech, established business. Worthwhile innovation is not a matter of sheer luck; it requires systematic and rational work, well organized and managed for results.

What does entrepreneurship imply? It suggests dissatisfaction with how things are and an awareness of a need to do things differently. Innovation comes about because of some of the following situations:

1. The unexpected event, failure, or success2. The incongruous-what is assumed and what really is3. The process or task that needed improvement4. Changes in the market or industry structure5. Changes in demographics6. Changes in meaning or in the way things are perceived7. Newly acquired knowledge.

The most successful innovations are often the mundane ones. Take the Japanese, who make minor innovations (providing, for example, little conveniences that customers like) in their cars or in their electronic equipment. James Brian Quinn found in his research that successful large companies are listening carefully to the needs of their customers. They establish teams that search for creative alternatives to serve their customers-but within a limiting framework and with clear goals in mind.

1.4 Change and the Importance of InnovationBecause customer needs and desires as well as competitive offerings are constantly changing, the company needs to innovate continually just to stay even with competition. This means the firm needs to search perpetually for new and improved products, services, and messages to give to the customer. Furthermore, it needs to improve its manufacturing or service delivery process continually. The company that loses its ability to innovate quickly falls behind.

Responsibility - the duty or task to be performed.Authority - the power to act for someone else.Accountability - the obligation to be held responsible for what was expected or what happened that was unexpected.Managerial strategy - the long-term goals and objectives of the enterprise, the allocation of resources, and the adoption of appropriate courses of action (to carry out these goals).Long-range objectives - the owners’ business objectives that extend beyond the current budget cycle of the organization.Policies - general broad guidelines to action that relate to goal attainment.Organizational purpose - the reason the business is in existence. It is the current and future business and can be viewed as the primary objective of the organization.

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2. Functions within Business Organizations

There are three basic functions in typical business organization: finance, marketing, and production/operations. Often the success of an organization depends not only on how well each area performs but also on how well the areas interface with each other.

2.1 MarketingMarketing consists of selling and/or promoting the goods or services of an

organization. Advertising and pricing decisions are made by marketing people. Marketing is also responsible for assessing customer wants and needs, and for communicating those to operations people (short term) and to design people (long term). That is, operations needs information about demand over the short-to-intermediate term so that it can plan accordingly (e.g., purchase materials or schedule work), while design needs information that would relate to improving current products and services and would suggest new ones.

Marketing, design, and production must work closely in order to successfully implement design changes and to develop and produce new products. Marketing can supply information on consumer preferences so that design will know the kinds of products and features needed; operations can supply information about capacities and judge the manufacturability of designs. Operations will also have advance warning if new equipment or skills will be needed for new products or services. Finance people should be included in these exchanges in order to provide information on what funds might be available (short term) and to learn what new funds might be needed for new products or services (intermediate to long term). One important piece of information marketing needs from operations is the manufacturing or service lead time so that customers can be given realistic estimates of how long it will take to fill their orders.

Thus, marketing, operations, and finance must interface on product and process design, forecasting, setting realistic schedules, quality and quantity decisions, and keeping each other informed on the other’s strengths and weaknesses.

2.2 OperationsThe operations function consists of all activities that are directly related to

producing goods or providing services. The production function exists not only in manufacturing and assembly operations, which are goods-oriented, but also in such areas as health care, transportation, food handling, and retailing, which are primarily service-oriented.

The operations function is the core of most business organizations; it is responsible for the creation of an organization’s goods or services. Inputs are used to obtain finished goods or services using one or more transformation processes (e.g.,

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storing, transporting, cutting). To insure that the desired outputs are obtained, measurements are taken at various points in the transformation process (feedback) and then compared to previously established standards to determine if corrective action is needed (control).

2.4 Other FunctionsThere are a host of other supporting functions that interface with operations,

finance, and marketing. Among them are accounting and purchasing. Depending on the nature of the organization, there may also be personnel, product design and development, industrial engineering, and maintenance.

Review Questions: How would you define “management”? Does your definition differ from the one

offered in this book? Explain. What are the managerial functions? How do the required managerial skills differ in the organizational hierarchy? In what fundamental way are the basic goals of all managers at all levels and in

all kinds of enterprises the same? What are some of the characteristics of excellent companies (according to Peters

and Waterman)? Do the companies you know have these characteristics? What are the differences between productivity, effectiveness, and efficiency? How would you define “entrepreneurship”? What does entrepreneurship imply? What are several problems managing innovation? What kind of resources are required to make a change in each component? Why do management analysis and practice require a system approach (Models)? Briefly describe the term Marketing Management, Production/Operations

Management, Purchasing, Personnel, Public relations, Industrial engineering, Maintenance).

Describe the Pareto phenomenon and tell why it is important in problem solving. Identify the three major functional areas of business organizations and briefly

describe how they interrelate. Describe the operations function and the nature of the operations manager’s job. Identify some of the current trends in operations management. Contrast the terms mass production and job shop. What kinds of products does

each system produce?

6. Demand Measurement and Forecasting

The forecasting of sales is a critical input to decision making as well as that of other functional areas such as production, finance, and personnel. Poor forecasting

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can result in excessive inventory, inefficient sales-force expenditures, costly price reductions, lost sales, inefficient scheduling of production, and inadequate planning for Cash flow and capital investments. Business forecasting pertains to more than predicting demand. Forecasts are also used to predict profits, revenues, costs, productivity changes, prices and availability of energy and raw materials, interest rates, movements of key economic indicators (e.g., GNP, inflation, government borrowing), and prices of stocks and bonds, as well as other variables.

6.1 ForecastingForecast can help managers by reducing some of the uncertainty, thereby

enabling them to develop more meaningful plans than they might otherwise.

A forecast is a statement about the future.

6.2 Features common to all forecasts1. The same underlying causal system that existed in the past will continue to exist

in the future.2. Forecasts are rarely perfect; actual results usually differ from predicted values.3. Forecasts for groups of items tend to be more accurate than forecasts for

individual items.4. Forecast accuracy decreases as the time period covered by the forecast-the time

horizon-increases.

There are two general approaches to forecasting:

Qualitative:Judgmental methods:Consumer surveys Questioning consumers on future plans.Sales force composites Joint estimates obtained from salespeople.Executive opinion Finance, marketing, and manufacturing

managers join to prepare forecast.Delphi technique Series of questionnaires answered anonymously

by managers and staff; successive questionnaires are based on information obtained from previous surveys.

Outside opinion Consultants or other outside experts prepare the forecast.

Quantitative:Time series:Naive Next value in a series will equal the previous

value.

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Moving averages Forecast is based on an average of recent values.Exponential smoothing Sophisticated form of averaging.Associative models:Simple regression Values of one variable are used to predict

values of another variable.Multiple regression Two or more variables are used to predict

values of another variable.

6.3 Steps in the Forecasting ProcessThere are five basic steps in the forecasting process:1. Determine the purpose of the forecast and when it will be needed. This will

provide an indication of the level of detail required in the forecast, the amount of resources (manpower, computer time, dollars) that can be justified, and the level of accuracy necessary.

2. Establish a time horizon that the forecast must cover, keeping in mind that accuracy decreases as the time horizon increases.

3. Select a forecasting technique.4. Gather and analyze the appropriate data, and then prepare the forecast. Identify

any assumptions that are made in conjunction with preparing and using the forecast.

5. Monitor the forecast to see if it is performing in a satisfactory manner. If it is not, reexamine the method, assumptions, validity of data, and so on; modify as needed; and prepare a revised forecast.

Moving AveragesA moving average forecast uses a number of the most recent actual data

values in generating a forecast. The moving average forecast can be computed using the following equation:

MAn =

Where i = „Age“ of the data (i = 1,2,3 …)n Number of periods in the moving averageAi Actual value with age i

Exponential Smoothing:Exponential Smoothing is a sophisticated weighted averaging method that is

still relatively easy to use and understand. Each new forecast is based on the previous forecast plus a percentage of the difference between that forecast and the actual value of the series at that point. That is:

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New forecast = Old forecast + a (Actual – Old forecast)

Where α is a percentage and (Actual – Old forecast) represents the forecast error. More concisely,

Ft = Ft-1 + a ( At-1 - Ft-1 )

Where:Ft = Forecast for period tFt-1 = Forecast for period t - 1

α = Smoothing constantAt-1 = Actual demand or sales for period t-1

Trend Equation:A linear trend equation has the form

yt = a + bt

where: t = Specified number of time periods from t = 0yt Forecast for period ta Value of yt at t = 0,b Slope of yt the line

The coefficients of the line, a and b, can be computed from historical data using these two equations:

b = a =

where: n = Number of periodsy = Value of the time series

Techniques for Seasonality:The term seasonal variation is also applied to daily, weekly, monthly, and

other regularly recurring patterns in data.

Centered Moving Average:Computations are the same as for a moving average forecast, as are the

resulting values. However, the values are not projected as in a forecast; instead, they are positioned in the middle of the periods used to compute the moving average.

Simple Linear Regression:The simplest and most widely used form of regression involves a linear

relationship between two variables. The object in linear regression is to obtain an

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equation of a straight line that minimizes the sum of squared vertical deviations of data points from the line.

Correlation measures the strength and direction of relationship between two variables. Correlation can range from -1,0 to + 1,0. A correlation of +1,0 indicates that changes in one variable are always matched by changes in the other; a correlation of -1,0 indicates that increases in one variable are matched by decreases in the other; and a correlation close to zero indicates little linear relationship between two variables. The correlation between two variables can be computed using the equation:

r =

6.5 Accuracy and control of forecastsThere are two aspects of forecast accuracy that have potential significance

then deciding among forecasting alternatives. One is the historical error performance of a forecast, and the other is the ability of a forecast to respond to changes.Two commonly used measures for summarizing historical errors are the mean absolute deviation (MAD) and the mean squared error (MSE). MAD is the average absolute error, and MSE is the average of squared errors. The formulas used to compute MAD and MSE are:

MAD =

MSE =

The sample standard deviation, s, equals the square root of MSE. From a computational standpoint, the difference between these two measures is that one weights all errors evenly (MAD) and the other weights errors according to their squared values (MSE).

Forecasts can be monitored using either tracking signals or control charts. A tracking signal focuses on the ratio of cumulative forecast error to the corresponding value of MAD:

Tracking signal =

The resulting values are compared to predetermined limits. These are based on judgment and experience and often range from ± 3 to ± 8. We shall use limits of ± 4 for the most part. These are roughly comparable to three standard deviation limits. Values within the limits suggest – but do not guarantee – that the forecast is performing adequately. After an initial value of MAD has been computed, MAD can be updated using exponential smoothing:

MADt = MADt-1 + α (│Actual - Forecast│t - MADt-1)

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The control chart approach involves setting upper and lower limits for individual forecast errors (instead of cumulative errors, as is the case with a tracking signal). The limits are multiples of the square root of MSE. This method assumes the following:

a) Forecast error are randomly distributed around a mean of zero.b) The distribution of errors is normal.

In effect, the square root of MSE is an estimate of the standard deviation of the distribution of errors. That is: s = .

Selection of a forecasting technique involves choosing a technique that will serve the intended purpose at an acceptable level of cost and accuracy.

Review Questions:1. Outline the steps in the forecasting process.2. What are the main advantages that quantitative techniques for forecasting have

over qualitative techniques? What limitations do quantitative techniques have?3. What is the purpose of establishing control limits for forecasts?4. Outline the features common to all forecasts.5. Describe at least four qualitative forecasting techniques and the advantages and

disadvantages of each.6. What advantages does exponential smoothing have over moving averages as a

forecasting tool?7. How does the number of periods in a moving average affect the responsiveness

of the forecast?8. What factors enter into the choice of a value for the smoothing constant in

exponential smoothing?

Logistics:

Logistics refers to the movement of materials within a production facility and to incoming and outgoing shipments of goods and materials.The numerous instances of materials movement include:

From incoming vehicles to receiving. From receiving to storage. From storage to the point of use (e.g., work center, office, maintenance). From one work center to the next, or to temporary storage. From the last operation to final storage. From storage to packaging/shipping. From shipping to outgoing vehicles.

Movement of materials must be coordinated to arrive at the appropriate destinations at appropriate times. Care must be taken so that items are not lost, stolen, or damaged during movement.Traffic management – overseeing the shipment of incoming and outgoing goods.

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Bar codes – patterns of black lines and white spaces that can be read by scanning devices, containing a variety of information.Distribution is the shipping of goods from the company through a distribution system to warehouses, retail customers, or final customers.

Review Questions:

Define materials and briefly describe the materials management function.

Describe how purchasing interfaces with other areas of the organization and with suppliers.

Outline the objectives of purchasing. Describe the purchasing cycle, especially determination of price and

sources of supply. Discuss the issue of centralized purchasing versus decentralized

purchasing. Describe and discuss value analysis. Discuss the importance of good vendor relations. Discuss the logistics aspects of materials management.

Just-in-Time Systems Just-in-time (JIT) is a system of lean production used mainly in repetitive

manufacturing, in which goods move through the system and tasks are completed just in tie to maintain the schedule. Such systems require very little inventory because successive operations are closely coordinated.

Lean systems require that sources of potential disruption to the even flow of work eliminated. High quality is stressed because problems with quality can disrupt the process. Quick, low-cost setups; special layouts; allowing work to be pulled through the system rather than pushed through; and a spirit of cooperation are all important features of lean systems. So, too, are problem solving aimed at reducing disruptions and making the system more efficient, and an attitude of working toward continual improvement.

Key benefits of JIT / lean systems are reduced inventory levels, high quality, flexibility, reduced lead times, increased productivity and equipment utilization, reduced amounts of scrap and rework, and reduced space requirements.

JIT differs in many ways from traditional systems The benefits of JIT systems have attracted the attention of Czech manufacturers, causing many to consider converting their operations to JIT. In doing so, careful attention must be given to obtaining the support of top management, achieving a cooperative spirit throughout

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the organization, reducing setup times, and establishing good relationships with a small number of vendors.

The JIT approach was developed at the Toyota Motor Company of Japan by Mr. Taiichi Ohno (vice president of manufacturing) and several of his colleagues. The development of JIT in Japan was probably influenced by the fact that Japan is a crowded country with few natural resources. JIT systems are designed to achieve a smooth flow of production using minimal inventories. The systems are fairly flexibly, with a high degree of worker participation in problem solving, continuous improvement, and attention to detail. However, the most important aspect of a JIT system is that quality is built into the system.

High quality is a prerequisite for this system; no other element is as critical. The key elements of the system are these:

a) Production smoothing.b) High quality levels.c) Low inventories.d) Small lot sizes.e) Quick, low-cost setups.f) Layout.g) Preventive maintenance and repair.h) Multifunctional workers.i) A cooperative spirit.j) Few, reliable suppliers.k) A pull system of moving goods.l) Continual improvement.m) Problem solving.

The terms push and pull are used to describe two different systems for moving work through a production process. In a push system, when work is finished at a workstation, the output is pushed to the next station; or, in the case of the final operation, it is pushed on to final inventory. Conversely, in a pull system, control of moving the work rests with the following operation; each workstation pulls the output from the preceding station as it is needed; output of the final operation is pulled by customer demand or the master schedule.

Thus, in a pull system, work is moved in response to demand from the next stage in the process, whereas in a push system, work is pushed on as it is completed, with no regard for whether the next station is ready for the work. Consequently, work may pile up at workstations that fall behind schedule, say, because of equipment failure or the detection of a problem with quality.

„Just-in-time“, Lean Manufacture“, „World-Class Manufacturing“ … all these labels describe excellence in manufacturing. Precise and universally accepted

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definitions of these terms are hard to come by. But there is general agreement that all these concepts have eight objectives in common, at least:

1) Low inventory2) Short throughput time3) Reliable delivery performance4) Rapid response capability5) Low reject and rework percentages6) Committed trained workforce7) Customer focus8) Continuous improvement.

Very few companies achieve all of these objectives, though many are striving to do so. Normally they find that by addressing one of them they are impacting on another. So the pace of change increases. The point is to make a deliberate start. Just-in-Time in factory can be introduced and developed by the following eight efforts:

Reduce the lead time - the time it takes from launching the batch of work into the first operation queue to the time it is available for sale to the customer.

Reduce the batch size - the number of items that travel together through the factory.

Reduce work – in – progress - the number of batches available to be worked on at all the operations in the factory.

Don’t launch a batch of work until you have to Minimize the distance between operations - the distance a batch travels on its

journey through the factory. Make operators responsible for their work quality - rather than leaving it to a

separate quality control section. Integrate testing into the production process. Make labor, processes and machines available when and where the work is -

capacity availability and machine reliability.All these efforts are geared to creating smooth flow in the factory.

In some systems the Kan Ban linkage is between the slowest operation (bottleneck), no matter where it is, and the release of a batch to the first operation in the production system. The principle is based on ‘bottleneck’ or ‘constraint’ management theory. Its guiding rule: If you identify the slowest operation, the capacity upstream and downstream of that slowest operation will be greater than the ‘bottleneck’. Consequently, the system can deliver to or consume from the ‘bottlenecks’ at a faster rate than the ‘bottleneck’ can consume or deliver. So the imperative is clear: as the ‘bottleneck’ limits the throughput of the system – it must work to maximum utilization and must never be starved of work. If you release into the system at the consumption rate of the ‘bottleneck’, then there will always be

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work for it. Batch reduction and bottleneck focus are crucial. But they can be enhanced by space compression!These control principles are simple in essence. But they are complex in application. They require in-depth treatment in their own right and will be the subject of a later video.

Kanban is a Japanese term that means signal or visible record. When a worker needs materials or work from the preceding station, he or she uses a kanban card to communicate this. In effect, the kanban card is the authorization to move or work on parts. In kanban systems, no part or lot can be moved or worked on without one of these cards. The system works this way:

A kanban card is affixed to each container. When a workstation needs to replenish its supply of parts, a worker goes to the area where these parts are stored and withdraws one container of parts. Each container holds a predetermined quantity. The worker removes the kanban card from the container and posts it in a designated spot where it will be clearly visible, and the worker then moves the lot to the workstation. The posted kanban is then picked up by a stock person who replenishes the stock with another container, and so on down the line.

Demand for parts triggers a replenishment, and parts are supplied as usage dictates. Similar withdrawals and replenishments occur all the way up and down the line from vendors to finished-goods inventories, all controlled by kanbans. In fact, if supervisors decide the system is too loose because inventories are building up, they may decide to withdraw some kanbans, thereby tightening the system. Conversely, if the system seems too tight, additional kanbans may be introduced to bring the system into balance.

Important questions: What is the impact of halving the batch size? On lot delay? On throughput time? On set-ups? What is the impact of halving the set-up time? On throughput time? Can you identify major contributors to queue time? How many line items does your manufacturing store carry? How many products do you produce? How many customers do you have? How many suppliers do you have? What is the total value of purchases of materials and components? What is the expenditure on the top 10% of your suppliers? How many suppliers make up this 10%? What % of total purchases does this represent? How many times have these suppliers been visited in the last year?

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What is the value of raw materials? What is the value of work-in-progress? What is the value of finished goods? What is the value of inventory? What is the direct cost of annual production? What is the work-in-progress turn ratio?

Inventory ManagementGood inventory management is often the mark of a well-run organization. The

models described in this chapter are relevant for instances where demand for inventory items is independent. Three classes of models are described: EOQ, ROP, and fixed-interval. These are all appropriate if unused items can be carried over into subsequent periods. The single-period model is appropriate when items cannot be carried over.

EOQ models address the question of how much to order. The ROP models address the question of when to order and are particularly helpful in dealing with situations that include variations in either demand rate or lead time. ROP models involve service level and safety stock considerations. When the time between orders is fixed, the FOI model is useful. An inventory is a stock or store of goods.

Many firms stock hundreds or even thousands of items. Raw materials, purchased parts, partially completed items, and finished goods, as well as spare parts for machines, tools, and other supplies.Inventories serve a number of important functions. Among the most salient reasons for holding inventories are the following:

To meet anticipated demand. To smooth production requirements. To decouple components of the production-distribution system. To protect against stock-outs. To take advantage of order cycles. To hedge against price increases, or to take advantage of quantity discounts. To permit operations.

The overall objective of inventory management is to achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds. Toward this end, the decision maker’s problem is to achieve a balance in stocking, avoiding both overstocking and under stocking. The two fundamental decisions that must be made relate to the timing and under stocking. The two fundamental decisions that must be made relate to the timing and size of orders (i.e., when to order and how much to order).

To be effective, management must have the following: A system to keep track of the inventory on hand and on order.

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A reliable forecast of demand that includes an indication of possible forecast error.

Knowledge of lead times and lead time variability. Reasonable estimates of inventory holding costs, ordering costs, and

shortage costs. A classification system for inventory items.

Periodic system – physical count of items in inventory made at periodic intervals (weekly, monthly).

Perpetual inventory system – System that keeps track of removals from inventory continuously, thus monitoring current levels of each item.

Two-bin system – two containers of inventory; reorder when the first is empty.Universal product code (UPC) – bar code printed on a label that has information about the item to which it is attached.

Holding (carring) costs relate to physically holding items in storage. They include interest, insurance, taxes, depreciation, obsolescence, deterioration, spoilage, pilferage, breakage, and warehousing costs (heat, light, rent, security). Holding costs also include opportunity costs associated with having funds tied up in inventory that could be used elsewhere.

Ordering costs are the costs associated with ordering and receiving inventory. These include determining how much is needed, typing up invoices, inspecting goods upon arrival for quality and quantity, and moving the goods to temporary storage. Ordering costs are generally expressed as a fixed dollar amount per order, regardless of order size.

Shortage costs result when demand exceeds the supply of inventory on hand. These costs can include the opportunity cost of not making a sale, loss of customer goodwill, lateness charges, and similar costs. Furthermore, if the shortage occurs in an item carried for interval use (e.g., to supply an assembly line), the cost of lost production or downtime is considered a shortage cost.

16.1 How much to order: Economic order quantity models:

The question of how much to order is frequently determined by using an economic order quantity (EOQ) model. EOQ models identify the optimal order quantity in terms of minimizing the sum of certain annual costs that vary with order size. Three order size models are described in the following sections:A. The economic order quantity model.B. The order quantity model with noninstantaneous delivery.C. The quantity discount model.

A. Basic economic order quantity (EOQ) model :

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Annual carrying cost is computed by multiplying the average amount of inventory on hand by the cost to carry one unit for a year, even though any given unit would not be held for a year.

Annual carrying cost = H Annual ordering cost = S

The total annual cost (TC) associated with carrying and ordering inventory when Q units are ordered each time is:

TC = H + S

Where: D = Demand, usually in units per yearQ = Order quantity, in unitsS  = Ordering cost, in dollarsH = Carrying cost, usually in dollars per unit per year.

(D, H in the same units).Thus, Q0:

1.

2. 0 = H/2 – DS/Q2, so Q2 = or

Q0 =

Number of orders per year: D/ Q0 and Length of order cycle: Q0/D .

B. The order quantity model with noninstantaneous delivery:The basic EOQ model assumes that orders are delivered as whole units at a

single point in time (instantaneous replenishment). However, in some instances such as when a firm is both a producer and user, or when deliveries are spread over time, inventories tend to build up gradually instead of instaneously. When a company makes the product itself, there are no ordering costs as such. Nonetheless, with every run there are setup costs – costs required to prepare the equipment for the job, such as cleaning, adjusting, and changing tools and fixtures. These are analogous to ordering costs.The number of runs is D/Q, and the annual setup cost is equal to the number of runs per year times the setup cost per run: (D/Q)S.Total cost is:

TCmin = Carrying cost + Setup cost =

Imax = maximum inventory

The economic run quantity is: Q0 =

where: p = Production or delivery rateu = Usage rate

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The maximum and average inventory levels are: Imax = and Iprům =

The cycle time (the time between orders, or between the beginnings of runs) for the economic run size is a function of the run size and usage (demand) rate:

Cycle time =

Similarly, the run time (the production time) is a function of the run size and the production rate:

Run time =

C. The quantity discount model.Quantity discounts are price reductions for large orders offered to customers

to induce them to buy in large quantities.If quantity discounts are offered, the customer must weigh the potential benefits of reduced purchase price and fewer orders that will result from buying in large quantities against the increase in carrying costs caused by higher average inventories. Hence, the buyer’s goal in the case of quantity discounts is to select the order quantity that will minimize total cost, where total cost is the sum of carrying cost, ordering cost, and purchasing cost:

TC = Carrying cost + Ordering cost + Purchasing cost

TC = where: P … unit price

16.2 When to reorder:EOQ models answer the question of how much to order, but not the question

of when to order. The latter is the function of models that identify the reorder point (ROP) in terms of a quantity: the reorder point occurs when the quantity on hand drops to a predetermined amount. That amount generally includes expected demand during lead time and perhaps an extra cushion of stock, which serves to reduce the probability of experiencing a stock-out during lead time. We will consider reorder point models for these cases:

Constant demand rate, constant lead time. Variable demand rate, constant lead time. Constant demand rate, variable lead time. Variable demand rate, variable lead time.

The following symbols are used in the various models:d = Constant demand rate, LT = Constant lead time,

= Average demand rate, = Average lead time,d = Standard deviation of demand rate or forecast error,LT = Standard deviation of lead time.

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Constant demand rate, constant lead time. Variable demand rate, constant lead time.

ROP = Expected demand during lead time + Safety stock= LT + z (d)

where: z = Number of standard deviation from the meanThe standard deviation of lead time demand is (d).

Constant demand rate, variable lead time.In this case, the expected demand during lead time is equal to d , and the

standard deviation of demand during lead time is equal to dLT.The reorder point is: ROP = d + zdLT.

where: d = Constant demand rate, = Average lead time, LT = Standard deviation of lead time.

Variable demand rate, variable lead time.Standard deviation of total demand during lead time = where: demand =

lead time = Hence:

dLT = = ROP =

Review Questions:1. What are the primary reason for holding inventory?2. What are the requirements for effective inventory management?3. Briefly describe each of the costs associated with inventory.4. Contrast independent and dependent demand with respect to inventories.5. List the major assumptions of the EOQ model.6. Why isn’t price considered explicity in the basic EOQ model? What are

quantity discounts? What three costs enter into the order quantity decision when discounts are available?

7. What is safety stock, and why is it held?8. What is meant by the term service level?9. Generally speaking, how is service level related to the amount of safety

stock held?10.Describe briefly the A,B,C approach to inventory control.

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