inventory management 03

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EngineeringManagement MSE407

Manufacturing Systems

Chapter 6

Single-Stage Inventory Control


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Learning Objectives

Single-stage production systems Independent-demand items

Explain economic order quantity (EOQ) concept

Explain models available for guiding inventoryplanning decisions in various production anddistribution environments

Present a more technical explanation of trade-offs

associated with inventory control

Explain decision models for determining optimalpolicies


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Types of Inventory


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Inventory & inventory system

Inventory is the set of items that an organization holdsfor later use by the organization

An inventory system is a set of policies that monitorsand controls inventory

How much of each item should be kept When low items should be replenished

How many items should be ordered or made whenreplenishment is needed


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Basic types of inventory

Independent demand

Dependent demand

Supplies


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Independent Demand

Independent demanditems are those items that wesell to customers

Dependent demanditems are those items whosedemand is determined by other items.

Demand for a car translates into demand for fourtires, one engine, one transmission, and so on.

The items used in the production of that car (theindependent demand item) are the dependentdemand items

Supplies are items such as copier paper, cleaningmaterials, and pens that are not used directly in theproduction of independent demand items


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Why hold Inventory

1. To decouple work centers

2. To meet variations in demand

3. To allow flexible production schedules

4. As a safeguard against variations in delivery time5. To get a lower price


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Uses of Inventory

Anticipation or seasonal inventory

Safety stock: buffer demand fluctuations

Lot-size or cycle stock: take advantage of quantitydiscounts or purchasing efficiencies

Pipeline or transportation inventory Speculative or hedge inventory protects against some

future event, e.g. labor strike

Maintenance, repair, and operating (MRO) inventories


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Inventory Management Objectives

Provide desired customer service level: Percentage of orders shipped on schedule

Percentage of line items shipped on schedule

Percentage of dollar volume shipped on schedule

Idle time due to material and component shortages Provide for cost-efficient operations:

Buffer stock for smooth production flow

Maintain a level work force

Allowing longer production runs & quantitydiscounts

Minimize inventory related investments:

Inventory turnover

Weeks (or days) of supply


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Customer Service Level Examples

Percentage of Orders Shipped on Schedule Good measure if orders have similar value. Does not capture

value.

If one company represents 50% of your business but only 5%of your orders, 95% on schedule could represent only 50% ofvalue

Percentage of Line Items Shipped on Schedule Recognizes that not all orders are equal, but does not capture

$ value of orders.

More expensive to measure.

Ok for finished goods. A 90% service level might mean shipping 225 items out of thetotal 250 line items totaled from 20 orders scheduled

Percentage Of Dollar Volume Shipped on Schedule Recognizes the differences in orders in terms of both line items

and $ value


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The Coach Motor Home Company has annual cost of goods sold of$10,000,000. The average inventory value at any point in time is $384,615.

Calculate inventory turnover and weeks/days of supply.

Inventory Turnover:

Weeks/Days of Supply:

turns26$384,615

0$10,000,00

valueinventoryaverage

soldgoodsofcostannualTurnover !!!

weeks2

0/52$10,000,00

$384,615

COGSweeklyaverage

valueinventoryaverageSupplyofWeeks !!!

days100/260$10,000,00

$384,615SupplyofDays !!

Inventory Investment MeasuresExample


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Relevant Inventory Costs

Item Cost Cost per item plus any other direct costsassociated with getting the item to the plant

Holding Costs Capital, storage, and risk cost typically stated as a

% of the unit value,e.g. 15-25%

Ordering Cost Fixed, constant dollar amount incurred for eachorder placed

ShortageCosts

Loss of customer goodwill, back order handling,and lost sales


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Determining Order Quantities

Lot-for-lot Order exactly what is needed

Fixed-order

quantity

Order a predetermined amount each time an

order is placed-Q System

Min-max system When on-hand inventory falls below apredetermined minimum level, order enough to

refill up to maximum level

Ordern periods Order enough to satisfy demand for the next nperiods


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Examples of Ordering Approaches

Lot for Lot Example1 2 3 4 6 7 8

Re iremens 70 70 6 60 8 7 8Proec ed on and 30) 0 0 0 0 0 0 0OrderPlacemen 40 70 6 60 8 7 8

Fixed Order Quantity Example with Order Quantity of 200

1 2 3 4 6 7 8Re iremens 70 70 6 60 8 7 8Proec ed on and 30) 160 90 25 165 110 25 150 65OrderPlacemen 200 200 200

Min-Max Example with min.= 50 and max.= 250 units

1 2 3 4 5 6 7 8Re iremens 70 70 65 60 55 85 75 85

Proec ed on and 30) 180 110 185 125 70 165 90 165OrderPlacemen 220 140 180 160

Ordern eriods with n = 3 periods

1 2 3 4 5 6 7 8Requirements 70 70 65 60 55 85 75 85Projected-on-Hand (30) 135 65 0 140 85 0 85 0Order Placement 175 200 160


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Three Mathematical Models forDetermining Order Quantity

Economic Order Quantity (EOQ or Q System)

An optimizing method used for determining orderquantity and reorder points

Part ofcontinuous review system which trackson-hand inventory each time a withdrawal is made

Economic Production Quantity (EPQ)

A model that allows for incremental product delivery

Quantity Discount Model Modifies the EOQ process to consider cases where

quantity discounts are available


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Economic Order Quantity

EOQ Assumptions: Demand is known & constant

- no safety stock is required

Lead time is known &constant

No quantity discounts areavailable

Ordering (or setup) costs areconstant

All demand is satisfied (noshortages)

The order quantity arrives in asingle shipment


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The Economic Order Quantity Model

Assumptions: Production is instantaneous. There is no capacity

constraint and the entire lot is produced simultaneously. Delivery is immediate. There is no time lag between

production and availability to satisfy demand.

Demand is deterministic. There is no uncertainty about thequantity or timing of demand. Demand is constant over time. In fact, it can be

represented as a straight line, so that if annual demand is365units this translates into a daily demand of one unit.

A production run incurs a constant setup cost.

Regardless of the size of the lot or the status of the factory,the setup cost is the same.

Products can be analyzed singly. Either there is only asingle product or conditions exist that ensure reparability ofproducts.


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Notation

D = Demand rate (in units per year).

c=Unit production cost, not counting setup or

inventory costs (in dollars per unit).

A = Constant setup (ordering) cost to produce

(purchase) a lot (in dollars).

h =Holding cost

Q=Lot size (in units); this is the decision variable


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The model

Inventory versus time in the EOQ model


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The model

Average inventory level:

The holding cost per unit:

The setup cost per unit:

The production cost per unit:

2Q!

D

h

D

h

22!

v

!

Q

A!

c!


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Economic order quantity

condition)order(secondfor

conditionorderfirst

002/

02

/

2/

32

2

2

""!

!

!

!

QQ

A

dQ

TimeCostd

h

Q

A

dQ

TimedCost

hQCQATimeCost

Where:A= Fixed cost to place an orderD= Demand rate in units per timeC=Unit purchase cost of producth = Inventory holding cost = lead-time for order delivery

h

AQ

2!


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Total Annual Inventory Cost withEOQ Model

Total annual cost= annual ordering cost + annual holding costs

H

2DSQandH;

2

QS

Q

DTC *Q !

!


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A computer company has annual demand of 10,000. They want to

determine EOQ for circuit boards which have an annual holding cost (H)of $6 per unit, and an ordering cost (S) of $75. They want to calculate TCand the reorder point (R) if the purchasing lead time is 5 days.

EOQ (Q)

ReorderPoint (R)

Total Inventory Cost (TC)

units

6

7*,*!!!

unitsdays*days

,TimeLeadxemandailyR !!!

67,

TC !!

!

Continuous ( ) Review ystemExample


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Economic Production Quantity (EPQ)

Same assumptions as the EOQ except: inventory arrives inincrements & is drawn down as it arrives


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EPQ Equations

Total cost:

Maximum inventory: d=avg. daily demand rate

p=daily production rate

Calculating EPQ

! H2

IS

Q

DTC MAXEPQ

!

p

d1QIMAX

!

p

d1H

2DSEPQ


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Quantity Discount Model

Same as the EOQ, except: Unit price depends upon the quantity ordered

Use the total cost equation:

! H

2

QS

Q

DTCQD PD

Unit Price X Demand


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Quantity Discount Procedure

Calculate the EOQ at the lowest price Determine whether the EOQ is feasible at that price

Will the vendor sell that quantity at that price?

If yes, stop if no, continue

Check the feasibility of EOQ at the next higher price

Continue to the next slide ...


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QD Procedure (continued)

Continue until you identify a feasible EOQ Calculate the total costs (including total item cost) for

the feasible EOQ model

Calculate the total costs of buying at the minimum

quantity required for each of the cheaper unit prices Compare the total cost of each option & choose

the lowest cost alternative

Any other issues to consider?


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Collins Sport store is considering going to a different hat supplier. The

present supplier charges $10 each and requires minimum quantities of490hats. The annual demand is 12,000 hats, the ordering cost is $20, and theinventory carrying cost is 20% of the hat cost, a new supplier is offering hatsat $9 in lots of4000. Who should he buy from?

EOQ at lowest price $9. Is it feasible?

Since the EOQ of 516 is not feasible, calculate the total cost (C) for eachprice to make the decision

4000 hats at $9 each saves $9,320 annually. Space?

hats516$1.80

20)2(12,000)(EOQ $9 !!!hS2

$111,66

012

,000$9

$1.8

02

4000

$2

04000

12,000

C

$120,98012,000$10$22

490$20

490

12,000C

$9

$10

!!

!!

Quantity Discount Example


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Periodic Review Systems

Orders are placed at specified, fixed-time intervals (e.g.every Friday), for a order size (Q) to bring on-handinventory (OH) up to the target inventory (TI), similar to themin-max system.

Advantages are: No need for a system to continuously monitor item

Items ordered from the same supplier can be reviewedon the same day saving purchase order costs

Disadvantages: Replenishment quantities (Q) vary

Order quantities may not qualify for quantity discounts

On the average, inventory levels will be higher than Q

systems-more stockroom space needed


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Single Period Inventory Model

The SPI model is designed for products that share the followingcharacteristics:

Sold at their regular price only during a single-time period

Demand is highly variable but follows a known probability distribution

Salvage value is less than its original cost so money is lost when these

products are sold for their salvage value Objective is to balance the gross profit of the sale of a unit with

the cost incurred when a unit is sold after its primary sellingperiod


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Tee shirts are purchase in multiples of 10 for a charity event for $8 each. When

sold during the event the selling price is $20. After the event their salvage valueis just $2. From past events the organizers know the probability of sellingdifferent quantities of tee shirts within a range from 80 to 120

Payoff Table

Prob. Of Occurrence .20 .25 .30 .15 .10Customer Demand 80 90 100 110 120# of Shirts Ordered Profit

80 $960 $960 $960 $960 $960 $96090 $900 $1080 $1080 $1080 $1080 $1040

Buy 100 $840 $1020 $1200 $1200 $1200 $1083110 $780 $ 960 $1140 $1320 $1320 $1068

120 $720 $ 900 $1080 $1260 $1440 $1026

Sample calculations:Payoff (Buy 110)= sell 100($20-$8) ((110-100) x ($8-$2))= $1140Expected Profit (Buy 100)= ($840 X .20)+($1020 x .25)+($1200 x .30) +

($1200 x .15)+($1200 x .10) = $1083

Single Period Inventory Example


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ABC Inventory Classification

ABC classification is a method for determining levelof control and frequency of review of inventory items

A Pareto analysis can be done to segment items intovalue categories depending on annual dollar volume

A Items typically 20% of the items accounting for80% of the inventory value-use Q system

B Items typically an additional 30% of the itemsaccounting for 15% of the inventory value-use Q or P

C ItemsT

ypically the remaining 50% of the itemsaccounting for only 5% of the inventory value-use P


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Justifying Smaller Order Quantities

JIT or Lean Systems would recommend reducing orderquantities to the lowest practical levels

Benefits from reducing Qs:

Improved customer responsiveness (inventory =Lead time)

Reduced Cycle Inventory

Increase InventoryT

urns Reduced raw materials and purchased components

Justifying smallerEOQs:

Reduce Qs by reducing setup time (S). Setup reduction is awell documented, structured approach to reducing S

H

2!


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Inventory Record Accuracy

Inaccurate inventory records can cause: Lost sales Disrupted operations Poor customer service Lower productivity

Planning errors and expediting

Two methods are available for checking record accuracy Periodic counting-physical inventory Cycle counting-daily counting of pre-specified items

provides the following advantages: Timely detection and correction of inaccurate records Elimination of lost production time due to unexpected

stock outs Structured approach using employees trained in cycle

counting


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Summary

Inventory has several categories and is used to supportdaily operations.

Inventory management intends to provide a desired servicelevel, to allow cost efficient operations, and to minimizeinventory investment.

Inventory performance is measured by turns/supply.

Inventory costs include item cost, holding cost, orderingcost, and shortage cost.

Order Qs can be determined by using L4L, fixed order Qs,min-max, ordern periods, quantity discounts, and singleperiod systems.

Ordering decisions can be improved by analyzing total cost


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Summary (continued)

Smaller lot sizes increase flexibility and reduceresponse time.

Safety stock can be added to reorder point calculationsto meet desired service level.

Inventory decisions about perishable products can bemade by using the single-period inventory model.

ABC analysis can be used to assign the appropriatelevel of control and review frequency based on the

annual dollar volume of each item. Cycle counting of pre-specified items is an accepted

method for maintaining inventory records


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Interactive Workshop (1 of5)

Inventory is:

a) The set of items that an organization holds for lateruse by the organization.

b) The set of policies that monitors and controlsinventory.

c) A tool used to balance capacity and demand

d) All of the above


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The types of costs associated with inventory are:

a) Holding costs, selling costs, ordering costs, andshortage costs

b) Holding costs, buying costs, ordering costs, andshortage costs

c) Holding costs, stocking costs, ordering costs, andshortage costs

d) Item cost, holding cost, ordering costs, andshortage costs


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One of the assumptions of EOQ model is:

a) Delivery is intermediate

b) Production is intermediate and constant

c) Demand is constant over time

d) A production run incurs variable setup costs


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One of the advantages of periodic review systems is:

a) No need for a system to continuously monitor item

b) Replenished quantity (Q) vary

c) Order quantities may quality for quantity discounts

d) Inventory levels will be higher than (Q)


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ABC classification is a method for:

a) Determining level of inventory and production ofinventory items

b) Determining level of control and frequency of reviewof inventory items

c) Determining level of production and frequency ofreview of inventory items

d) None of the above


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Homework Assignment

Page 216 problems 6.1

6.2

6.3

6.7 Read Chapter 7

Pages 221-262


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Questions? Comments?

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