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Chapter 7:

Inventory Decision Making


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Chapter 7 Management of Business Logistics, 7th Ed. 2

Learning Objectives - After reading this

chapter, you should be able to do the following:

Understand the fundamental differencesamong approaches to managing inventory.

Appreciate the rationale and logic behind theEconomic Order Quantity (EOQ) approach toinventory decision making, and be able tosolve some problems of a relatively

straightforward nature.

Understand alternative approaches tomanaging inventory --- JIT, MRP, and DRP.


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Learning Objectives Realize how variability in demand and order

cycle length affects inventory decision

making. Know how inventory will vary as the number

of stocking points decreases or increases.

Recognize the contemporary interest in andrelevance of time-based approaches toinventory management.


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Learning Objectives Make needed adjustments to the basic EOQ

approach to respond to several special types

of applications.


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Fundamental Approaches to

Managing Inventory Basic issues are simplehow much to order

and when to order.

Additional issues arewhere to store inventoryand what items to order. Traditionally, conflicts were usually presentas

customer service levels increased, investment

in inventory also increased. Recent emphasis is on increasing customer

service and reducing inventory investment.


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Fundamental Approaches to

Managing Inventory Four factors might permit this apparent

paradox, that is, the firm can achieve higher

levels of customer service without actuallyincreasing inventory:

More responsive order processing

Ability to strategically manage logistics data

More capable and reliable transportation

Improvements in the location of inventory


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Figure 7-1 Relationship between

Inventory and Customer Service Level


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Key Differences among Approaches

to Managing Inventory Dependent versus Independent Demand

Dependent demand is directly related to the

demand for another product. Independent demand is unrelated to the

demand for another product.

For many manufacturing processes, demand

is dependent. For many end-use items, demand is

independent.


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to Managing Inventory Of the inventory management processes in

this chapter, JIT, MRP and MRPII are

generally associated with items havingdependent demand.

Alternatively, DRP and the EOQ models aregenerally associated with items exhibiting

independent demand.


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to Managing Inventory Pull versus Push

Pull approach is a reactive system, relying

on customer demand to pull productthrough a logistics system. MacDonalds isan example.

Push approach is a proactive system, anduses inventory replenishment to anticipatefuture demand. Catering businesses areexamples of push systems.


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to Managing Inventory Pull versus Push

Pull systems respond quickly to sudden or

abrupt changes in demand, involve one-waycommunications, and apply more toindependent demand situations.

Push systems use an orderly and disciplinedmaster plan for inventory management, andapply more to dependent demandsituations.


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On the Line:

American Cancer Society ACS constructed a world class automated order

fulfillment center in Atlanta.

Order cycle time was reduced to five businessdays.

Centralized storage reduced waste andobsolescence of educational materials.

Centralized shipment reduced freight rates. The new center saved $8 million in the first year

alone.


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Fixed Order Quantity Approach

(Condition of Certainty): Inventory Cycles In this example, each cycle starts

with 4,000 units:

Demand is constant at the rateof 800 units per day.

When inventory falls below 1,500 units, anorder is placed for an additional 4,000 units.

After 5 days the inventory is completely used. Just as the 4,000th unit is sold, the next order

of 4,000 units arrives and a new cycle begins.


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Figure 7-2 Fixed Order Quantity

Model under the Condition of Certainty


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Fixed Order Quantity Approach (Conditionof Certainty): Simple EOQ Model

Simple EOQ Model Assumptions

Continuous, constant, known and infinite rate

of demand on one item of inventory. A constant and known replenishment time.

Satisfaction of all demand.

Constant cost, independent of order quantityor time.

No inventory in transit costs.

No limits on capital availability.


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Simple EOQ Model Variables

R = annual rate of demand

Q = quantity ordered (lot size in units) A = order or setup cost

V = value or cost of one unit in dollars

W = carrying cost per dollar value in percent

S = VW = annual storage cost in $/unit per year

t = time in days

TAC = total annual costs in dollars per year


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Figure 7-3Inventory Carrying Cost


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Figure 7-4Order or Setup Cost


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Figure 7-5Inventory Costs


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TAC = QVW +AR or TAC = QS +AR

2 Q 2 Q

First term is the average carrying cost

Second term is order or setup costs per year


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Figure 7-6Sawtooth Model


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TAC = QVW +AR or TAC = QS +AR

2 Q 2 Q

Solving for Q gives the following expressions:

Q= 2 RA or Q = 2RA or Q = 2RAVW or S VW S


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Where R = 3600 units V = $100; W = 25%;S (or VW)= $25; A = $200 per order

Q= 2 RA or Q = 2RA or Q = 2RAVW or S VW S

2*3600*$200 2*3600*$200$100*25% $25

Q = 240 units Q = 240 units


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Figure 7-7Sawtooth Models


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Table 7-1Total Costs for Various EOQ Amounts


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Figure 7-8 Graphical Representation ofthe EOQ Example


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Fixed Order Quantity Approach(Condition of Certainty)

Summary and Evaluation of theFixed Order Quantity Approach:

EOQ is a popular inventory model. EOQ doesnt handle multiple locations as well as a

single location.

EOQ doesnt do well when demand is not constant.

Minor adjustments can be made to the basic model.

Newer techniques will ultimately take the place of EOQ.


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Fixed Order Quantity Approach(Condition of Uncertainty)

Uncertainty is a more normal condition.

Demand is often affected by exogenous

factors---weather, forgetfulness, etc. Lead times often vary regardless of carrier

intentions.

Examine out Figure 7-9. Note the variability in lead times and

demand.


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Figure 7-9 Fixed Order Quantity Modelunder Conditions of Uncertainty


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Reorder Point A Special Note

With uncertainty of demand, the reorder

point becomes the average daily demandduring lead time plus the safety stock.

Examine Figure 7-9 again.


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Uncertainty of Demand Affects Simple EOQModel Assumptions:

a constant and known replenishment time.

constant cost/price, independent of orderquantity or time.

no inventory in transit costs.

one item and no interaction amongthe inventory items.

infinite planning horizon.

no limit on capital availability.


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Table 7-2 Probability Distributionof Demand during Lead Time

Demand Probability

100 units 0.01

110 0.06

120 0.24

130 0.38

140 0.24150 0.06

160 0.01

bl bl f


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Table 7-3 Possible Units of InventoryShort or in Excess during Lead Time withVarious Reorder Points

ActualDemand

Reorder Points

100 110 120 130 140 150 160

100 0 10 20 30 40 50 60110 -10 0 10 20 30 40 50

120 -20 -10 0 10 20 30 40

130 -30 -20 -10 0 10 20 30

140 -40 -30 -20 -10 0 10 20

150 -50 -40 -30 -20 -10 0 10

160 -60 -50 -40 -30 -20 -10 0

bl 3 bl f


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Table 7-3 Possible Units of InventoryShort or in Excess during Lead Time withVarious Reorder Points

ActualDemand

Proba-bility

Reorder Points

100 110 120 130 140 150 160

100 0.01 0.0 0.1 0.2 0.3 0.4 0.5 0.6

110 0.06 -0.6 0 0.6 1.2 1.8 2.4 3.0

120 0.24 -4.8 -2.4 0 2.4 4.8 7.2 9.6

130 0.38 -11.4 -7.6 -3.8 0 3.8 7.6 11.4140 0.24 -9.6 -7.2 -4.8 -2.4 0 2.4 4.8

150 0.06 -3.0 -2.4 -1.8 -1.2 -0.6 0 0.6

160 0.01 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0


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Table 7-4 Calculation of Lowest-Cost Reorder Point

Dmnd 100 110 120 130 140 150 160

(e) 0.0 0.1 0.8 3.9 10.8 20.1 30.0

(VW) 0 $2.50 $20 $97.50 $270 $502.50 $750

(g) 30 20.1 10.8 3.9 0.8 0.1 0.0

G=gw $300 $201 $108 $39 $8 $1 $0

GR/Q $4500 $3015 $1620 $585 $120 $15 $0

TAC $4500 $3018 $1640 $682.50 $390 $517.50 $750


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Fixed Order Quantity Approach (Conditionof Certainty): Expanded EOQ Model

Where R = 3600 units V = $100; W = 25%;A = $200 per order; G = 8

Q= 2 R(A + G)VW

2 * 3600 * ($200 + 8)$100 * 25%

Q = approximately 242 units


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Fixed Order Quantity Approach (Conditionof Certainty): Expanded EOQ Model

Where R = 3600 units V = $100; W = 25%;A = $200 per order; G = 8; Q = 242; e = 10.8

TAC = QVW + AR + eVW + GR

2 Q Q

TAC = (242*$100*25%) + (200*3600) + (10.8*$100*25%) + (8*3600)

2 242 242

TAC = $3025 + $2975 + $270 + $119

TAC = $6389 (New value for TAC when uncertainty introduced)


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Fixed Order Quantity Approach (Conditionof Uncertainty): Conclusions

Following costs will rise to cover the uncertainty:

Stockout costs.

Inventory carrying costs of safety stock

Results may or may not be significant.

In text example, TAC rose $389 or

approximately 6.5%. The greater the dispersion of the probability

distribution, the greater the cost disparity.


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Figure 7-10Area under the Normal Curve


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Table 7-5 Reorder Point Alternatives andStockout Possibilities


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Fixed Order Interval Approach

A second basic approach

Involves ordering at fixed intervals and

varying Q depending upon the remainingstock at the time the order is placed.

Less monitoring than the basic model

Examine Figure 7-11.

Amount ordered over each five weeks in theexample varies each week.


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Figure 7-11 Fixed Order Interval Model(with Safety Stock)


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Summary and Evaluation of EOQApproaches to Inventory Management

Four basic inventory models:

Fixed quantity/fixed interval

Fixed quantity/irregular interval

Irregular quantity/fixed interval

Irregular quantity/irregular interval

Where demand and lead time are known,

basic EOQ or fixed order interval model best. If demand or lead time varies, then safety

stock model should be used


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Relationship to ABC analysis

A items suited to a fixed quantity/irregular

interval approach.C items best suited to a irregular

quantity/fixed interval approach.

Importance of trade-offs Familiarity with EOQ approaches assists the

manager in trade-offs inherent in inventorymanagement.


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New concepts

JIT, MRP, MRPII, DRP, QR, and ECR also take

into account a knowledge and understandingof applicable logistics trade-offs.

Number of DCs

The issue of inventory at multiple locations in alogistics network raises some interestingquestions concerning the number of DCs, theSKUs at each, and their strategic positioning.


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Additional Approaches toInventory Management

Three approaches to inventory managementthat have special relevance to supply chain

management: JIT (Just in Time)

MRP (Materials Requirements into Planning)

DRP (Distribution Resource Planning)


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Time-Based Approaches toReplenishment Logistics: JIT

Definition and Components of JIT Systems - designedto manage lead times and eliminate waste.

Kanban - refers to the informative signboards oncarts in a Toyota system of delivering parts to theproduction line. Each signboard details the exactquantities and necessary time of replenishment.

JIT operations - Kanban cards and light warning

system communicate possible productioninterruptions.

Fundamental concepts - JIT can substantially reduceinventory and related costs.


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Definition and Components of JIT Systems -designed to manage lead times and eliminatewaste.

Goal is zero inventory, and zero defects.

Similarity to the two-bin system - one binfills demand for part, the other is used when

the first is empty. Reduces lead times through requiring small

and frequent replenishment.


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JIT is a widely used and effective strategy formanaging the movement of parts, materials,

semi-finished products from points of supplyto production facilities.

Product should arrive exactly when a firmneeds it, with no tolerance for early or late

deliveries. JIT systems place a high priority on short,

consistent lead times.


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JIT versus EOQ Approaches toInventory Management

Six major differences:

First, JIT attempts to eliminate excess

inventories for both buyer and seller. Second, JIT systems involve short

production runs with frequentchangeovers.

Third, JIT minimizes waiting lines bydelivering goods when and where needed.


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JIT versus EOQ Approaches toInventory Management

Fourth, JIT uses short, consistent leadtimes to satisfy inventory needs in a timelymanner.

Fifth, JIT relies on high-quality incomingproducts and on exceptionally high-qualityinbound logistics operations.

Sixth, JIT requires a strong, mutualcommitment between buyer and seller,emphasizing quality and win-win outcomesfor both partners.


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Table 7-6 EOQ versus JIT Attitudes andBehaviors


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JIT versus Traditional Inventory Management

Reduces excess inventories

Shorter, more frequent production runs Minimize waiting lines by delivering materials when

and where needed

Short, consistent lead times through proximate

location Quality stressed throughout supply chain

Win-win relationships necessary to a healthy supplychain


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Examples of JIT Successes: Apple Computers increase in IT from 10 weeks

to 2 weeks resulted in 18-month $20 million

payback on plant. GM increased production by 100%, but

inventories increased by only 6%.

Norfolk Southern mini-train hauls direct from

one GM plant to another without switchingdelays.

Ryder handles all inbound logistics for Saturn.


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Figure 7-12The Orderly Pickup Concept


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Time-Based Approaches toReplenishment Logistics: MRP

A Materials Requirements Planning (MRP)system consists of a set of logically related

procedures, decision rules, and recordsdesigned to translate a master productionschedule into time-phased net inventoryrequirements for each component item

needed to implement this schedule. MRPs re-plan net requirements based on

changes in schedule, demand, etc.


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Goals of an MRP:

Ensure the availability of materials,

components, and products forplanned production.

Maintain lowest possible inventorylevel.

Plan manufacturing activities, deliveryschedules, and purchasing activities.


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Key elements of an MRP:

Master production schedule

Bill of materials file Inventory status file

MRP program

Outputs and reports


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Figure 7-13An MRP System

Master Production Schedule

MRP Program

Output and Reports

Bill of Material File Inventory Status File

Customer Orders Demand Forecasts


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Figure 7-14 Relationship of Parts to FinishedProduct: MRP Egg Timer Example

1 Egg Timer

2 Ends 1 Bulb 3 Supports

1 Gram of Sand


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Table 7-7 Inventory Status File:MRP Egg Timer Example

Product Gross Req. Inventory Net Req. Lead Time

Egg Timers 1 0 1 1

Ends 2 0 2 5

Supports 3 2 1 1

Bulbs 1 0 1 1

Sand 1 0 1 4


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Figure 7-15 Master Schedule: MRPEgg Timer Example


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Principal advantages of MRP:

Maintain reasonable safety stock.

Minimize or eliminate inventories. Identification of process problems.

Production schedules based on actualdemand.

Coordination of materials ordering. Most suitable for batch or intermittent

production schedules.

d h


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Principal shortcomings of MRP:

Computer intensive.

Difficult to make changes once operating. Ordering and transportation costs may rise.

Not usually as sensitive to short-term

fluctuations in demand. Frequently become quite complex.

May not work exactly as intended.


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Time-Based Approaches to ReplenishmentLogistics: Distribution Resource Planning

MRP sets a master production schedule andexplodes into gross and net requirements.

DRP starts with customer demand and worksbackwards toward establishing a realisticsystem-wide plan for ordering the necessaryfinished products.

Then DRP works to develop a time-phasedplan for distributing product from plants andwarehouses to the consumer.


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Time-Based Approaches to ReplenishmentLogistics: Distribution Resource Planning

DRP develops a projection for each SKU andrequires17:

Forecast of demand for each SKU.

Current inventory level for each SKU.

Target safety stock.

Recommended replenishment quantity.

Lead time for replenishment.

T bl 7 8 DRP T bl f


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Table 7-8 DRP Table forChicken Noodle Soup

Columbus Distribution CenterDistribution Resource Planning

Month January February March

Week 1 2 3 4 5 6 7 8 9

CN Soup Current BOH=4314; Q=3800; SS=1956; LT=1

Forecast 974 974 974 974 989 1002 1002 1002 1061

Schedule

Receipt

0 0 3800 0 0 0 3800 0 0

BOH-End 3340 2366 5192 4218 3229 2227 5025 4023 2962

PlannedOrder

0 3800 0 0 0 3800 0 0 3800


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Figure 7-16Combining DRP Tables

I t t M lti l L ti


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Inventory at Multiple LocationsThe Square Root Law (SQL)

Used to reduce inventory at multiple locations.

As locations increase, inventory also increases,

but not in the same ratio as the growth infacilities.

The square root law (SRL) states that totalsafety stock can be approximated by

multiplying the total inventory by the squareroot of the number of future facilities dividedby the current number of facilities.

I t t M lti l L ti


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Inventory at Multiple LocationsThe Square Root Law

X2= (X1) * (n2/n1) Where:

n1 = number of existing facilities

n2 = number of future facilities

X1= total inventory in existing facilities

X2 = total inventory in future facilities


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Square Root Law Example

Current distribution 40,000 units

Eight facilities shrinking to two

Using the square root law:

X2= (40,000) *(2/8) X2 = 20,000 units

Table 7-9 Example Impacts of Square Root Law


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Table 7 9 Example Impacts of Square Root Lawon Logistics Inventories

Warehouses n Total Av Inv % Change

1 1.0000 3,885 ---

2 1.4142 5,494 141%

3 1.7321 6,729 173%

4 2.0000 7,770 200%5 2.2361 8,687 224%

10 3.1623 12,285 316%

15 3.8730 15,047 387%

20 4.4721 17,374 447%

23 4.7958 18,632 480%

25 5.0000 19,425 500%


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Figure 7-17 Four Directions forReplenishment Logistics


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Time-Based Approaches to ReplenishmentLogistics: Quick Response (QR)

Structure of QR

Shorter, compressed time horizons.

Real-time information available by SKU. Seamless, integrated logistics networks

with rapid transportation, cross-dockingand effective store receipt and distribution

systems.


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Time-Based Approaches to ReplenishmentLogistics: Quick Response (QR)

Structure of QR

Partnership relationships present among

supply chain members. Redesign of manufacturing processes to

reduce lot sizes, changeover times andenhanced flexibility.

Commitment to TQM.


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Figure 7-18Basic Elements of Quick Response (QR)

d h l h


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Time-Based Approaches to ReplenishmentLogistics: Efficient Consumer Response (ECR)

Structure of ECR Grocery industry estimates U.S. savings at

approximately $30 billion.

Ultimate goal is a responsive, consumer-drivensystem in which distributors and suppliers worktogether as business allies to maximize consumersatisfaction and minimize cost. Accurateinformation and high-quality products flow

through a paperless system betweenmanufacturing and check-out counter withminimum degradation or interruption

Figure 7-19 Efficient Consumer


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gResponse: Broad Operating CapabilitiesTailored to Each Unique Partner


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Chapter 7:Summary and Review Questions

Students should review their knowledge of thechapter by checking out the Summary and Study

Questions for Chapter 7.

This is the last slide for Chapter 7


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Figure A7-1 Sawtooth Model Modified forInventory in Transit


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Figure A7-2 EOQ Costs ConsideringVolume Transportation Rate

Table 7A-1 Annual Savings, Annual Cost,


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and Net Savings by Various QuantitiesUsing Incentive Rates


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Figure A7-3 Net Savings Function forIncentive Rate


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End of Chapter 7 and 7A Slides

Inventory Decision Making

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