Chapter 4Chapter 4

Inventory ControlInventory Control

Known DemandKnown Demand

IntroductionIntroduction

Importance of inventoryImportance of inventory Types of inventoriesTypes of inventories Motivation for holding inventoriesMotivation for holding inventories Characteristics of inventory systemsCharacteristics of inventory systems Relevant costsRelevant costs

Importance of inventoryImportance of inventory

Investment in inventories is enormousInvestment in inventories is enormous

Companies that use scientific inventory Companies that use scientific inventory control methods have a significant control methods have a significant competitive advantagecompetitive advantage in the in the marketplacemarketplace

Breakdown of the Total Breakdown of the Total Investment in Inventories Investment in Inventories

in the U.S. Economy (1999)in the U.S. Economy (1999)

Fig. 4-1

Types of inventoriesTypes of inventories

Raw materialsRaw materials ComponentsComponents WIPWIP Finished goodsFinished goods Other (spare parts…)Other (spare parts…)

Motivation for holding inventoriesMotivation for holding inventories

Economies of scale (Economies of scale (setup costsetup cost)) Uncertainties: Uncertainties: (demand, lead time, supply)(demand, lead time, supply)

Speculation Speculation (price increase)(price increase)

Transportation Transportation (pipeline inventories)(pipeline inventories)

Smoothing Smoothing (seasonality)(seasonality)

Logistics Logistics (supply, production, distribution)(supply, production, distribution)

Control costs Control costs (large inv. Of inexpensive items)(large inv. Of inexpensive items)

Characteristics of inventory systemsCharacteristics of inventory systems DemandDemand

• Constant versus variableConstant versus variable• Known versus randomKnown versus random

Lead timeLead time Review time Review time (continuous review, periodic review)(continuous review, periodic review)

Excess demandExcess demand• BackorderedBackordered• lostlost

Changing inventory Changing inventory (perishability, obsolescence(perishability, obsolescence

Relevant costsRelevant costs

Holding costHolding cost• Warehousing Warehousing (Providing space, Material handling, Labor)(Providing space, Material handling, Labor)

• Taxes and insuranceTaxes and insurance• Spoilage, deterioration, and obsolescenceSpoilage, deterioration, and obsolescence• Opportunity cost of alternative Opportunity cost of alternative

investmentinvestment Ordering cost (setup cost)Ordering cost (setup cost)

Inventory as a Inventory as a Function of TimeFunction of Time

Fig. 4-2

Relevant costs (cont’d)Relevant costs (cont’d)

Order costOrder cost Penalty cost (shortage cost)Penalty cost (shortage cost)

Order Cost FunctionOrder Cost FunctionFig. 4-3

Inventory ControlInventory Control

The EOQ ModelThe EOQ Model

AssumptionsAssumptions

Demand rate Demand rate λλ (units per unit time) (units per unit time) is known and constantis known and constant

Shortages are not permittedShortages are not permitted No lead timeNo lead time

Inventory Levels Inventory Levels for the EOQ Modelfor the EOQ Model

Fig. 4-4

Choose Choose QQ to minimize the average cost per unit to minimize the average cost per unit

timetime

fixed+proportional order cost per cycle: fixed+proportional order cost per cycle: K+cQK+cQ

Cycle length: Cycle length: T=Q / T=Q / λλ

Average inventory level per cycle: Average inventory level per cycle: Q/2Q/2

Average cost per unit time:Average cost per unit time:

G(Q) = (K+cQ)/T + hQ/2G(Q) = (K+cQ)/T + hQ/2

= K = K λλ/Q+ /Q+ λλc+hQ/2c+hQ/2

The Average Annual The Average Annual Cost Function G(Q)Cost Function G(Q)

Fig. 4-5

Reorder Point Calculation Reorder Point Calculation for Example 4.1for Example 4.1

Fig. 4-6

Reorder Point Calculation forReorder Point Calculation forLead Times Exceeding One CycleLead Times Exceeding One Cycle

Fig. 4-7

All-Units Discount All-Units Discount Order Cost FunctionOrder Cost Function

Fig. 4-9

Incremental Discount Incremental Discount Order Cost FunctionOrder Cost Function

Fig. 4-10

Average Annual Cost Function Average Annual Cost Function for Incremental Discount for Incremental Discount

ScheduleSchedule

Fig. 4-12