McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.

1212

Inventory Management

12-2

Learning ObjectivesLearning Objectives Define the term inventory and list the major

reasons for holding inventories; and list the main requirements for effective inventory management.

Discuss the nature and importance of service inventories

Discuss periodic and perpetual review systems. Discuss the objectives of inventory management. Describe the A-B-C approach and explain how it

is useful.

12-3

Learning ObjectivesLearning Objectives Describe the basic EOQ model and its

assumptions and solve typical problems. Describe the economic production quantity

model and solve typical problems. Describe the quantity discount model and

solve typical problems. Describe reorder point models and solve

typical problems. Describe situations in which the single-

period model would be appropriate, and solve typical problems.

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Independent Demand

A

B(4) C(2)

D(2) E(1) D(3) F(2)

Dependent Demand

Independent demand is uncertain. Dependent demand is certain.

Inventory: a stock or store of goods

InventoryInventory

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Inventory ModelsInventory Models

Independent demand – finished goods, items that are ready to be sold E.g. a computer

Dependent demand – components of finished products E.g. parts that make up the computer

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Types of InventoriesTypes of Inventories

Raw materials & purchased parts Partially completed goods called

work in progress Finished-goods inventories

(manufacturing firms) or merchandise (retail stores)

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Types of Inventories (Cont’d)Types of Inventories (Cont’d) Replacement parts, tools, & supplies

Goods-in-transit to warehouses or customers

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Functions of InventoryFunctions of Inventory

To meet anticipated demand

To smooth production requirements

To decouple operations

To protect against stock-outs

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Functions of Inventory (Cont’d)Functions of Inventory (Cont’d)

To take advantage of order cycles

To help hedge against price increases

To permit operations

To take advantage of quantity discounts

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Objective of Inventory ControlObjective of Inventory Control

To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds Level of customer service

Costs of ordering and carrying inventory

Inventory turnover is the ratio ofaverage cost of goods sold toaverage inventory investment.

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A system to keep track of inventory A reliable forecast of demand Knowledge of lead times Reasonable estimates of

Holding costs Ordering costs Shortage costs

A classification system

Effective Inventory ManagementEffective Inventory Management

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Inventory Counting SystemsInventory Counting Systems

Periodic SystemPhysical count of items made at periodic intervals

Perpetual Inventory System System that keeps track of removals from inventory continuously, thus monitoringcurrent levels of each item

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Inventory Counting Systems Inventory Counting Systems (Cont’d)(Cont’d)

Two-Bin System - Two containers of inventory; reorder when the first is empty

Universal Bar Code - Bar code printed on a label that hasinformation about the item to which it is attached 0

214800 232087768

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Lead time: time interval between ordering and receiving the order

Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year

Ordering costs: costs of ordering and receiving inventory

Shortage costs: costs when demand exceeds supply

Key Inventory TermsKey Inventory Terms

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ABC Classification SystemABC Classification System

Classifying inventory according to some measure of importance and allocating control efforts accordingly.

AA - very important

BB - mod. important

CC - least important

Figure 12.1

Annual $ value of items

AABB

CC

High

LowLow High

Percentage of Items

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Cycle CountingCycle Counting

A physical count of items in inventory

Cycle counting management How much accuracy is needed?

When should cycle counting be performed?

Who should do it?

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Economic order quantity (EOQ) model The order size that minimizes total annual

cost

Economic production model

Quantity discount model

Economic Order Quantity ModelsEconomic Order Quantity Models

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Only one product is involved

Annual demand requirements known

Demand is even throughout the year

Lead time does not vary

Each order is received in a single delivery

There are no quantity discounts

Assumptions of EOQ ModelAssumptions of EOQ Model

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The Inventory CycleThe Inventory CycleFigure 12.2

Profile of Inventory Level Over Time

Quantityon hand

Q

Receive order

Placeorder

Receive order

Placeorder

Receive order

Lead time

Reorderpoint

Usage rate

Time

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Total CostTotal Cost

Annualcarryingcost

Annualorderingcost

Total cost = +

TC = Q2 H D

QS+

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Cost Minimization GoalCost Minimization Goal

Order Quantity (Q)

The Total-Cost Curve is U-Shaped

Ordering Costs

QO

Ann

ual C

ost

(optimal order quantity)

TC QH DQS

2

Figure 12.4C

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Deriving the EOQDeriving the EOQ

Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

Q = 2DSH

= 2(Annual Demand)(Order or Setup Cost)Annual Holding CostOPT

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Minimum Total CostMinimum Total Cost

The total cost curve reaches its minimum where the carrying and ordering costs are equal.

Q2 H D

QS=

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Production done in batches or lots Capacity to produce a part exceeds the

part’s usage or demand rate Assumptions of EPQ are similar to EOQ

except orders are received incrementally during production

Economic Production Quantity (EPQ)Economic Production Quantity (EPQ)

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Only one item is involved Annual demand is known Usage rate is constant Usage occurs continually Production rate is constant Lead time does not vary No quantity discounts

Economic Production Quantity Economic Production Quantity AssumptionsAssumptions

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Economic Run SizeEconomic Run Size

Q DSH

pp u

02

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Total Costs with Purchasing CostTotal Costs with Purchasing Cost

Annualcarryingcost

PurchasingcostTC = +

Q2 H D

Q STC = +

+Annualorderingcost

PD +

12-28

Total Costs with PDTotal Costs with PDC

ost

EOQ

TC with PD

TC without PD

PD

0 Quantity

Adding Purchasing costdoesn’t change EOQ

Figure 12.7

12-29

Total Cost with Constant Carrying Total Cost with Constant Carrying Costs Costs

OC

EOQ Quantity

Tota

l Cos

t TCa

TCc

TCbDecreasing Price

CC a,b,c

Figure 12.9

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When to Reorder with EOQ When to Reorder with EOQ OrderingOrdering

Reorder Point - When the quantity on hand of an item drops to this amount, the item is reordered

Safety Stock - Stock that is held in excess of expected demand due to variable demand rate and/or lead time.

Service Level - Probability that demand will not exceed supply during lead time.

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Determinants of the Reorder Determinants of the Reorder PointPoint

The rate of demand The lead time Demand and/or lead time variability Stockout risk (safety stock)

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Safety StockSafety Stock

LT Time

Expected demandduring lead time

Maximum probable demandduring lead time

ROP

Qua

ntity

Safety stock

Figure 12.12

Safety stock reduces risk ofstockout during lead time

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Reorder PointReorder Point

ROP

Risk ofa stockout

Service level

Probability ofno stockout

Expecteddemand Safety

stock0 z

Quantity

z-scale

Figure 12.13

The ROP based on a normalDistribution of lead time demand

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Orders are placed at fixed time intervals Order quantity for next interval? Suppliers might encourage fixed

intervals May require only periodic checks of

inventory levels Risk of stockout Fill rate – the percentage of demand

filled by the stock on hand

Fixed-Order-Interval ModelFixed-Order-Interval Model

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Tight control of inventory items Items from same supplier may yield

savings in: Ordering Packing Shipping costs

May be practical when inventories cannot be closely monitored

Fixed-Interval BenefitsFixed-Interval Benefits

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Requires a larger safety stock Increases carrying cost Costs of periodic reviews

Fixed-Interval DisadvantagesFixed-Interval Disadvantages

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Single period model: model for ordering of perishables and other items with limited useful lives

Shortage cost: generally the unrealized profits per unit

Excess cost: difference between purchase cost and salvage value of items left over at the end of a period

Single Period ModelSingle Period Model

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Continuous stocking levels Identifies optimal stocking levels

Optimal stocking level balances unit shortage and excess cost

Discrete stocking levels Service levels are discrete rather than

continuous

Desired service level is equaled or exceeded

Single Period ModelSingle Period Model

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Optimal Stocking LevelOptimal Stocking Level

Service Level

So

Quantity

Ce Cs

Balance point

Service level =Cs

Cs + CeCs = Shortage cost per unitCe = Excess cost per unit

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Example 15Example 15

Ce = $0.20 per unit Cs = $0.60 per unit Service level = Cs/(Cs+Ce) = .6/(.6+.2) Service level = .75

Service Level = 75%

Quantity

Ce Cs

Stockout risk = 1.00 – 0.75 = 0.25

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Too much inventory Tends to hide problems Easier to live with problems than to

eliminate them Costly to maintain

Wise strategy Reduce lot sizes Reduce safety stock

Operations StrategyOperations Strategy