13-1

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

Chapter 13

Inventory Management

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

Inventory

• Inventory--a stock or store of goods

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

Types 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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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

Types of Inventories (Cont’d)

• Replacement parts, tools, & supplies

• Goods-in-transit to warehouses or customers (aka “pipeline” inventory)

13-5

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

Functions of Inventory

• To permit operations• To meet anticipated demand• To smooth production requirements• To decouple components of the production-

distribution• To protect against stock-outs• To take advantage of order cycles• To hedge against price increases or take

advantage of quantity discounts

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

• Poor inventory management can result in either overstocking or understocking

• Effective inventory management:– 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

Inventory Management

13-7

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

Inventory 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 Management

• 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 Terms

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

ABC 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 13-1

Annual $ volume of items

AA

BB

CC

High

Low

Few ManyNumber of Items

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

• Economic order quantity model

• Economic production model

• Quantity discount model

Economic Order Quantity Models

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

• 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 Model

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

EOQ Total Cost of Inventory

Annualcarryingcost

Annualorderingcost

Total cost = +

Q2H D

QSTC = +

Where: Q=Order quantityH=Holding cost per unit per yearD=Demand in units per yearS=Ordering costs per order

13-13

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

Cost Minimization Goal

Order Quantity (Q)

The Total-Cost Curve is U-Shaped

Ordering Costs

QO

An

nu

al C

os

t

(optimal order quantity)

TCQ

HD

QS

2

Figure 13-4

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

Deriving 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 = 2DS

H =

2(Annual Demand)(Order or Setup Cost)

Annual Holding CostOPT

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

Minimum Total Cost

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

Q = 2DS

H =

2(Annual Demand)(Order or Setup Cost)

Annual Holding CostOPT

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Inventory Management

When to Reorder with EOQ Ordering

• 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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Inventory Management

Safety Stock

LT Time

Expected demandduring lead time

Maximum probable demandduring lead time

ROP

Qu

an

tity

Safety stock

Figure 13-12

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

• 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

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

• 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 Assumptions

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

EPQ Total Cost of Inventory

Carryingcost

SetupcostTotal cost = +

Imax2H D

QSTC = +

Where: Imax=Maximum inventoryQ=Run quantityH=Holding cost per unit per yearD=Demand in units per yearS=Setup costs per run

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

Deriving the EPQ

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

u-p

p

H

2DS = QOPT

Where: p=production rateu=usage rate

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

EPQ Equations

• Cycle time--time between the beginning of runs

• Run time--the length of the production run

• Maximum & average inventory

u

Qo timeCycle

p

QoRun time

upp

Qo maxI2

I maxIavg

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

• 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

Fixed-Order-Interval Model

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

• Tight control of type A items• Items from same supplier may yield

savings in:– Ordering– Packing– Shipping costs

• May be practical when inventories cannot be closely monitored

Fixed-Interval Benefits

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

• Requires a larger safety stock

• Increases carrying cost

• Costs of periodic reviews

Fixed-Interval Disadvantages

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McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Inventory Management

• 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 Strategy