13-1 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

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


13-2



Inventory

• Inventory--a stock or store of goods

13-3



Types of Inventories

• Raw materials & purchased parts

• Partially completed goods called work in progress

• Finished-goods inventories – (manufacturing firms)

or merchandise (retail stores)

13-4



Types of Inventories (Cont’d)

• Replacement parts, tools, & supplies

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

13-5



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

13-6



• 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


13-7



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

13-8



• 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

13-9



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

13-10



• Economic order quantity model

• Economic production model

• Quantity discount model

Economic Order Quantity Models

13-11



• 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

13-12



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



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

13-14



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

13-15



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

13-16



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.

13-17



Safety Stock

LT Time

Expected demandduring lead time

Maximum probable demandduring lead time

ROP

Qu

an

tity

Safety stock

Figure 13-12

13-18



• 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

13-19



• 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

13-20



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

13-21



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

13-22



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

13-23



• 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

13-24



• 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

13-25



• Requires a larger safety stock

• Increases carrying cost

• Costs of periodic reviews

Fixed-Interval Disadvantages

13-26



• 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

13-1 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

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