Chapter 12

Inventory Management

McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved.

Inventory

• Inventory– A stock or store of goods

• Independent demand items– Items that are ready to be sold or used

12-2

Types of Inventory

• Raw materials and purchased parts• Work-in-process• Finished goods inventories or merchandise• Maintenance and repairs (MRO) inventory, tools and

supplies• Goods-in-transit to warehouses or customers (pipeline

inventory)

12-3

Inventory Functions

• Inventories serve a number of functions such as:1. To meet anticipated customer demand

2. To smooth production requirements

3. To decouple operations

4. To protect against stockouts

5. To take advantage of order cycles

6. To hedge against price increases

7. To permit operations

8. To take advantage of quantity discounts

12-4

Inventory Management

• Management has two basic functions concerning inventory:1. Establish a system for tracking items in inventory

2. Make decisions about• When to order

• How much to order

12-5

Effective Inventory Management

• Requires:1. A system keep track of inventory

2. A reliable forecast of demand

3. Knowledge of lead time and lead time variability

4. Reasonable estimates of• holding costs• ordering costs• shortage costs

5. A classification system for inventory items

12-6

Inventory Counting Systems

• Periodic System– Physical count of items in inventory made at periodic

intervals

• Perpetual Inventory System– System that keeps track of removals from inventory

continuously, thus monitoring current levels of each item• Two-bin system

– Two containers of inventory; reorder

when the first is empty

12-7

Inventory Counting Technologies

• Universal product code (UPC)– Bar code printed on a label that has information about

the item to which it is attached

• Radio frequency identification (RFID) tags– A technology that uses radio waves to identify objects,

such as goods in supply chains

12-8

Demand Forecasts and Lead Time

• Forecasts– Inventories are necessary to satisfy customer demands, so it is

important to have a reliable estimates of the amount and timing of demand

• Lead time– Time interval between ordering and receiving the order

• Point-of-sale (POS) systems– A system that electronically records actual sales– Such demand information is very useful for enhancing

forecasting and inventory management

12-9

ABC Classification System

• A-B-C approach– Classifying inventory according to some measure of importance, and

allocating control efforts accordingly

– A items (very important)

• 10 to 20 percent of the number of items in inventory and about 60 to 70 percent of the annual dollar value

– B items (moderately important)

– C items (least important)

• 50 to 60 percent of the number

of items in inventory but only

about 10 to 15 percent of the

annual dollar value

Annual $ value of items

High

LowFew ManyNumber of Items

AA

CCBB

12-10

Cycle Counting

• Cycle counting– A physical count of items in inventory

• Cycle counting management– How much accuracy is needed?

• A items: ± 0.2 percent

• B items: ± 1 percent

• C items: ± 5 percent

– When should cycle counting be performed?

– Who should do it?

12-11

How Much to Order: EOQ Models

• The basic economic order quantity model• The economic production quantity model• The quantity discount model

12-12

Basic EOQ Model

• The basic EOQ model is used to find a fixed order quantity that will minimize total annual inventory costs

• Assumptions– Only one product is involved

– Annual demand requirements are 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

12-13

The Inventory Cycle

Profile of Inventory Level Over Time

Quantityon hand

Q

Receive order

Placeorder

Receive order

Placeorder

Receive order

Lead time

Reorderpoint

Usagerate

Time

12-14

Total Annual Cost

cost Ordering

yearper unit in usually Demand,

unitper cost (carrying) Holding

unitsin quantity Order

where

2

Cost Ordering AnnualCost Holding AnnualCost Total

S

D

H

Q

SQ

DH

Q

12-15

Goal: Total Cost Minimization

Order Quantity (Q)

The Total-Cost Curve is U-Shaped

Ordering Costs

Q*

An

nu

al C

ost

(optimal order quantity)

Holding Costs

SQ

DH

QTC

2

12-16

Deriving EOQ

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

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

cost holdingunit per annual

cost)der demand)(or annual(22* H

DSQ

12-17

Economic Production Quantity (EPQ)

• Assumptions– Only one product is involved

– Annual demand requirements are known

– Usage rate is constant

– Usage occurs continually, but production occurs periodically

– The production rate is constant

– Lead time does not vary

– There are no quantity discounts

12-18

EPQ: Inventory Profile

Q

Q*

Imax

Productionand usage

Productionand usage

Productionand usage

Usageonly

Usageonly

Cumulativeproduction

Amounton hand

Time

12-19

EPQ – Total Cost

rate Usage

ratedelivery or Production

inventory Maximum

where

2

Cost SetupCost CarryingTC

max

max

u

p

upp

Q

I

SQ

DH

I

12-20

EPQ

up

p

H

DSQp

2*

12-21

Quantity Discount Model

• Quantity discount– Price reduction offered to customers for placing large

orders

priceUnit

where

2

Cost PurchasingCost OrderingCost CarryingCost Total

P

PDSQ

DH

Q

12-22

Quantity Discounts

12-23

Quantity Discounts

12-24

When to Reorder

• Reorder point– When the quantity on hand of an item drops to this amount, the

item is reordered.– Determinants of the reorder point

1. The rate of demand

2. The lead time

3. The extent of demand and/or lead time variability

4. The degree of stockout risk acceptable to management

12-25

Reorder Point: Under Certainty

) as units timesame(in timeLeadLT

per week) day,per period,per (units rate Demand

where

LTROP

d

d

d

12-26

Reorder Point: Under Uncertainty

• Demand or lead time uncertainty creates the possibility that demand will be greater than available supply

• To reduce the likelihood of a stockout, it becomes necessary to carry safety stock– Safety stock

• Stock that is held in excess of expected demand due to variable demand and/or lead time

StockSafety timelead during

demand Expected ROP

12-27

Safety Stock

LT Time

Expected demandduring lead time

Maximum probable demandduring lead time

ROP

Qu

an

tity

Safety stock

12-28

Safety Stock?

• As the amount of safety stock carried increases, the risk of stockout decreases.– This improves customer service level

• Service level– The probability that demand will not exceed supply during lead

time– Service level = 100% - Stockout risk

12-29

How Much Safety Stock?

• The amount of safety stock that is appropriate for a given situation depends upon:1. The average demand rate and average lead time

2. Demand and lead time variability

3. The desired service level

demand timelead ofdeviation standard The

deviations standard ofNumber

where

timelead duringdemand Expected

ROP

dLT

dLT

z

z

12-30

Reorder Point

ROP

Risk ofstockoutService level

Expecteddemand

Safetystock

0 z

Quantity

z-scale

The ROP based on a normalDistribution of lead time demand

12-31

Reorder Point: Demand Uncertainty

) as units time(same timeLead LT

) as units time(same periodper demand of stddev. The

per week) day,(per periodper demand Average

deviations standard ofNumber

where

LT ROP

d

d

d

z

zd

d

d

LT :Note ddLT 12-32

Reorder Point: Lead Time Uncertainty

) as units time(same timelead Average LT

) as units time(same timelead of stddev. The

per week) day,(per periodper Demand

deviations standard ofNumber

where

LT ROP

LT

LT

d

d

d

z

zdd

12-33

How Much to Order: FOI

• Fixed-order-interval (FOI) model– Orders are placed at fixed time intervals

• Reasons for using the FOI model– Supplier’s policy may encourage its use– Grouping orders from the same supplier can produce savings in

shipping costs– Some circumstances do not lend themselves to continuously

monitoring inventory position

12-34

Fixed-Quantity vs. Fixed-Interval Ordering

12-35

FOI Model

order of at timeposition Inventory

levelinventory Target

order Amount to

where

Order of Timeat PositionInventory

LevelInventoryTarget

Order toAmount

IP

T

Q

IPTQ

12-36

FOI Model

orders)between timeof(length intervalOrder OI

where

LTOILT OI

dzdT

interest of frame-Time*

* D

QOI

OI* represents the optimal time between orders. Time-frame of interest is an appropriate period (e.g., days or weeks). This is usually based on the time-frame expressed by the average demand rate, d-bar.

12-37

Single-Period Model

• Single-period model– Model for ordering perishables and other items with limited

useful lives– Shortage cost

• Generally, the unrealized profit per unit

• Cshortage = Cs = Revenue per unit – Cost per unit

– Excess cost• Different between purchase cost and salvage value of items

left over at the end of the period

• Cexcess = Ce = Cost per unit – Salvage value per unit

12-38

Single-Period Model

• The goal of the single-period model is to identify the order quantity that will minimize the long-run excess and shortage costs

• Two categories of problem:– Demand can be characterized by a continuous distribution– Demand can be characterized by a discrete distribution

12-39

Stocking Levels

Service level

So Balance Point

Quantity

Cs Ce

So =OptimumStocking Quantity

unitper cost excess

unitper cost shortage

where

level Service

e

s

es

s

C

C

CC

C

12-40