11-1 Inventory Management

William J. Stevenson

Operations Management

8th edition

11-2 Inventory Management

CHAPTER11

Inventory Management

McGraw-Hill/IrwinOperations Management, Eighth Edition, by William J. StevensonCopyright © 2005 by The McGraw-Hill Companies, Inc. All rights

reserved.

11-3 Inventory Management

Economic order quantity model

Economic production model

Quantity discount model

Economic Order Quantity ModelsEconomic Order Quantity Models

11-4 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 ModelAssumptions of EOQ Model

11-5 Inventory Management

The Inventory CycleThe Inventory CycleFigure 11.2

Profile of Inventory Level Over Time

Quantityon hand

Q

Receive order

Placeorder

Receive order

Placeorder

Receive order

Lead time

Reorderpoint

Usage rate

Time

11-6 Inventory Management

Total CostTotal Cost

Annualcarryingcost

Annualorderingcost

Total cost = +

Q2H D

QSTC = +

TC= Total annual costQ= Order quantity in unitsH= Holding cost per unitD= Annual DemandS= Ordering cost

11-7 Inventory Management

Cost Minimization GoalCost 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 11.4C

11-8 Inventory Management

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

QDyearperordersofNo

DQcycleorderofLength

SQ

DtorderingAnnual

/ .

/

cos

Cost Holding Annual

Cost) Setupor der Demand)(Or 2(Annual =

H

2DS = QOPT

QOPT= Optimum order quantityQ= Order quantity in unitsH= Holding cost per unitD= Annual DemandS= Ordering cost

11-9 Inventory Management

EOQ MODEL EXAMPLEEOQ MODEL EXAMPLE

A local distributor for a national tire company expects to sell approximately 9600 steel-belted radial tires of a certain size and tread design next year. Annual carrying cost is $16 per tire, and ordering cost is $75. The distributor operates 288 days a year.

D= $ 9600 H= $ 16 S= $ 75 a) What is the EOQ?

b) No. Of orders per year=D/Q=9600/300=32

tires 30016

2(9600)75

H

2DS = QOPT

11-10 Inventory Management

EOQ MODEL EXAMPLEEOQ MODEL EXAMPLE

D= $ 9600 H= $ 16 S= $ 75 c) Length of order cycle= Q/D= 300/9600

=1/32 of a year*288 =9 work days. d) Total Cost=Carrying cost+Ordering cost

=(Q/2)H+(D/Q)S

=(300/2)16+(9600/300)75

=2400+2400

=$ 4800

11-11 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 AssumptionsEconomic Production Quantity Assumptions

11-12 Inventory Management

Economic RunEconomic Run (Batch) (Batch) Size Size

p

QtimeRun

u

QtimeCycle

upMaximumI

SQDHI

CostSetupCostCarryingTC

up

p

H

DSQ

p

p

p

)(p

Qinventory

/2

2

pmax

maxmin

Qp= Optimum production quantityH= Holding cost per unitD= Annual DemandS= Setup costP= Production or delivery rateU= Usage rate

11-13 Inventory Management

Economic RunEconomic Run (Batch) (Batch) Size Size Example Example

A toy manufacturer uses 48000 rubber wheels per year for its popular dump truck series. The firm makes its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $ $1 per wheel a year. Setup cost for a production run of wheels is $45. The firm operates 240 days per year. D= 48000 S=$45 H=$1 per year p=800 wheels per day u= 48000 wheels per 240 days or 200 wheels per day.a)Optimal run size

b) Minimum total annual cost

wheelsup

p

H

DSQp 2400

200800

800

1

45)48000(22

1800$452400

48001

2

1800

2

1800)200800(800

2400)(

p

Q

maxmin

pmax

SQ

DH

ITC

wheelsupI

11-14 Inventory Management

Economic RunEconomic Run (Batch) (Batch) Size Size Example Example

D= 48000 S=$45 H=$1 per year p=800 wheels per day u= 48000 wheels per 240 days or 200 wheels per day.

c)

Thus, a run of wheels will be made every 12 days.

d)

Thus, each run will require three days to complete.

dayperwheelswheelsu

QtimeCycle p 200/ 2400

daysdayperwheelswheelsp

QtimeR p 3 800/ 2400un