© 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Chapter 12 Inventory Management

© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Chapter 12

Inventory Management

2000 by Prentice-Hall, Inc 2Ch 12 - 2© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Inventory

Stock of items held to meet future demand

Inventory management answers two questions

How much to order When to order


Types of Inventory

Raw materials Purchased parts and supplies Labor In-process (partially completed) products Component parts Working capital Tools, machinery, and equipment Finished goods


Reasons To Hold Inventory

Meet unexpected demandSmooth seasonal or cyclical demandMeet variations in customer demandTake advantage of price discountsHedge against price increases


Two Forms Of Demand

Dependent items used to produce final products

Independent items demanded by external customers


Inventory Costs

Carrying Cost cost of holding an item in inventory

Ordering Cost cost of replenishing inventory

Shortage Cost temporary or permanent loss of sales

when demand cannot be met


Inventory Control Systems

Fixed-order-quantity system (Continuous)

constant amount ordered when inventory declines to predetermined level

Fixed-time-period system (Periodic) order placed for variable amount after

fixed passage of time


ABC Classification System

Demand volume & value of items varyClassify inventory into 3 categories

Class% of Units% of DollarsA 5 - 15 70 - 80

B 30 15

C 50 - 60 5 - 10


ABC Classification ExampleCost Usage Part Value Value Quantity Cumulative

60 90 9 30,600 35.8 6.0 6.0350 40 8 16,000 18.7 5.0 11.030 130 2 14,000 16.4 4.0 15.080 60 1 5,400 6.3 9.0 24.030 100 4 4,800 5.6 6.0 30.020 180 3 3,900 4.6 13.0 43.010 170 6 3,600 4.2 18.0 61.0

320 50 5 3,000 3.5 10.0 71.0510 60 10 2,400 2.8 12.0 83.020 120 7 1,700 2.0 17.0 100.0

85,400$

Class Items % Value % UnitsA 9,8,2 71 15B 1, 4, 3 16.5 25C 6, 5, 10, 7 12.5 60


Assumptions Of Basic EOQ ModelDemand is known with certainty Demand is relatively constant over timeNo shortages are allowedLead time for the receipt of orders is

constantThe order quantity is received all at

once


The Inventory Order Cycle

Demand rate

0 TimeLead time

Lead time

Order Placed

Order Placed

Order Received

Order Received

Inve

nto

ry L

eve

l

Reorder point, R

Order qty, Q


EOQ Cost Model

CO - cost of placing order

D - annual demand

CC - annual per-unit carrying cost

Q - order quantity

Annual ordering cost = COD/Q

Annual carrying cost = CCQ/2

Total cost = COD/Q + CCQ/2

TCCoD

QCcQ

TCQ

CoD

Q

Cc

CoD

Q

Cc

QoptCoDCc

2

2 2

02 2

2


EOQ Model Cost Curves

Slope = 0

Total Cost

Ordering Cost = CoD/Q

Order Quantity, Q

Annualcost ($)

Minimumtotal cost

Optimal order Qopt

Carrying Cost = CcQ/2


EOQ With Noninstantaneous Receipt

Q(1-d/p)

Inventorylevel

(1-d/p)Q2

Time0

Orderreceipt period

BeginOrderreceipt

EndOrderreceipt

Maximuminventory level

Averageinventory level


Quantity Discounts

Price per unit decreases as order quantity increases

Order

Size Price

0-99 $10

100-199 8 (d1)

200+ 6 (d2)

demand annual=D

priceunit

2

perP

PDQC

Q

DCTC co


Quantity Discount Model

Qopt

Carrying cost

Ordering cost

Inve

ntor

y co

st (

$)

Q(d1 ) = 100 Q(d2 ) = 200

TC (d2 = $6 )

TC (d1 = $8 )

TC = ($10 )


When to Order

Reorder Point -level of inventory at which to place a new order

R = dL

where

d = demand rate per period

L = lead time


Safety Stocks

Safety stock buffer added to on hand inventory during

lead timeStockout

an inventory shortageService level

probability that the inventory available during lead time will meet

demand


Reorder Point With A Safety Stock

Reorderpoint, R

Q

0

Inve

ntor

y le

vel

LT LTTime

Safety stock


Reorder Point With Variable Demand

R dL z d L

where

d

d

z d L safety stock

= average daily demand

L = lead time

standard deviation of daily demand

z = number of standard deviations for desired service level

Variance

L

S dard deviation L

d L

(

tan

daily variances) x (number of days of lead time)

= d2

d2


Reorder Point For A Service Level

Safety stock

R

Probability of meeting demand during lead time = service level

dLDemand

z d L

Probability of a stockout


Determining Z Value For Service LevelZ 0.00 0.01 ... 0.05

1.6 0.4452 0.4463 … 0.4505...

Z = 1.650

Probability of a stockout = 5%

0.45050.5000

Service level = area to left of Z value or 95%

......

...


Order Quantity For A Periodic Inventory System

Q d t L z t L I

where

d

t

z t L

b d b

b

d

d b

= average demand rate

fixed time between orders

L = lead time

standard deviation of demand

safety stock

I = inventory in stock

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© 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Chapter 12 Inventory Management