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Learning Objectives:Understand the practical aspects of various inventory systemsIdentify the major factors affecting inventory system performanceUnderstand how to calculate the optimal order quantity in various circumstance

IES 303

Chapter 15: Inventory ManagementSupplement E

Week 13

February 2, 2006

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Inventory Management

Inventory : Stock of items held to meet future demand

Determine the amount of inventory to keep in stock

Inventory management answers two questions:

_________________________

________________ or

________________ (EOQ)

_________________________

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Physical Types of Inventory

Raw materials

Purchased parts and supplies

Labor

In-process (partially completed) products

Component parts

Tools, machinery, and equipment

Reasons to Hold Inventory

Meet unexpected demand

Smooth seasonal or cyclical demand

Meet variations in customer demand

Take advantage of price discounts

Quantity discounts

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Pressures for Low Inventories When keeping inventory, there are

always some cost incurred ________

___________________________

The variable cost of keeping items on hand

$/ unit-period

Inventory holding cost generally includes:

_________________________

_________________________

_________________________

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Pressures for High Inventories Customer service

Ordering cost ($ / order)

Setup cost

Transportation cost

Payment to suppliers

Labor and equipment utilization

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Types of Inventory Cycle Inventory

Safety stock inventory

Anticipation inventory

Pipeline inventory

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Inventory Reduction Approach Cycle Inventory

Safety stock inventory

Anticipation inventory

Pipeline inventory

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ABC Analysis

Class A 5 – 15 % of units 70 – 80 % of value

Class B 30 % of units 15 % of value

Class C 50 – 60 % of units 5 – 10 % of value

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ABC Analysis

1010 2020 3030 4040 5050 6060 7070 8080 9090 100100

Percentage of itemsPercentage of items

Per

cen

tag

e o

f d

oll

ar v

alu

eP

erce

nta

ge

of

do

llar

val

ue

100 100 —

90 90 —

80 80 —

70 70 —

60 60 —

50 50 —

40 40 —

30 30 —

20 20 —

10 10 —

0 0 —

Figure 15.2Figure 15.2

Class C

Class A

Class B

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Economic Order Quantity (EOQ)

EOQ: the lot size or order size that minimizes total annual inventory holding and ordering cost

Total inventory cost = Holding cost (HC) + ordering cost (OC)

Assumptions for Basic EOQ Model

____________________________________________

____________________________________________

____________________________________________

____________________________________________

____________________________________________

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Basic EOQ Model Cycle Inventory Levels

TimeLead time

Order placed

Order placed

Order receipt

Order receipt

Inve

nto

ry L

evel

Order quantity, Q

0

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Basic EOQ Model Graphs of Annual Holding, Ordering, and Total Costs

An

nu

al c

os

t (d

olla

rs)

An

nu

al c

os

t (d

olla

rs)

Lot Size (Lot Size (QQ))Figure 15.4Figure 15.4

Holding cost (Holding cost (HCHC))

Ordering cost (Ordering cost (OCOC))

Total cost = Total cost = HCHC + + OCOC

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Basic EOQ Model Derivation of total annual inventory cost and economic order quantity order

quantity functions

)()(2

SQ

DH

QC )()(

2S

Q

DH

QC

Q = order size (units)D = annual demand (units/year)S = ordering cost per order ($/order)H = annual per unit carrying cost ($/unit)

H

DSEOQ

2 H

DSEOQ

2

r)months/yea 12(D

EOQTBOEOQ r)months/yea 12(

D

EOQTBOEOQ

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Basic EOQ Model Ex 1:Carpet Sell

The I-75 Carpet store stocks carpet in its warehouse and sells it through a showroom. The store keeps several brands and styles of carpet in stock; however, its bigger seller is the BIG C carpet. The store wants to determine the optimal order size and total inventory cost for this brand of carpet given an estimated annual demand of 10,000 yards of carpet, an annual carrying cost of $0.75 per yard, and an ordering cost of $150.

The store would like to know the number of orders that will be made annually and the time between orders given that the store is open every except Sunday, Thanksgiving Day and Christmas Day.

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EOQ Sensitivity Analysis

Use estimates of relevant costs

Ignore uncertainty in demand

What happen if the holding / ordering cost is off by 20%, 30%? Consider 4 cases of variations of the model parameters.

1. Both ordering and carrying costs are 10% less than the original estimates

2. Both are 10% higher

3. Ordering cost is 10% higher and carrying cost is10% lower

4. Ordering cost is 10% lower and carrying cost is 10% higher

Determine EOQ in each case. Remark on the sensitivity of Q on the estimated total cost.

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Basic Types of Inventory Control System Continuous review system

________________________

________________________

The ordering interval may not be consistent

Manager has direct control

Periodic review System (P) ________________________

________________________

No direct control

Tend to have higher inventory to prevent stockout

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Continuous review system

Figure 15.7Figure 15.7

TimeTime

On

-han

d i

nve

nto

ryO

n-h

and

in

ven

tory

RR

TBOTBO

LL

TBOTBO

LL

TBOTBO

LL

OrderOrderreceivedreceived

OrderOrderreceivedreceived

QQ

OHOH

OrderOrderplacedplaced

IPIP

OrderOrderreceivedreceived

QQ

OHOH

OrderOrderplacedplaced

IPIP

OrderOrderreceivedreceived

OrderOrderplacedplaced

IPIP

QQ

OHOH

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Continuous review system Selecting Reorder Point

When demand is certain

Reorder point (R) = demand during lead time

When demand is uncertain

Reorder point (R) = Avg demand during lead time + Safety stock

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Variable Demand Safety Stocks

Safety stock

____________________

____________

Stockout an inventory shortage

Service level • ____________________

____________

Variable Demand with Reorder Point

Reorderpoint, R

Q

LTTime

LT

Inve

nto

ry le

vel

0

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Variable Demand Safety Stocks

Prevent stockout under uncertain demand

ReorderReorderpoint, point, RR

QQ

LTLT

TimeTimeLTLT

Inve

nto

ry le

vel

Inve

nto

ry le

vel

00

Safety Stock

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Reorder Point for a Service Level

Probability of meeting demand during lead time = service level

Probability of a stockout

R

Safety stock

Demand

zt L

Average demand during lead time

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Reorder Point with Variable Demand Reorder point with safety stock

Service level = probability of NO stockout

LzdLR t LzdLR t

stocksafety

yprobabilit level service the

toingcorrespond deviations standard ofnumber

demand ofdeviation standard

timelead

demand average

Lz

z

σ

L

d

t

t

stocksafety

yprobabilit level service the

toingcorrespond deviations standard ofnumber

demand ofdeviation standard

timelead

demand average

Lz

z

σ

L

d

t

t

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Variable Demand Ex 2: PM computer

PM Computers assembles microcomputers from generic

components. It purchases its color monitors from a

manufacturer in Taiwan. There is a long lead time of 25

days. Daily demand is normally distributed with a mean of

2.5 monitors and a standard deviation of 1.2 monitors.

Determine the safety stock and reorder point corresponding

to a 90% service level

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Periodic Review System (P system)

Figure 15.12Figure 15.12

PP PPTimeTime

On

-han

d i

nve

nto

ryO

n-h

and

in

ven

tory

TT

QQ11

OrderOrderplacedplaced

LL

OrderOrderplacedplaced

OrderOrderreceivedreceived

OrderOrderreceivedreceived

OrderOrderplacedplaced

QQ22

QQ33

OrderOrderreceivedreceived

OHOH

LL LL

Protection intervalProtection interval

IPIP11

IPIP33

IPIP22

IPIP IPIPIPIP

OHOH

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Special Inventory ModelNoninstantaneous Replenishment

Production Production and demandand demand

Demand Demand onlyonly

TBOTBO

Production quantityProduction quantity

Demand during Demand during production intervalproduction interval

Maximum inventoryMaximum inventory

On

-han

d i

nve

nto

ryO

n-h

and

in

ven

tory QQ

TimeTime

IImaxmax

p – d

Figure E.1Figure E.1

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Special Inventory ModelNoninstantaneous Replenishment

Imax = (p – d) = Q( )Qp

p – dp

C = (H) + (S)Imax

2DQ C = ( ) + (S)

DQ

Q p – d2 p

ELS =p

p – d2DS

H

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Noninstantaneous Replenishment Ex 3: Cheese Maker

The Wood Valley Dairy makes cheese to supply to stores in its area. The dairy can make 250 lbs of cheese per day, and the demand at area stores is 180 lbs per day. Each time the dairy makes cheeses, it costs $125 to set up the production process. The annual cost of carrying a pound of cheese is $12.

Determine the followings:

- The optimal order size and the minimum total annual inventory cost

- Length of time to receive an order, production run

- Number of orders per year

- Maximum inventory level

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Special Inventory ModelQuantity Discount

Price discount for higher quantity orders

Include the purchase price in EOQ model

P = Unit price of item

PDSQ

DH

QC

2

Qopt

Carrying cost

Ordering cost

Inve

nto

ry c

ost

($)

Q(P1 ) = 100 Q(P2 ) = 200

TC (P2 = $6 )

TC (P1 = $8 )

TC = ($10 )

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Quantity Discount Ex 4: Sweatshirt in bookstore

The UW bookstore purchases sweatshirts with school logo from a vendor. The vendor sells the sweatshirts to the store for $38 a piece. The cost to bookstore for placing an order is $120, and the annual carrying cost is 25% of the cost of sweatshirt. 1700 sweatshirts are estimated to be sold during the year. The vendor has offered the bookstore the following volume discount:

What is an optimal order quantity?

Order Size Discount

1-299

300-499

500-799

800 and up

0%

2%

4%

5%