Chapter 13 Inventory Decision Self

7/31/2019 Chapter 13 Inventory Decision Self

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved.

Chapter 13

InventoryManagement



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Inventory

Stock of items kept by anorganization to meet internal or

external customer demand. Inventory management answers

two questions

How much to orderWhen to order


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Types of Inventory

Raw materials

Purchased parts and supplies

Labor

In-process (partially completed) products

Component parts

Working capital

Tools, machinery, and equipment


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Reasons to Hold

InventoryMeet unexpected demand

Smooth seasonal or cyclical demand

Meet variations in supplier deliveries

Take advantage ofprice discounts

Hedge against priceincreases

Quantity discounts


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Two Forms of Demand

Dependent

Items used internally to produce finalproducts

Independent Items demanded by external customers


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Inventory CostsCarrying Cost/Holding Cost

Cost of holding an item in inventory

Ordering Cost Cost of replenishing inventory

Shortage Cost/Stock Out cost

Temporary or permanent loss ofsales when demand cannot be met

Set Up Cost

Costs for arranging specifice ui ment setu s, etc


7/61To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved.

Carrying Cost Cost of holding an item in inventory

Cost depends on Quantity of inventory

Length of time

Cost that increases linearly the number of units

Examples Facility of Storage ( rent, power, heat cooling etc)

Material Handling Equipment

Labor

Record keeping

Production deterioration, spoilage

Two ways to specify carrying cost

Assign total carrying cost(sum all the individual cost on perunit per time bases. (Example Rs 10 per unit per year)

Percentage of value of an item or % of average inventory



Ordering Cost The cost of replenishing inventory

Expressed as amount/order and areindependent of the order size.

Any cost that increases linearly with

number of orders

Examples Requisition and purchase order

Transportation and shipping Receiving

Inspection

Handling

Accounting and auditing

Increase in order size , decrease in order cost, increase in carrying



Shortage Cost

Temporary or permanent loss ofsales when demand can not be met

Result into

loss of profit Customer dissatisfaction

Loss of goodwill

Permanent loss of customer and futuresale

Work stopage result into downtimecost and cost of lost production


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Single-Period Inventory Model One time purchasing decision (Example:

vendor selling t-shirts at a football game)

Seeks to balance the costs of inventory

overstock and under stock Multi-Period Inventory Models

Fixed-Order Quantity Models

Event triggered (Example: running out of

stock) Fixed-Time Period Models

Time triggered (Example: Monthly sales callby sales representative)

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11

uo

u

CC

CP

soldbeunit willy that theProbabilit

estimatedunderdemandofunitperCostCestimatedoverdemandofunitperCostC

:Where

u

o

P

This model states that we

should continue toincrease the size of theinventory so long as theprobability of selling the

last unit added is equal toor greater than the ratioof: Cu/Co+Cu

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12

Our college basketball team is playing in atournament game this weekend. Based on ourpast experience we sell on average 2,400 shirtswith a standard deviation of 350. We make Rs100

on every shirt we sell at the game, but lose Rs50on every shirt not sold. How many shirts shouldwe make for the game?Cu=Rs100 and Co= Rs50; P 100 / (100 + 50) = .667

Z.667 = .432 (use NORMSDIST(.667) or Appendix E)therefore we need 2,400 + .432(350) = 2,551 shirts



Inventory ControlSystems (Multi Period

Inventory Models)Continuous system (fixed-order-

quantity Model/ Perpetual system/EOQor Q Model)

Periodic system (fixed-time-period/Period Review system/P Model)


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Continuous System

Constant amount ordered when inventory declines toreorder point (predetermined level)

The order that is placed is of fixed amount that

minimize the total inventory cost. This amount iscalled EOQ(Economic Order Quantity).

Positive features is continuous monitoring.

Negative aspect :: maintaining a continuous

record is costly Check out system with a laser scanner used by

super malls


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Periodic system

Order placed for variable amount after fixedpassage of time

Decision of order quantity is taken each timewhen order is placed

No need to monitor inventory in betweenthe time intervals

Positive aspects :: no need of recordkeeping, larger inventory level to guardagainst unexpected stockouts

Disadvantage :: less direct control

Exam le :: Colle e bookstore


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ABC Classification

System An inventory classification system wheresmall % of items account for most of theinventory value

Demand volume and value of items vary Classify inventory into 3 categories,

typically on the basis of the dollar valueto the firm

PERCENTAGE PERCENTAGECLASS OF UNITS OF DOLLARS

A 5 - 15 70 - 80B 30 15

C 50 - 60 5 - 10


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Each class requires different level of

inventory monitoring and control

the higher the value of the inventorythe tighter the control

Rationale for ABC Classification ::

Continuous inventory monitoring wasexpensive and not justified for manyitems


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First Step in ABC Analysis is to classify allinventory items as either A,B or C

Assign a dollar value to each item, which is computedby multiplying the dollar cost of one unit by the annualdemand for that item.

Rank all the items according to their annual dollar value( the top 10% as A items, the next 30% as B items andthe last 60% as C items

Second Step is to determine the level of inventorycontrol for each classification

Class A ::

tight inventory control.

Inventory level should be as low as possible,

minimized safety stock

Need accurate demand forecast and detailed recordkeeping

Appropriate inventory ctrl system and inventory modelingprocedure should be used to determine the order quantity

Close attention to be given to purchasing policies andprocedures


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Class B and C need less stringent inventory

control

Carrying cost of Class C is usually lower,therefore it is possible to maintain a largersafety stock

No need to control C items beyond simpleobservation

Apart from cost, the scarcity of parts

or difficulty of supply may also bereasons for giving high priority


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ABC Classification

1 $ 60 902 350 40

3 30 1304 80 605 30 1006 20 1807 10 1708 320 509 510 60

10 20 120

PART UNIT COST ANNUAL USAGE

Example 10.1


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ABC Classification

Example 10.1

1 $ 60 902 350 403 30 1304 80 605 30 1006 20 1807 10 170

8 320 509 510 60

10 20 120

PART UNIT COST ANNUAL USAGETOTAL % OF TOTAL % OF TOTALPART VALUE VALUE QUANTITY % CUMMULATIVE

9 $30,600 35.9 6.0 6.08 16,000 18.7 5.0 11.02 14,000 16.4 4.0 15.0

1 5,400 6.3 9.0 24.04 4,800 5.6 6.0 30.03 3,900 4.6 10.0 40.06 3,600 4.2 18.0 58.05 3,000 3.5 13.0 71.0

10 2,400 2.8 12.0 83.07 1,700 2.0 17.0 100.0

$85,400


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ABC Classification

Example 10.1

1 $ 60 902 350 403 30 1304 80 605 30 1006 20 1807 10 170

8 320 509 510 60

10 20 120


9 $30,600 35.9 6.0 6.08 16,000 18.7 5.0 11.02 14,000 16.4 4.0 15.0

1 5,400 6.3 9.0 24.04 4,800 5.6 6.0 30.03 3,900 4.6 10.0 40.06 3,600 4.2 18.0 58.05 3,000 3.5 13.0 71.0

10 2,400 2.8 12.0 83.07 1,700 2.0 17.0 100.0

$85,400

A

B

C


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ABC Classification

Example 10.1

1 $ 60 902 350 403 30 1304 80 605 30 1006 20 1807 10 170

8 320 509 510 60

10 20 120


9 $30,600 35.9 6.0 6.08 16,000 18.7 5.0 11.02 14,000 16.4 4.0 15.0

1 5,400 6.3 9.0 24.04 4,800 5.6 6.0 30.03 3,900 4.6 10.0 40.06 3,600 4.2 18.0 58.05 3,000 3.5 13.0 71.0

10 2,400 2.8 12.0 83.07 1,700 2.0 17.0 100.0

$85,400

A

B

C

% OF TOTAL % OF TOTAL

CLASS ITEMS VALUE QUANTITY

A 9, 8, 2 71.0 15.0B 1, 4, 3 16.5 25.0C 6, 5, 10, 7 12.5 60.0


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ABC Classification

100

80

60

40

20

0| | | | | |

0 20 40 60 80 100

% of Quantity

%o

fValue

A

B

C


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EOQ Model

A formula to determine the optimalorder size that minimizes the sum ofcarrying cost and ordering cost

Assumptions of Basic EOQ Model Demand is known with certainty and

is constant over time

No shortages are allowed

Lead time for the receipt of orders isconstant

The order quantity is received all atonce


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The Inventory Order Cycle

Time

Inventor

yLevel

Reorder point, R

Order quantity, Q

0

Figure 10.1


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The Inventory Order Cycle

Demandrate

TimeLeadtime

Leadtime

Orderplaced

Orderplaced

Orderreceipt

Orderreceipt

Inventor

yLevel

Reorder point, R

Order quantity, Q

0

Figure 10.1

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R = Reorder point

Q = Economic order quantity

L = Lead time

L L

Q QQ

R

Time

Number

of unitson hand

1. You receive an order quantity

Q.

2. Your startusing them up

over time.

3. When you reach down

to a level of inventory of

R, you place your next Q

sized order.

4. The cycle thenrepeats.


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EOQ Cost ModelCo

- cost of placing order D- annual demandCc

- annual per-unit carrying cost Q- order quantity

Annual ordering cost =

CoD

Q

Annual carrying cost =CcQ

2

Total cost = +

CoD

Q

CcQ

2


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EOQ Cost ModelCo

- cost of placing order D- annual demandCc

- annual per-unit carrying cost Q- order quantity

Annual ordering cost =

CoD

Q

Annual carrying cost =CcQ

2

Total cost = +

CoD

Q

CcQ

2

TC = +CoD

Q

CcQ

2

= +CoD

Q2

Cc

2

TC

Q

0 = - +C

0D

Q2

Cc

2

Qopt =2C

oD

Cc

Deriving Qopt Proving equality ofcosts at optimal point

=

CoD

Q

CcQ

2

Q2 =2C

oD

Cc

Qopt =2CoD

Cc

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H2

Q+S

Q

D+DC=TC

Total

Annual =

Cost

Annual

Purchase

Cost

Annual

Ordering

Cost

Annual

Holding

Cost+ +

TC=Total annual

cost

D =Demand

C =Cost per unit

Q =Order quantity

S =Cost of placing

an order or setup

costR =Reorder point

L =Lead time

H=Annual holding

and storage cost

per unit of inventory

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Using calculus, we take the first derivative of

the total cost function with respect to Q, andset the derivative (slope) equal to zero,solving for the optimized (cost minimized)

value of QoptQ =

2DS

H=

2(Annual D em and)(Order or Setup Cost)

Annual Holding CostO PT

R eorder point, R = d L_

d = average daily demand (constant)

L = Lead time (constant)

_

We also need areorder point totell us when toplace an order


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EOQ Cost Model

Order Quantity, Q

Annualcost ($)

Figure 10.2


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EOQ Cost Model

Figure 10.2

Order Quantity, Q

Annualcost ($)

Ordering Cost =

CoD

Q


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EOQ Cost Model

Order Quantity, Q

Annualcost ($)

Carrying Cost =

CcQ

2

Ordering Cost =

CoD

Q

Figure 10.2


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EOQ Cost Model

Slope = 0

Total Cost

Order Quantity, Q

Annualcost ($)

Minimumtotal cost

Optimal orderQopt

Carrying Cost =

CcQ

2

Ordering Cost =

CoD

Q

Figure 10.2


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EOQ Example

Cc

= $0.75 per yard Co

= $150 D= 10,000 yards

Qopt =2C

oD

Cc

Qopt =2(150)(10,000)

(0.75)

Qopt = 2,000 yards

TCmin = +CoD

Q

CcQ

2

TCmin = +(150)(10,000)

2,000

(0.75)(2,000)

2

TCmin = $750 + $750 = $1,500

Orders per year = D/Qopt

= 10,000/2,000

= 5 orders/year

Order cycle time = 311 days/(D/Qopt)

= 311/5

= 62.2 store days

Example 10.2


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EOQ with

Noninstantaneous Receipt

Q(1-d/p)

Inventorylevel

(1-d/p)Q2

Time0

Maximum

inventorylevel

Averageinventorylevel

Figure 10.3


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EOQ with

Noninstantaneous Receipt

Q(1-d/p)

Inventorylevel

(1-d/p)Q2

Time0

Orderreceipt period

Beginorder

receipt

Endorder

receipt

Maximum

inventorylevel

Averageinventorylevel

Figure 10.3


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EOQ with

Noninstantaneous Receiptp= production rate d= demand rate

Maximum inventory level = Q- d

= Q1 -

Q

p

dp

Average inventory level = 1 -

Q

2

d

p

TC= + 1 -dp

CoD

Q

CcQ

2

Qopt =

2CoD

Cc 1 - d

p


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Production QuantityCc

= $0.75 per yard Co

= $150 D= 10,000 yards

d= 10,000/311 = 32.2 yards per day p= 150 yards per day

Qopt = = = 2,256.8 yards

2CoD

Cc 1 - d

p

2(150)(10,000)

0.75 1 -32.2150

TC= + 1 - = $1,329dp

CoD

Q

CcQ

2

Production run = = = 15.05 days per orderQp

2,256.8

150

Example 10.3


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Production QuantityCc

= $0.75 per yard Co

= $150 D= 10,000 yards

d= 10,000/311 = 32.2 yards per day p= 150 yards per day

Qopt = = = 2,256.8 yards

2CoD

Cc 1 - d

p

2(150)(10,000)

0.75 1 -32.2150

TC= + 1 - = $1,329dp

CoD

Q

CcQ

2

Production run = = = 15.05 days per orderQp

2,256.8

150

Number of production runs = = = 4.43 runs/yearDQ

10,0002,256.8

Maximum inventory level = Q 1 - = 2,256.8 1 -

= 1,772 yards

d

p

32.2

150

Example 10.3


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Quantity Discounts Price per unit decreases as order

quantity increases

TC= + + PDCoDQ

CcQ2

where

P= per unit price of the itemD= annual demand


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Quantity Discounts Price per unit decreases as order

quantity increases

TC= + + PDCoDQ

CcQ2

where

P= per unit price of the itemD= annual demand

ORDER SIZE PRICE

0 - 99 $10100 - 199 8 (d1)

200+ 6 (d2)


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Quantity Discount Model

Figure 10.4

Inventorycost($)


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Quantity Discount Model

Figure 10.4

Qopt

Carrying cost

Ordering cost

Inventorycost($)

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

TC(d2 = $6 )

TC(d1 = $8 )

TC= ($10 )


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Quantity Discount

QUANTITY PRICE

1 - 49 $1,400

50 - 89 1,100

90+ 900

Co= $2,500

Cc= $190 per computer

D= 200

Qopt = = = 72.5 PCs2C

oD

Cc

2(2500)(200)

190

TC= + + PD= $233,784

CoD

Qopt

CcQopt

2

For Q= 72.5

TC= + + PD= $194,105CoD

Q

CcQ

2

For Q= 90

Example 10.4


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When to Order

Reorder Point is the level of inventoryat which a new order is placed

R= dL

where

d= demand rate per periodL = lead time


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Reorder Point Example

Demand = 10,000 yards/year

Store open 311 days/yearDaily demand = 10,000 / 311 = 32.154 yards/day

Lead time = L = 10 days

R = dL = (32.154)(10) = 321.54 yards

Example 10.5


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Safety Stocks

Safety stock

buffer added to on hand inventory during

lead time Stockout

an inventory shortage

Service level

probability that the inventory availableduring lead time will meet demand


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Variable Demand with

a Reorder Point

Figure 10.5

Reorder

point, R

Q

Time

Inventorylevel

0


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Variable Demand with

a Reorder Point

Figure 10.5

Reorder

point, R

Q

LT

Time

LT

Inventorylevel

0


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Reorder Point with

a Safety Stock

Figure 10.6

Reorderpoint, R

Q

LT

Time

LT

Inventorylevel

0

Safety Stock


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Reorder Point With

Variable DemandR= dL + z d L

where

d= average daily demandL = lead time

d= the standard deviation of daily demand

z= number of standard deviationscorresponding to the service levelprobability

z d L = safety stock


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Reorder Point for

a Service LevelProbability ofmeeting demand duringlead time = service level

Probability ofa stockout

R

Safety stock

dLDemand

z d L

Figure 10.7


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Reorder Point for

Variable DemandThe carpet store wants a reorder point with a95% service level and a 5% stockout probability

d= 30 yards per dayL = 10 days

d = 5 yards per day

For a 95% service level, z= 1.65

R= dL + z d L

= 30(10) + (1.65)(5)( 10)

= 326.1 yards

Safety stock = z d L

= (1.65)(5)( 10)

= 26.1 yards

Example 10.6


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Order Quantity for a

Periodic Inventory SystemQ= d(tb+ L) + z d tb+ L - I

where

d = average demand ratetb = the fixed time between ordersL = lead time

d = standard deviation of demand

z d tb+ L = safety stock

I = inventory level


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Fixed-Period Model with

Variable Demandd= 6 bottles per day

d = 1.2 bottlestb = 60 days

L = 5 daysI= 8 bottlesz= 1.65 (for a 95% service level)

Q= d(tb+ L) + z d tb+ L - I= (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8

= 397.96 bottles

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T+L d

i 1

T+L

d

T+L d

2

=

Since each day is independent and is constant,

= (T + L)

i

2

The standard deviation of a sequenceof random events equals the squareroot of the sum of the variances

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Average daily demand for a product

is 20 units. The review period is 30days, and lead time is 10 days.Management has set a policy ofsatisfying 96 percent of demand

from items in stock. At thebeginning of the review period thereare 200 units in inventory. The daily

Given the information below, how many

units should be ordered?

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Chapter 13 Inventory Decision Self