Inventory Modeling for Independent Demand. Explain what inventory is Describe how inventory is classified Explain ABC analysis Explain cycle counting.

MBA 570Summer 2011

Inventory Modeling for Independent Demand

Learning Objectives Explain what inventory is Describe how inventory is classified Explain ABC analysis Explain cycle counting Compare inventory models Use inventory models to find how much &

when to order

What Is Inventory? Stock of materials Stored capacity

What Is Inventory? Stock of materials Stored capacity Examples

© 1995 Corel Corp.© 1984-1994 T/Maker Co.

© 1984-1994 T/Maker Co.

© 1995 Corel Corp.

The Functions of Inventory

To ”decouple” or separate various parts of the production process

To provide a stock of goods that will provide a “selection” for customers

To take advantage of quantity discounts

To hedge against inflation and upward price changes

Types of Inventory

Raw material Work-in-progress Maintenance/repair/

operating supply Finished goods

Disadvantages of Inventory Higher costs

◦ Item cost (if purchased)◦ Ordering (or setup) cost Costs of forms, clerks’ wages etc.

◦ Holding (or carrying) cost Building lease, insurance, taxes etc.

Difficult to control Hides production problems

Inventory Holding Costs

Housing (building) cost 6%Material handling costs 3%Labor cost 3%Inventory investment costs 11%Pilferage, scrap, & obsolescence 3%Total holding cost 26%

% of Category Inventory Value

Inventory

ProcessStage

DemandType

Number& Value

Other

Raw Mat'lWIP

Fin. Goods

IndependentDependent

A ItemsB ItemsC Items

Mainten.Repair

Operating

Inventory Classifications

© 1984-1994

T/Maker Co.

Inventory Management

ABC Analysis

Divides on-hand inventory into 3 classes◦ A class, B class, C class

Basis is usually annual $ volume◦ $ volume = Annual demand x Unit cost

Policies based on ABC analysis◦ Develop class A suppliers more◦ Give tighter physical control of A items◦ Forecast A items more carefully

Classifying Items as ABC

0

20

40

60

80

100

0 20 40 60 80 100

% of Inventory Items

% Annual $ Usage Class % $ Vol % Items

Classifying Items as ABC

0

20

40

60

80

100

0 20 40 60 80 100

% of Inventory Items

% Annual $ Usage

A

B C

Class % $ Vol % ItemsA 80 15B 15 30C 5 55

ABC Classification Example

You’re a buyer for Auto Palace. Classify the following items as A, B, or C.

Stock # Annual Volume (Units) Unit Cost

206 26,000 $ 36

105 200 600

019 2,000 55

144 20,000 4

207 7,000 10Note: Example is for illustration only; too few items.

ABC Classification Solution

Stock # Vol. Cost $ Vol. % ABC

206 26,000 $ 36 $936,000 71.1 A

105 200 600 120,000 9.1 A

019 2,000 55 110,000 8.4 B

144 20,000 4 80,000 6.1 B

207 7,000 10 70,000 5.3 C

Total 1,316,000 100.0

ABC Classification Thinking Challenge

You’re an inventory control supervisor for USX. Classify the following items as A, B, or C.

Stock # Annual Volume (Units) Unit Cost

Z-206 13,000 $ 22

W-105 75 200

Z-019 1,700 25

P-144 12,000 1

K-207 3,000 2

ABC Classification Solution*

Stock # Vol. Cost $ Vol. % ABC

Z-206 13,000 $ 22 $286,000 79.1 A

W-105 75 200 15,000 4.1 B

Z-019 1,700 25 42,500 11.8 B

P-144 12,000 1 12,000 3.3 C

K-207 3,000 2 6,000 1.7 C

Total $361,500 100.0

Physically counting a sample of total inventory on a regular basis

Used often with ABC classification A items counted most often

(e.g., daily)

Cycle Counting

Advantages of Cycle Counting Eliminates shutdown and

interruption of production necessary for annual physical inventories

Eliminates annual inventory adjustments

Provides trained personnel to audit the accuracy of inventory

Allows the cause of errors to be identified and remedial action to be taken

Maintains accurate inventory records

Basic Inventory Planning Questions How much to order? When to order?

Purchase OrderDescripti

onQty.

Microwave

1000

Inventory Models

Fixed order quantity models◦ Economic order quantity◦ Production order quantity◦ Quantity discount

Help answer the inventory planning questions!

Help answer the inventory planning questions!

© 1984-1994 T/Maker Co.

Economic Order Quantity (EOQ) Model

EOQ Assumptions

Known & constant demand Known & constant lead time Instantaneous receipt of material No quantity discounts Only order (setup) cost & holding cost No stockouts

Goal of an Inventory System

Minimize Total Cost (TC)

TC = Holding + Order/Setup Cost

TC = H + S

EOQ Model: How Much to Order?

Order Quantity

Annual Cost


Order Quantity

Annual Cost

Holding Cost


Order Quantity

Annual Cost

Holding Cost

Order (Setup) Cost


Order Quantity

Annual Cost

Holding Cost

Total Cost Curve

Order (Setup) Cost


Order Quantity

Annual Cost

Holding Cost

Total Cost Curve

Order (Setup) Cost

Optimal Order Quantity (Q*)

Why Holding Cost Increases

More units must be stored if more ordered


onQty.

Microwave

1000


onQty.

Microwave

1

Order quantity

Order quantity

Why Order Cost Decreases Cost is spread over more units

Example: You need 1000 microwave ovens


onQty.

Microwave

1000


onQty.

Microwave

1


onQty.

Microwave

1


onQty.

Microwave

1


onQty.

Microwave

1

1 Order (Postage $ 0.32) 1000 Orders (Postage $320)

Order quantity

EOQ Model: When to Order?

Inventory Level


Time


Inventory LevelOptimal Order Quantity (Q*) Decrease due

to constant demand

Time


Inventory Level


Instantaneous receipt of optimal order quantity

Time


Inventory Level


Time


Inventory LevelOptimal Order Quantity (Q*)

Lead Time

Reorder

Point (ROP) Time

Reorder

Point (ROP)


Time

Inventory Level

Optimal Order Quantity(Q*)

AverageInventory (Q*/2)

Lead Time

EOQ Model Output Example When the inventory of microwaves gets

down to 15 units (reorder point), order 35 units (EOQ).

15 left


onQty.

Microwave

35

EOQ Model Equations

Optimal Order Quantity

Expected Number Orders

Expected Time Between OrdersWorking Days / Year

Working Days / Year

QD SH

NDQ

TN

dD

ROP d L

*

*

2

D = Demand per yearS = Setup (order) cost per orderH = Holding (carrying) cost d = Demand per dayL = Lead time in days

EOQ Thinking Challenge

You’re a buyer for Wal-Mart. Wal-Mart needs 1000 coffee makers per year. The cost of each coffee maker is $78. Ordering cost is $100 per order. Carrying cost is 40% of per unit cost. Lead time is 5 days. Wal-Mart is open 365 days/yr. What is the optimal order quantity & ROP?

EOQ Model Equations

Optimal Order Quantity

Expected Number Orders

Expected Time Between OrdersWorking Days / Year

Working Days / Year

QD SH

NDQ

TN

dD

ROP d L

*

*

2

D = Demand per yearS = Setup (order) cost per orderH = Holding (carrying) cost d = Demand per dayL = Lead time in days

EOQ Solution*

QH

dD

ROP d L

*.

.

. .

= = =

= = =

= × = =

2X1000X10040 (78)

80

1000365

274

274 X 5 137

units

units/day

units

Working Days/Year

2 X D X S

Production Order Quantity Model

Production Order Quantity Model

Answers how much to order & when to order

Allows partial receipt of material◦ Other EOQ assumptions apply

Suited for production environment◦ Material produced, used immediately◦ Provides production lot size

Lower holding cost than EOQ model

POQ Model: Inventory Levels

Time

Inventory Level

Supply

Begins


Time

Inventory Level

Supply

Begins

Supply

Ends


Time

Inventory Level

Supply

Begins

Supply

Ends

Inventory level with NO demand during supply of optimum order quantity


Time

Inventory Level

Supply

Begins

Supply

Ends

Inventory level with NO demand during supply of optimum order quantity

Q*

Q* is optimum order qty


Time

Inventory Level

Supply

Begins

Supply

Ends

Inventory level with CONSTANT demand during supply of optimum order quantity

Q*

Q* is optimum order qty


Time

Inventory Level

Supply

Begins

Supply

Ends

Q* Quantity used before becoming inventory


Time

Inventory Level

Supply

Begins

Supply

Ends

Decrease due to no supply & constant demand

Inventory Level


TimeSuppl

y Begin

s

Supply

Ends

Production portion of cycle

Demand portion of cycle with no supply


Time

Inventory Level

Next Cycle


Time

Inventory Level

Supply

Begins

Next Cycle


Time

Inventory Level

Supply

Begins

Supply

Ends


Time

Inventory Level

Supply

Begins

Supply

Ends


Time

Inventory Level

Max. Inventory Q*·(1- d/p)


Time

Inventory Level

Production Portion of Cycle

Max. Inventory Q·(1- d/p)

Q*

Supply Begins

Supply Ends

Inventory level with no demand

Demand portion of cycle with no supply

POQ Model Equations

Max. Inventory Level

Setup Cost

Holding Cost =

= -

=

Qdp

DQ

SD = Demand per yearS = Setup costH = Holding cost d = Demand per dayp = Production per day

Optimal Order Quantity = Qp* = 2 x D x S

H x (1- d/p)

x 1

x

Q 1 - (d/p) H

POQ Model Thinking Challenge

You’re a production planner for Stanley Tools. Stanley Tools makes 30,000 screw drivers per year. Demand is 100 screw drivers per day & production is 300 per day. Production setup cost is $150 per order. Carrying cost is $1.50 per screw driver. What is the optimal lot size?

POQ Model Equations

Max. Inventory Level

Setup Cost

Holding Cost =

= -

=

Qdp

DQ

SD = Demand per yearS = Setup costH = Holding cost d = Demand per dayp = Production per day

Optimal Order Quantity = Qp* = 2 x D x S

H x (1- d/p)

x 1

x

Q 1 - (d/p) H

Production Order Quantity Model Solution*

QD S

Hdp

p*=× ×

×=

× ×

× -=

= × - =

2 2 30000 150

1.5 1100300

3000

3000100300

2000Max. Inventory Level

D = Demand Per YearS = Setup CostH = Holding Cost d = Demand Per Dayp = Production Per Day

1 -

1

Quantity Discount Model

Answers how much to order & when to order

Allows quantity discounts◦ Reduced price when item is purchased in larger

quantities◦ Other EOQ assumptions apply

Trade-off is between lower price & increased holding cost

Quantity Discount Model: How Much to Order?

Order Quantit

y

Total Cost


Order Quantit

y

Total Cost

Discount Quantity 1

Price 1


Order Quantit

y

Total Cost

Discount Quantity 1

Discount Quantity 2

Price 1 Price 2

Order Quantit

y


Total Cost

Discount Quantity 1

Discount Quantity 2

Price 1 Price 2 Price 3


Order Quantit

y

Total Cost TC for Discount 1

Discount Quantity 1

Discount Quantity 2



Order Quantit

y


Discount Quantity 1

Discount Quantity 2


Q*


Order Quantit

y


Discount Quantity 1

Discount Quantity 2


Q*

Outside discount range


Order Quantit

y

Total Cost

Discount Quantity 1

TC for Discount 2

Discount Quantity 2

Price 1 Price 2 Price 3TC for

Discount 1


Order Quantit

y

Total Cost

Disc Qty 1

TC for Discount 2

Discount Quantity 2


Q*

TC for Discount 1


Order Quantit

y

Total Cost

Disc Qty 1

TC for Discount 2

Discount Quantity 2


Q*



TC for Discount 1


Order Quantit

y

Total Cost

Disc Qty 1

TC for Discount 2

Discount Quantity 2


Q* adjuste

d

TC for Discount 1

X


Order Quantit

y

Total Cost

TC for Discount 3

Discount Quantity 2


Discount Quantity 1

TC for Discount 2

TC for Discount 1


Order Quantit

y

Total Cost

TC for Discount 3

Discount Quantity 2


Q*Discount Quantity 1

TC for Discount 2

TC for Discount 1


Order Quantit

y

Total Cost

TC for Discount 3

Discount Quantity 2


Disc Qty 1

Outside discount range Q*

TC for Discount 2

TC for Discount 1


Order Quantit

y

Total Cost

TC for Discount 3

Disc Qty 2


Q* adjusted

Discount Quantity 1

X

TC for Discount 2

TC for Discount 1


Order Quantit

y


Discount Quantity 1

TC for Discount 2

TC for Discount 3

Discount Quantity 2

Lowest cost not in discount range

Quantity Ordered


Quantity Discount Model Steps

Compute EOQ for each quantity discount price

Is computed EOQ in discount range?◦ If not, use the lowest cost quantity in discount

range Compute total cost for EOQ or lowest cost

quantity in discount range Select quantity with lowest total cost

Inventory Modeling for Independent Demand. Explain what inventory is Describe how inventory is classified Explain ABC analysis Explain cycle counting.

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