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IM 322Inventory Management

Chapter 3Chapter 3 Economic Order Quantity Model(EOQ)

Textbook:

Donald Waters, Inventory Control and Management, 2nd

ed-1-

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Chapter Outline

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Quantitative Inventory management

Quantitative Inventory

management answers twoprimary questions:

How much to order:

Order Quantity or

Economic Order Quantity (EOQ)

When to order:

Reorder point

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Typical pattern of stock level over time

Reorderpoint

Q1

Lead Time

Time

Inv

entory

level

0Lead Time

Q2

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Economic Order Quantity (EOQ)

Idealized stock

To find the fixed order size that minimizes costs Basis of most independent demand

DemandDemand

raterate

TimeTimeLeadLeadtimetime

LeadLeadtimetime

Order placedOrder placedOrder placedOrder placedOrderOrderreceiptreceipt

Order receiptOrder receipt

Inventory

Level

Inventory

Level

Reorder point,Reorder point, RR

Order quantity,Order quantity, QQ

00

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Basic Economic Order Quantity (EOQ)

Model Assumptions

Demand is known exactly, is continuous and is

constant over time

All costs are known exactly and do not vary

Ex: holding cost, purchase price, and reorder costs donot vary with the quantity ordered

No shortages are allowed

Lead time is constant

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Pressures for Low Inventories

When keeping inventory, there arealways some cost incurred Inventoryholding cost (or carrying cost)

The variable cost of keeping items on hand

$/ unit-period Inventory holding cost generally

includes:

Interest of opportunity cost

Storage and handling costs (e.g., electricity,utilities, documentation, labor costs)

Tax, insurance, and shrinkage

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Pressures for High Inventory

Customer service

Reorder or Ordering cost ($ /order)

Setup cost Transportation cost

Payment to suppliers

Labor and equipmentutilization

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Variables used in the analysisUnit Cost (UC) Price charged by the suppliers for one unit of item, or Total cost to organization of acquiring one unit

$ / unit

Reorder cost (RC) Cost of placing a routine order $ / order, $/setup

Holding cost (HC) Cost of holding one unit of the item in stock for one period of

time $ / unit-period

Shortage cost (SC) Cost of having a shortage and not being able to meet demand

from stock $ / unit-period

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Variables used in the analysisOrder quantity (Q)

Fixed order size

Cycle time (T)

Time between two consecutive replenishment

Depends on Q

Demand (D)

The number of units to be supplied from stock in a given

time period Basic EOQ assumes known constant demand

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Derivation of the EOQ

EOQ: the lot size or order size that minimizes

total annual inventory holding and ordering cost

Under basic EOQ

Amount enteringstock in cycle,

Q

Amount leaving stockin cycle,

D x T=

Total cost per cycle =Unit cost

componentReorder

Costcomponent

HoldingCost

component+ +

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Derivation of the EOQ

Total CostTotal Cost

Holding CostHolding Cost

Slope = 0Slope = 0

MinimumMinimum

total costtotal cost

Optimal orderOptimal orderQQoo

Reorder CostReorder Cost

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Ex 1: Carpet SalesThe 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. Thestore 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 openevery except Sunday, Thanksgiving Day and Christmas Day.

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Adjusting EOQ

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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 originalestimates

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 theestimated total cost.

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Adding Finite Lead Time

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Reorder Level Additional assumption: Lead time is known and constant

No need to carrying stock from one cycle to the next

So each order should be scheduled to arrive as existing stock runsout

Reorder level = demand during lead time = lead time x demand per unit tiROL = LT x D

Reorder level = demand during lead time = lead time x demand per unit tiROL = LT x D

Revisit Ex 1: Carpet Sell. Given that product lead time is 5 days. Calculate reorderlevel (ROL)17

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Reorder Level with Longer Lead Time When lead time is longer than the stock cycle

There is always one order outstanding.

Example: when it is time to place order B, there is one order, A

outstanding and due to arrive before B.

The stock on hand plus the outstanding order must be

enough to last until B arrive or equal the lead timedemand

Stock on hand Stock on order+ = LT x DROL

ROL Stock on order-= LT x D

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Reorder Level with Longer Lead Time When lead time is very long

Several orders are outstanding at anytime

When lead time is between nand n+1 cycle length

n x T < LT < (n+1) x T

There are nordersoutstanding

ROL Stock on order-Lead time demand=

n x Qo-LT x D=

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Ex 2Demand for an item is steady at 1,200 units a year

with an ordering cost of $16 and holding cost of

$0.24 per unit per year. Describe a appropriateordering policy if the lead time is constant at

(a) 3 months

(b) 9 months

(c) 18 months

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Discussion Questions

What are the benefit of short lead times? How canthese be achieved in practice?

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EOQ. Derivation

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EX1 Carpet Sales

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