Copyright 2013 John Wiley & Sons, Inc.

Chapter 7: Supplement B

The Economic Order Quantity

7B-2

The Economic Order Quantity Model (EOQ)

• EOQ model applier to items that are:– Replenished in batches or orders– Not produced and delivered instantaneously

• Only two costs are considered:1. Carrying costs2. Ordering costs

• Will decide1. When to order2. How many to order

7B-3

Assumptions

1. Constant rate of demand2. Shortages not allowed3. Stock replenishment can be scheduled to

arrive exactly when inventory drops to zero4. Purchase price, ordering cost, and per unit

holding cost are independent of quantity ordered

5. Items are ordered independently of each other

7B-4

Notation

Q Order quantity

U Annual usage

CO Order cost per order

CH Annual holding cost per unit

7B-5

Water Distributor’s Inventory Pattern

Figure 7SB.1

7B-6

Water Distributor’s Inventory Graph

Figure 7SB.2

7B-7

Cost Equations

7B-8

Graph of Annual Inventory Costs

Figure 7SB.3

7B-9

Finding an Optimal Policy

H

O

H

O2

OH

2

OH

C

2UC=EOQ

C

UC2Q

UCC2

Q

CQ

UC

2

Q

7B-10

EOQ Example

• Sells 1,000 bottles a month

• Lead time is six days

• Cost of placing an order is $60

• Cost of holding one bottle in inventory is $10

7B-11

Cautions Regarding EOQ

• Garbage in, garbage out (GIGO)

• Exclude “sunk” costs

• Very small EOQ values my not be valid