**The Economic Order Quantity (EOQ) Models**

There are three order size models:

The Economic Order Quantity Model (Basic)

The Quantity Discount Model

**Basic Economic Order Quantity (EOQ) Model**

the simplest of the three models

used to identify the order size that will minimize the sum of the annual costs of holding inventory and ordering inventory.

Total Cost

Where:

TC = Total annual cost

D = Demand (usually in units per year)

Q = Order quantity, in units

S = Ordering cost or setup cost

(monetary value/currency)

H = Carrying cost or holding cost

(currency per unit per year)

Deriving the EOQ

After computing the optimum (economic) order quantity, the minimum total cost is then found by substituting EOQ for Q in the Total Cost Function

A local distributor for a national tire company expects to sell approximately 9,600 steel-belted radial tires of a certain size and tread design next year. Annual carrying costs are $16 per tire, and ordering costs are $75. The distributor operates 288 days a year.

a. Determine the EOQ.

b. How many times per

year does the store

reorder?

c. Determine the length of

an order cycle.

HOW MUCH

TO ORDER?

EOQ models identify the optimal order quantity in terms of minimizing the sum of certain annual costs that vary with order size.

The Economic Order Quantity Model with non instantaneous delivery

Assumptions of the basic EOQ model

1. There is only one product involved.

2. Annual usage (demand) requirements are known.

3. Usage is spread evenly throughout the year so

that the usage rate is reasonably constant.

4. Lead time does not vary.

5. Each order is received in a single delivery.

6. There are no quantity discounts.

The Inventory Cycle

Average inventory level and number of orders per year are inversely related: as one increases, the other decreases.

Total Cost =

Annual carrying cost

+

Annual ordering cost

TC =

Q

2

H

+

D

Q

S

Cost Minimization Goal

Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

Length of order cycle =

EOQ

D

Solution:

D = 9,600 tires per year

H = $16 per tire per year

S = $75

a. EOQ =

2DS

H

=

2(9,600) 75

16

=

300 tires

b. Number of orders per year:

D

EOQ

=

9,600 tires

300 tires

=

32

c. Length of order cycle:

EOQ

D

=

300 tires

9,600 tires

=

1/32 of a year

which is 1/32 x 288, or 9 workdays

**Quantity Discount Model**

Minimum Total Cost

The total cost curve reaches its minimum where the carrying and ordering costs are equal.

Annual carrying cost

=

Annual ordering cost