Question

M. Cotteleer Electronics supplies microcomputer circuitry to a company that incorporates microprocessors into refrigerators and other home appliances. One of the components has an annual demand of 250 units, and this is constant throughout the year. Carrying cost is estimated to be $1 per unit per year, and the ordering (setup) cost is $20 per order.

a) To minimize cost, how many units should be ordered each time an order is placed?

b) How many orders per year are needed with the optimal policy?

c) What is the average inventory if costs are minimized?

d) Suppose that the ordering (setup) cost is not $20, and Cotteleer has been ordering 150 units each time an order is placed. For this order policy (of Q=150) to be optimal, determine what the ordering (setup) cost would have to be.

Answer 1

Given values:

Annual demand, D = 250 units

Carrying cost, Cc = $1 per unit per year

Ordering cost, Co = $20 per order

Solution:

(a) The cost is minimum when the number of units ordered are in accordance with the Economic Order Quantity (EOQ).

EOQ is calculated as;

EOQ = SQRT (2*D*Co) / Cc

where,

D = Annual demand

Co = Cost of ordering

Cc = Carrying cost

Putting the given values in the above formula, we get;

EOQ = SQRT (2 x 250 x 20) / 1

EOQ = SQRT (10000)

EOQ = 100 units

To minimize cost, 100 units should be ordered each time an order is placed.

(b) Number of orders per year is calculated as;

Number of orders = Annual demand / EOQ

Number of orders = 250 / 100

Number of orders = 2.5 orders per year

(c) Average inventory is calculated as;

Average inventory = EOQ / 2

Average inventory = 100 / 2

Average inventory = 50 units

(d) Given, Ordering quantity, Q = 150 units

For, Q = 150 units to be optimal, it should be the New Economic Order Quantity (EOQ).

EOQ = SQRT (2*D*Co) / Cc

150 = SQRT (2 x 250 x Co) / 1

150 = SQRT (500 x Co)

500 Co = 150 ^ 2

500 Co = 22500

Co = $45

New ordering (setup) cost = $45