Question

The annual demand of a good is 8000 ​units, the fixed cost of placing an order is ​$100 and the annual cost of storing an item is ​$70. The same​ order, Q, is placed at regular intervals throughout the​ year, and the firm waits for stock levels to reduce to zero before ordering new stock.

​(a) Obtain an​ expression, for the total ordering cost​ C, in terms of Q.

​(b) Work out how many items should be ordered each time to minimise total cost. ​(c) What is the minimum total​ cost?

Answer 1

A.

Total ordering cost (C) = (annual demand / Order quantity)*ordering cost per order

Total ordering cost (C) = (8000/Q)*100

Total ordering cost (C) = 800000/Q

===

B.

To minimize the total cost, the order quantity will be EOQ as Q.

So,

EOQ (Q) = (2*annual demand*ordering cost / inventory cost per unit per year)^.5

EOQ (Q) = (2*8000*100/70)^.5

EOQ (Q) = 151.19 units or 151 units

So, 151.19 units or 151 units of product should be ordered each time to minimize the total cost.

==

C

The minimum total cost = annual ordering cost + annual holding cost

The minimum total cost = (8000/Q)*100 + (Q/2)*70

The minimum total cost = (8000/151 )*100 + (151/2)*70

The minimum total cost = $10583.01 or $10583

So, the minimum total cost will be $10583.01 or $10583, other than the product actual cost.