Question

Shorty Corporation uses 1,452 of Part 34B each week. For simplicity’s sake it places an order for the amount every Monday so that it receives the order by the start of the following week. A recent analysis of the company’s costs has determined that the carrying costs for unit of inventory is $8.54 per item of inventory and that it costs an average of $560 to place an order.

1. What is the optimal size of an order? (i-e, What is the Economic Order Quantity?). Prove your answer by showing that the total annual carrying costs are equal to the total annual ordering costs.

2. What additional steps could you take to ensure the orders are placed on time and that the possibility of out-of-stocks is minimized?

Answer 1

(a) Annual Demand = D = 1452*52 = 75504/year

Ordering Cost = C_o = $560

Holding Cost = C_c = $8.54/year

Economic Order Quantity Q* = √(2DC_o/C_c) = √(2*75504*560/8.54) = 3146.77

Annual Inventory Holding cost = average inventory * unit carrying cost = (Q*/2)*C_c = (3146.77/2)*8.54 = $13436.71

Annual Order cost = Number of orders * cost/order = (D/Q*) C_o = (75504/3146.77)*560 = $13436.71

Hence, Inventory Holding Cost and Ordering Costs are equal at the economic ordering quantity

(b) Orders are placed on each Monday so that it is received at the start of next week

Hence, Lead time = L = 1 week

Average demand d = 1452 / week

Reorder Point = 1452*1 = 1452

Hence, orders should be placed when the inventory level reaches 1452, to ensure that stockouts don't occur