Question

Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation.​ Thomas's fastest-moving inventory item has a demand of 5 comma 850 units per year. The cost of each unit is ​$99​, and the inventory carrying cost is ​$9 per unit per year. The average ordering cost is ​$29 per order. It takes about 5 days for an order to​ arrive, and the demand for 1 week is 117 units.​ (This is a corporate​ operation, and there are 250 working days per​ year). a) What is the​ EOQ? ​(round your response to two decimal​ places). ​b) What is the average inventory if the EOQ is​ used? ​(round your response to two decimal​ places). ​c) What is the optimal number of orders per​ year? ​(round your response to two decimal​ places). ​d) What is the optimal number of days in between any two​ orders? ​(round your response to two decimal​ places). ​e) What is the annual cost of ordering and holding​ inventory? ​ ​(round your response to two decimal​ places). ​f) What is the total annual inventory​ cost, including the cost of the 5 comma 900 ​units? ​ ​(round your response to two decimal​ places).

Answer 1

Given: Annual Demand = D = 5,850 units

Cost of each unit = P = $99

Inventory carrying cost = H = $9 per unit per year

Ordering cost = S = $29

Weekly Demand = d = 117 units

Lead Time = LT = 5 days = 1 week

No. of Operating days = OD = 250 days

a) Economic Order Quantity = EOQ = = = 194.17 units

b) Average Inventory = = EOQ / 2 = 194.17 / 2 = 97.09 units

c) Optimal No. of orders per year = N = D / EOQ = 5850 / 194.17 = 30.13 orders

d) Optimal number of days in between any two​ orders = OD / N = 250 / 30.13 = 8.30 days

e) The annual cost of ordering and holding​ inventory = Ordering cost + Holding cost = N * S + * H = 30.13 * 29 + 97.09 * 9 = 873.77‬ + 873.81‬ = $1,747.58‬

f) Total annual inventory​ cost, including the cost of the 5,850 ​units = Annual cost of ordering and holding​ inventory + D * P = 1747.58 + 5850 * 99 = $580,897.58‬

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