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 ,900 units per year. The cost of each unit is ​$101 and the inventory carrying cost is $8 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 118 units. (This is a corporate​ operation, and there are 250 working days per​ year).

a) What is the​ EOQ?____units ​(round your response to two decimal​ places).

​b) What is the average inventory if the EOQ is​ used?____units ​(round your response to two decimal​ places).

​c) What is the optimal number of orders per​ year?____orders ​(round your response to two decimal​ places).

d) What is the optimal number of days in between any two​ orders?____days ​(round your response to two decimal​ places).

​e) What is the annual cost of ordering and holding​ inventory?____per year ​(round your response to two decimal​ places).

​f) What is the total annual inventory​ cost, including the cost of the 6,100 ​units?____per year ​(round your response to two decimal​ places).

Answer 1

Annual demand (D) = 5900 units

Carrying cost (H) = $8

Ordering cost (S) = $29

Number of days per year = 250

Average daily demand (d) = D/Number of days per year = 5900/250 = 23.6 units

a) Economic order quantity (EOQ) = √(2DS/H)

= √[(2 × 5900 × 29) / 8]

= √(342200/8)

= √42775

= 206.82 units

b) Average inventory = EOQ/2 = 206.82/2 = 103.41 units

C) Number of orders per year = D/EOQ = 5900/206.82 = 28.53

D) Optimal number of days between order = (EOQ/D) Number of days per year = (206.82/5900) 250 = 8.76 days

E) Annual ordering cost = (D/EOQ) S =(5900/206.82) 29 = $827.29

Annual holding cost = (EOQ/2) H = (206.82/2) 8 = 827.28

F) with a per unit cost of $101, purchase cost of 5900 units = $101 × 5900 = $595900

Total annual inventory cost = Annual ordering cost + Annual holding cost + purchase cost

= $827.29 + $827.28 + $595900

= $597554.57