Freeport Corporation finds that demand for surfboards has average demand of 15 u

Question

Freeport Corporation finds that demand for surfboards has average demand of 15 units per day, with a standard deviation of 3 units. Lead time from the supplier averages 14 days, with a standard deviation of 2 days. The item costs $55 and the inventory carrying cost is 25 percent. Use Table 7-2.

a. Suppose management decides to offer a 90 percent service level; that is, it is willing to experience a stockout probability of 10 percent during the order cycle. How much safety stock should be carried? (Do not round intermediate calculations. Round up your answer to the next whole number.)

b. How much is the annual inventory carrying cost of the safety stock because of this decision? (Round your answer to the nearest dollar amount.)

c. You decide that you want this company to give better service to its customers. You decide that a 95 percent service level is appropriate. How much safety stock must be carried to offer this service level? (Do not round intermediate calculations. Round up your answer to the next whole number.)

d. What is the additional inventory carrying cost that will be incurred on this item because of your decision to increase the service level? (Round your answer to 2 decimal places.)

e. What will the reorder point be for the company if your decision is implemented? (Round your answer to the nearest whole number.)

Explanation / Answer

Average demand, d = 15 units per day

Std deviation, s = 3 units

Lead time, L = 14 days

Carrying cost, H = 55*0.25 = 13.75

a) For 90 % service leve, z = NORMSINV(0.9) = 1.2816

Safety stock = z * s * L^0.5 = 1.2816*3*14^0.5 = 15 (rounded up)

b) Annual inventory carrying cost of safety stock = 15*13.75 = $ 206

c) For 95 percent service level, z = NORMSINV(0.95) = 1.645

Safety stock = z * s * L^0.5 = 1.645*3*14^0.5 = 19 (rounded up)

d) Inventory caryring cost of safety stock = 19*13.75 = 261

Additional cost = 261 - 206 = $ 55

e) Reorder point = d*L + Safety stock = 15*14 + 19 = 229 units

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