Annual demand for a product is 10,400 units; weekly demand is 200 units with a s

Question

Annual demand for a product is 10,400 units; weekly demand is 200 units with a standard deviation of 60 units. The cost of placing an order is $125, and the time from ordering to receipt is four weeks. The annual inventory carrying cost is $0.80 per unit.

a. To provide a 90 percent service probability, what must the reorder point be? (Use Excel's NORMSINV() function to find the correct critical value for the given -level. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to the nearest whole number.)

b. Suppose the production manager is told to reduce the safety stock of this item by 110 units. If this is done, what will the new service probability be? (Use Excel's NORMSDIST() function to find the correct probability for your computed Z-value. Round your answer to the nearest whole number.)

Explanation / Answer

Weekly demand (d) = 200

standard deviation (s) = 60

Lead time (L) = 4 weeks

service level = 90%, z value using NORMSINV = 1.28

a)Reorder point = d*L + z*s*sqrt(L) = 200*4 + 1.28*60*sqrt(4) = 800 + 153.6 = 953.6 = 954

b) Safety stock = z*s*sqrt(L) = 154

New safety stock = 154-110 = 44

44 = z*s*sqrt(L) = z*60*sqrt(4)

z = 44/120 = 0.37

Service probability for z = 0.37 is 64%

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