Question

Annual demand for a product is 10,920 units; weekly demand is 210 units with a standard deviation of 40 units. The cost of placing an order is $155, and the time from ordering to receipt is four weeks. The annual inventory carrying cost is $0.70 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 α-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 80 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.)

Answer 1

Answer:

a) 942

Annual Demand (D) = 10920

Weekly Demand (d) = 210

Std deviation = 40

Ordering Cost (S) = $155

Holding cost per unit (H) = $0.70

Lead time (L) = 4 weeks

Reorder Point = Average demand during lead time + Safety Stock (SS)

Average demand during lead time = d*L = 210*4 = 840

For 90% service level,

Z =NORMSINV(0.9) = 1.28

$SS = Z*\sigma*\sqrt{L} = 1.28*40*\sqrt4 = 102.4$

Reorder Point = 840 + 102.4 = 942.4 ~ 942

b) 84%

SS = 80

From SS, we can find the value of Z

$SS = Z*\sigma*\sqrt{L}$

Z = 80/(40*2) = 1

For Z = 1, Service level = =NORMSDIST(1) = 0.8413 = 84.13% ~ 84%