Annual demand for a product is 17,680 units; weekly demand is 340 units with a s

Question

Annual demand for a product is 17,680 units; weekly demand is 340 units with a standard deviation of 75 units. The cost of placing an order is $80, and the time from ordering to receipt is four weeks. The annual inventory carrying cost is $0.60 per unit.

To provide a 95 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.)

Suppose the production manager is told to reduce the safety stock of this item by 100 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.)

To provide a 95 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.)

Explanation / Answer

a)

Weekly demand = 340 units

Standard deviation = 75 units

Ordering cost = $ 80

Lead time = 4 weeks

Annual inventory cost = $ 0.6

Reorder point = (weekly demand * lead time) + (z * standard deviation * Sqrt(lead time))

Reorder point = (340 * 4) + (1.64 * 75 * Sqrt(4)) = 1606 units

b)

(z * standard deviation * Sqrt(lead time)) = 100

(z * 75 * Sqrt(4)) = 100

(z * 150) = 100

Z = 0.67

From z table we get, Value of (z = 0.67) =   0.7486 = 74.86 % = 75%

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