Problem 10-35 (Algorithmic) Statewide Auto Parts uses a four-week periodic revie
ID: 449013 • Letter: P
Question
Problem 10-35 (Algorithmic)
Statewide Auto Parts uses a four-week periodic review system to reorder parts for its inventory stock. A one-week lead time is required to fill the order. Demand for one particular part during the five-week replenishment period is normally distributed with a mean of 19 units and a standard deviation of 6 units.
At a particular periodic review, 7 units are in inventory. The parts manager places an order for 18 units. What is the probability that this part will have a stock-out before an order that is placed at the next four-week review period arrives? If required, round your answer to four decimal places.
Assume that the company is willing to tolerate a 3% chance of a stock-out associated with a replenishment decision. How many parts should the manager have ordered in part (a)? If required, round your answer to the nearest whole number.
The manager should have ordered units.
What is the replenishment level for the four-week periodic review system? If required, round your answer to the nearest whole number.
The replenishment level for the four-week periodic review system is .
Explanation / Answer
In a periodic review system, target inventory T, given: P = 4 weeks L = 1 weeks Safety stock = z * std Dev (P,L) Std Dev (P,L) = Std Dev Demand * P+L = 7 * 4+1 = 15.65 or 16 units Safety stock = Z Value * (16 units) T = Average demand during the protection interval + Safety stock - Inventory in hand 18 = 19 + Z Value * (16 units) - 7 or, 6 = Z Value * 16 units or, Z Value = 0.3833 or, Required probability = 39% b. P = 4 weeks L = 1 weeks Safety stock = z * std Dev (P,L) Std Dev (P,L) = Std Dev Demand * P+L = 7 * 4+1 = 15.65 or 16 units At 97% Service Level Z-Value = 1.881 Safety stock = Z Value * (16 units) = 30units T = Average demand during the protection interval + Safety stock - Inventory in hand T = 19 + 30 - 7 or, T = 42 units
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