Scenario 9.12
Demand = 100,000 units/year
Number of days per year = 250 weeks
Standard deviation of weekly demand = 50 units
Average lead time = 5 days
Standard deviation of lead time: 2 days
Cycle-service level = 99%
A continuous review system is used to control inventory.
A normal distribution table is appended to this exam.
-Use the information in Scenario 9.12.What reorder point should the firm use for this product?
A)greater than 4,500 units
B)greater than 3,500 units but less than or equal to 4,500 units
C)greater than 2,500 units but less than or equal to 3,500 units
D)greater than 1,500 units but less than or equal to 2,500 units
E)greater than 0 but less than or equal to 1,500 units

Question

Quizplus · Accepted Answer

The reorder point is the sum of the average demand during the lead time and the safety stock. The average demand during the lead time is equal to the demand per year multiplied by the average lead time and divided by the number of days per year. The safety stock is equal to the standard deviation of demand during the lead time multiplied by the z-score corresponding to the desired cycle-service level. The standard deviation of demand during the lead time is equal to the square root of the sum of the squares of the standard deviation of weekly demand and the standard deviation of lead time multiplied by the average lead time. The z-score corresponding to the desired cycle-service level can be found using a normal distribution table. In this case, the average demand during the lead time is equal to 100,000 units/year * 5 days / 250 days/year = 2,000 units. The standard deviation of demand during the lead time is equal to the square root of (50 units)^2 + (2 days * 5 days)^2 = 100 units. The z-score corresponding to the desired cycle-service level of 99% is 2.326. Therefore, the safety stock is equal to 100 units * 2.326 = 232.6 units. The reorder point is equal to the average demand during the lead time plus the safety stock, which is 2,000 units + 232.6 units = 2,232.6 units. Therefore, the reorder point should be greater than 2,232.6 units.

Scenario 9.12 Demand = 100,000 Units/year