In a reorder point problem where both demand and lead time are variable, demand averages 200 units per day with a daily variance of 64, and lead time averages 6 days with a standard deviation of 1 day. What should the reorder point be for a 95% service level?
A) 330 units
B) 201 units
C) 417 units
D) 1,617 units
E) 1,531 units

Question

Quizplus · Accepted Answer

The reorder point formula for variable demand and lead time is: Reorder Point = (Average Demand * Average Lead Time) + (Safety Stock). Safety Stock can be calculated using the formula: Z * sqrt((Average Lead Time * Daily Demand Variance) + (Average Demand^2 * Lead Time Variance)), where Z is the Z-score corresponding to the desired service level. For a 95% service level, Z is approximately 1.65. Plugging in the given values: Average Demand = 200 units/day, Average Lead Time = 6 days, Daily Demand Variance = 64, Lead Time Standard Deviation = 1 day (so Lead Time Variance = 1^2 = 1), we get Safety Stock = 1.65 * sqrt((6*64) + (200^2*1)) = 1.65 * sqrt(384 + 40000) = 1.65 * sqrt(40384) ≈ 1.65 * 201 = 331.65. Therefore, Reorder Point = (200 * 6) + 331.65 ≈ 1200 + 331.65 ≈ 1531.65, which rounds to 1,531 units.

In a Reorder Point Problem Where Both Demand and Lead