Question

Given the following information, the reorder point to use to achieve a 99% service level would be:

Average weekly demand = 40 units
Replenishment Leadtime = 4 weeks
Standard deviation of demand = 5 units
z-score for a 99% service level = 2.33

184 units

160 units

45 units

165 units

Answer 1

Reorder Point (ROP) = (Average daily Demand * Lead Time) + Safety Stock

Where, Safety Stock = [z* standard deviation of daily demand * (square root of (lead time))]

And z is the number of standard deviations corresponding to the service level probability

The term [standard deviation of daily demand * (square root of (lead time))] in the above formula for the reorder point is the square root of the sum of the daily variance during lead time:

Variance = (daily variance) * (number of days of lead time) = (square of standard deviation of daily demand) * (number of days of lead time)

Therefore, standard deviation = square root of [(square of standard deviation of daily demand) * (number of days of lead time)]

= standard deviation of daily demand * (square root of (lead time))

Given in the problem,

Average weekly demand = 40 units

Replenishment Lead Time = 4 weeks

Standard deviation of demand = 5 units

Z-score for a 99% service level = 2.33

Hence, for a 99% service level, z = 2.33 (under the standardized normal curve)

Thus, Safety stock = (2.33) * (5) * (square root of (4)) = 2.33 * 5 * 2 = 23.3 units

Therefore, ROP = (40 * 4 ) + 23.3 = 183.3 (app. 184 units)