Problem 13-31 A drugstore uses fixed-order cycles for many of the items it stock
ID: 333268 • Letter: P
Question
Problem 13-31 A drugstore uses fixed-order cycles for many of the items it stocks. The manager wants a service level of .90. The order interval is 9 days, and lead time is 1 days. Average demand for one item is 60 units per day, and the standard deviation of demand is 3 units per day. Given the on-hand inventory at the reorder time for each order cycle shown in the following table. Use Table. CycleOn Hand 35 90 Determine the order quantities for cycles 1,2, and 3: (Round your answers to the nearest whole number) Cycle UnitsExplanation / Answer
Given are following data :
Order interval = 9 days
Lead time = 1 day
Therefore, Protection period = P = Order interval + Lead time = 9 + 1 = 10 days
Required service level = 0.90
Corresponding Z value = NORMSINV ( 0.90) = 1.2815
Standard deviation of daily demand = 3 units
Therefore, standard deviation of demand during protection period
= Standard deviation of daily demand x square root ( Protection period )
= 3 x square root ( protection period )
= 3 X square root ( 10 )
= 3 x 3.162
= 9.486
Therefore, safety stock = Z value x standard deviation of demand during protection period = 1.2815 x 9.486 = 12.15 ( 12 rounded to nearest whole number )
Reorder point = Daily demand x Protection period + safety stock = 60 x 10 + 12 = 612
Order quantity = Reorder point – Quantity on hand
Accordingly, please find below required answers :
CYCLE
UNITS
1
577
2
605
3
522
CYCLE
UNITS
1
577
2
605
3
522