Problem 13-31 A drugstore uses fixed-order cycles for many of the items it stock
ID: 334214 • 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 .98. The order interval is 14 days, and lead time is 3 days. Average demand for one item is 63 units per day, and the standard deviation of demand is 2 units per day. Given the on-hand inventory at the reorder time for each order cycle shown in the following table. Use Table. Cycle On Hand 47 2 103 Determine the order quantities for cycles 1, 2, and 3: (Round your answers to the nearest whole number) Units 2 3Explanation / Answer
Given are following data :
Order interval = 14 days
Lead time = 3 days
Therefore, Protection period = P = Order interval + Lead time = 14 + 3 = 17 days
Required service level = 0.98
Corresponding Z value = NORMSINV ( 0.98 ) = 2.0537
Standard deviation of daily demand = 2 units
Therefore, standard deviation of demand during protection period
= Standard deviation of daily demand x square root ( Protection period )
= 2 x square root ( protection period )
= 2 X square root ( 17 )
= 2 x 4.123
= 8.246
Therefore, safety stock = Z value x standard deviation of demand during protection period = 2.0537 x 8.246= 16.93 ( 17 rounded to nearest whole number )
Reorder point = Daily demand x Protection period + safety stock = 63 x 17 + 17 = 1071 + 17 = 1088
Order quantity = Reorder point – Quantity on hand
Accordingly, please find below required answers :
CYCLE
UNITS
1
1041
2
1082
3
985
CYCLE
UNITS
1
1041
2
1082
3
985