Problem 13-31 A drugstore uses fixed-order cycles for many of the items it stock
ID: 425104 • 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 .95. The order interval is 11 days, and lead time is 2 days. Average demand for one item is 69 units per day, and the standard deviation of demand is 7 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 Determine the order quantities for cycles 1,2, and 3: (Round your answers to the nearest whole number) Cycle UnitsExplanation / Answer
Protection period
= Order interval + Lead time
= 11 + 2 days
= 13 days
Standard deviation of daily demand = 7 units
Therefore, Standard deviation of demand during protection period
= Standard deviation of daily demand x Square root ( Protection period )
= 7 x Square root ( 13 )
= 7 x 3.605
= 25.235
Service level = 0.95
Z value for service level of 0.95 = NORMSINV ( 0.95 ) = 1.6448
Therefore,
Safety stock = Z value x Standard deviation of demand during protection period= 1.6448 x 25.235 = 41.506 ( 42 rounded to next higher whole number )
Reorder quantity when on hand inventory is zero
= Average daily demand x Protection period + Safety stock
= 69 x 13 + 42
= 897 + 42
= 939
Therefore,
Order quantity for cycle 1 = 939 – quantity on hand = 939 – 44 = 895
Order quantity for cycle 2 = 939 – quantity on hand = 939 – 9 = 930
Order quantity for cycle 3 = 939 – quantity on hand = 939 – 99 = 840
CYCLE
UNITS
1
895
2
930
3
840
CYCLE
UNITS
1
895
2
930
3
840