Problem 13-31 A drugstore uses fixed-order cycles for many of the items it stock
ID: 352637 • 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 14 days, and lead time is 2 days. Average demand for one item is 65 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 Cycle On Hand 40 12 95 Determine the order quantities for cycles 1, 2, and 3: (Round your answers to the nearest whole number) Cycle UnitsExplanation / Answer
Average daily demand (d) = 65 units
Standard deviation of daily demand(sigma d) = 3 units
Order interval (T) = 14 days
Lead time (L) = 2 days
Service level = 0.95 = 95%
At 95% service level value of Z = 1.65
For cycle 1 :
On hand inventory (I) = 40 units
Order quantity = [d(L +T)] + [Z x sigma d x sqrt of (L+T)] - I
= [65(2+14)] + [1.65 x 3 x sqrt of (2+14)] - 40
= (65 x 16) + (1.65 x 3 x 4) - 40
= 1040 + 19.8 - 40
= 1059. 8-40
= 1019. 8 or rounded to 1020 units
For cycle 2:
On hand inventory (I) = 12 units
Order quantity = [d(L +T)] + [Z x sigma d x sqrt of (L+T)] - I
= [65(2+14)] + [1.65 x 3 x sqrt of (2+14)] - 12
= (65 x 16) + (1.65 x 3 x 4) - 12
= 1040 + 19.8 - 12
= 1059.8 - 12
= 1047.8 or rounded to 1048 units
For cycle 3:
On hand inventory (I) = 95 units
Order quantity = [d(L +T)] + [Z x sigma d x sqrt of (L+T)] - I
= [65(2+14)] + [1.65 x 3 x sqrt of (2+14)] - 95
= (65 x 16) + (1.65 x 3 x 4) - 95
= 1040 + 19.8 - 95
= 1059.8 - 95
= 964.8 or rounded to 965 units