A food company is attempting to set the customer service level (in-stock probability in its warehouse) for a particular product line item. Annual sales for the items are 100,000 boxes, or 3,846 boxes biweekly. The product cost in inventory is $10 per box, to which $1 is added as profit margin. Stock replenishment is every two weeks and the demand during this time is assumed normally distributed with a standard deviation of 400 boxes. Inventory carrying costs are 30 percent per year of item value. Management estimates that a 0.156 percent change in total revenue would occur for each 1 percent change in the in-stock probability. Based on the information, find the optimal in-stock probability for the item.
SL Levels in % for Various z Values
SL (%) Zu - ZL = z
U L
87-86 1.125 -1.08 = 0.045
88-87 1.17 -1.125 = 0.045
89-88 1.23 -1.17 = 0.05
90-89 1.28 -1.23 = 0.05
91-90 1.34 -1.28 = 0.06
92-91 1.41 -1.34 = 0.07
93-92 1.48 -1.41 = 0.07
94-93 1.55 -1.48 = 0.07
95-94 1.65 -1.55 = 0.10
96-95 1.75 -1.65 = 0.10
97-96 1.88 -1.75 = 0.13
98-97 2.05 -1.88 = 0.17
99-98 2.33 -2.05 = 0.28
Developed from entries in a normal distribution table