Logistics Management Homework #3 Problem 1. (Chapter 4: Logistics/Supply Chain Customer Service) 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. (Hint: see the similar example on Module 3 Ch04 PPT file slides 19-22) ASL Levels in % for Various Az Values Zu ASL (%) U L ZL = Z = = = = = 87-86 88-87 89-88 90-89 91-90 92-91 93-92 94-93 95-94 96-95 97-96 98-97 99-98 1.125-1.08 0.045 1.17 -1.125 0.045 1.23 -1.17 = 0.05 1.28 -1.23 0.05 1.34 -1.28 0.06 1.41 -1.34 0.07 1.48 -1.41 = 0.07 1.55 -1.48 0.07 1.65 -1.55 0.10 1.75 -1.65 0.10 1.88 -1.75 = 0.13 2.05 -1.88 = 0.17 -2.33 -2.05 0.28 = *Developed from entries in a normal distribution table