Problem 4: Single-Period Inventory System (6 points) The hospital cafeteria make
ID: 452033 • Letter: P
Question
Problem 4: Single-Period Inventory System (6 points)
The hospital cafeteria makes one large batch of macaroni and cheese each morning. If the cafeteria runs out of macaroni and cheese, the last few customers are less than satisfied, but if the cafeteria makes too much, it can be sold to the local hog farmer for feed. Every serving costs $1.25 to make and can be sold for $7.00 to customers. The cafeteria has to pay $0.45 per serving to transport the extra servings to the hog farmer, but the hog farmer will pay $0.71 per serving. The average daily demand is 96 servings with a standard deviation of 19 servings.
a) What is the target service level? (3 points)
b) How many servings of macaroni and cheese should the cafeteria make each day to meet this service level? (3 points)
Explanation / Answer
The average daily demand is 96 servings with a standard deviation of 19 servings.
Loss profit(P) = $7.00 - $1.25 =$5.75 per serving short
Loss salvage(S) = $1.25+$0.45 -$0.71 = $0.99
probability critical = S / (P+S) = .99/6.74=.146884
Target service level=1-.146884=.8531 Corresponding value of Z standard normal is 1.049
Therefore the target service level is 85%.
b) Economic order quantity is =Mean + Z* Standard deviation = 96+1.049*19=115.94 or say 116 servings.