Single-Period Inventory System The hospital cafeteria makes one large batch of m
ID: 452190 • Letter: S
Question
Single-Period Inventory System 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. What is the target service level? How many servings of macaroni and cheese should the cafeteria make each day to meet this service level?Explanation / Answer
a.Cost of under-stocking (Cu) = $7 - $ 1.25 = $5.75
The profit that cafeteria lose not being able to sell the macaroni and cheese
Cost of over-stocking (Co) is: $1.25+$0.45 - $ 0.71 = $0.99
The amount that cafeteria lose because they have to sell at a discount to farmer
The optimal service level (SL) or target service level = Cu/(Cu +Co)
= 5.75 /(5.75+0.99) =0.8531 or 85.31%
b.Optimal order quantity Q = D+ z
Where D is the average daily demand = 96 servings
And is the standard deviation of demand = 19 servings
Z at 85.31 % service level = 1.04
Optimal order quantity Q = D+ z
Q = 96 + 1.04 * 19 = 96+ 19.76 = 115.76 serving