Problem 4: Single-Period Inventory System (4 points) A local sub shop across tow
ID: 332231 • Letter: P
Question
Problem 4: Single-Period Inventory System (4 points)
A local sub shop across town makes sandwiches every morning to sell to U.S. Cellular store employees and customers at lunch time. Sandwiches are sold for $6.25 and cost $4.25 to make and deliver to customers. It costs the sub shop $0.25 per sandwich to pick up any leftover sandwiches after lunch time, but these leftovers can be sold for $4.00 per sandwich. The average daily demand is 52 sandwiches with a standard deviation of 21 sandwiches.
What is the target service level? (2 points)
Selling cost = 6.25
Purchase cost = 4.25
Left over sold price = 4
Profit = selling cost – purchase cost
(p) = 6.25 – 4.25 = 2
Loss = 4.25 – 4 = .25
2/2+.25 = .888
Service level is .888 = 81.294
How many sub sandwiches should be made each day to meet this service level? (2 points)
Explanation / Answer
Underage cost Cu = Selling price – Purchase cost = 6.25 – 4.25 = 2
Overage cost Co= purchase cost – Salvage cost = 4.25 – 4 = 0.25
Service level = Cu/(Cu+Co) = 2/2.25 = 0.8889
Z = 1.22
No of sandwiches = Mean + z*Standard deviation = 52 + 1.22*21 = 77.62 or 78 sandwiches