Problem 4: Single-Period Inventory System (4 points) A local sub shop across tow

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

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