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 sel to Verizon store employees and customers at lunch time. Sandwiches are sold to customers for $2.25 and cost $0.75 to make. It costs the sub shop $0.25 per sandwich to pick up any leftover sandwiches and dispose of them after lunch time. The average daily demand is 61 sandwiches with a standard deviation of 21 sandwiches a) b) What is the target service level? (2 points) How many sub sandwiches should be made each day to meet this service level? (2 points)

Explanation / Answer

a) Service level= Cs / (Cs + Ce)

Where Cs = r c + p and Ce = h + c s

and r is revenue ,c is cost, p is penalty for not able to sell each unit, s is salvage value of item, h is holding cost overnight

Cs=(2.25-0.75+0.25) =1.75

Ce=(0+0.75-0)=0.75

Service level= Cs / (Cs + Ce) = 1.75/(1.75+0.75) = 0.7 or 70%

b) For 70% service level or probability

Z=0.52 =(x-u)/Standard Deviation= (x-61)/21

This implies X= 61 +0.52x21=71.92

Hence 72 sandwiches to be made to meet 70% service level

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