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 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 $O.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

given Sandwiches cost $0.75 to make and deliver and are sold for $2.25 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 $0 per sandwich. The average daily demand is 61 sandwiches

standard deviation of 21 sandwiches.

savage value=-0.25

overage cost C0=c-v=0.75-(-0.25)=$1.00

underage cost=Cu=p-c=2.25-0.75=$1.5

crtical ratio =Cu/(Cu+Co)=1.5/(1.5+1)=0.6

average demand=61

standard devation =61

z=0.253347(corresponding to 0.6 probability)

Q=Z*SD+mean=0.253347*21+61=66.320287

b)64 sandqwiches should be made each day to meat service level

target service level=critical ratio=0.6

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