Question

(12%) A small grocery store sells fresh produce, which it obtains from a local farmer. The grocery store buys fresh organic strawberries weekly for $2.5 per pound and sells for $5 per pound. Excess cost has been $2 per pound. The manager believes that weekly demand can be approximated by a normal distribution with a mean of 40 pounds and a standard deviation of 10 pounds.

a). How much should the store manager order (i.e., optimal stocking point)?

b). Based on (a) above, how much safety stock would be held?

Answer 1

Cost per pound = 2.5

Selling Price per Pound = 5

Cost of Underage (Cu) = Selling Pricce - Cost = 5 - 2.5 = 2.50

Cost of Overage (Co) = 2

Service Level = Cu/(Cu+Co)

Service Level = 2.50/(2.50+2.00)

Service Level = 2.50/4.50

Service Level = 0.5556

Z = NORM.S.INV(0.5556) = 0.1398

Mean Demand d = 40 pounds

SD of demand = 10

a)

Optimal Order quantity Q = d + Z*Sd of Demand

Q = 40 + 0.1398*10

Q = 41.398

Q = 41.40 pounds

b)

Safety Stock = Z*Sd of Demand

Safety Stock = 0.1398*10

Safety Stock = 1.398

Safety Stock = 1.40 pounds