Question

Supervalue Inc. has decided to make a policy that every product at its Econofood stores will receive enough shelf space to ensure a 90% fill rate. Consider potato chip bags. At each store, the demand is normally distributed with an average daily demand for this product to be 60 bags with a standard deviation of 20 bags. Potato chip bags can be stacked 20 deep per facing. (A facing is the width on a shelf required to display one item of a product. The store shelf is spring loaded such that when you take a bag of chips the next bag moves forward. ) Deliveries from Supervalue warehouse occur 3 days after a store manager submits an order. (Note in this problem the lead time is 3 days and a review period is 1 day. Before answering the questions below, you’ll need to figure out the mean demand and demand standard deviation for lead time plus one day, you’ll be using these parameters in your demand distribution)

On average, how many bags of potato chips is backordered if Supervalue allocates 12 facings at each Econofood store? (Hint: The order-up-to quantity S is the number of potato chip bags computed from the number of allocated facings.)

a. 6 bags

b. 12

c. 16

d. 20

e. 24

Answer 1

ANSWER: d. 24.

Given that,

Mean demand for lead time plus one day = d*(L+1) = 60*(3+1) = 240

Standard deviation for demand during lead time plus one day = 20*SQRT(3+1) = 40

Number of allocated facings = 12

Potato chip bags can be stacked 20 deep per facing. Therefore, order-upto quantity S = 12*20 = 240

Fill rate = 90%,

Therefore, expected sales = Mean demand * 90% = 240*90% = 216

Expected number of bags backordered = Mean demand - Expected sales = 240 - 216 = 24