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)

Approximately how many facings are needed to achieve a 98.75% in-stock probability?

a. 3 facings

b. 9

c. 11

d. 13

e. 17

Answer 1

for 98.75% in stock probability,we find the z-score using standard normal distribution table:

z = 2.24

Reorder point will define the facings needed:

ROP = d*L + z*s*L

d = daily demand = 60

L = lead time + review time = 3+1 = 4 days

s = standevation of daily demand = 20

ROP = 60*4 + 2.24*20*4

= 240 + 44.8*2

=240 + 89.6

= 329.6 bags

per facing holds 20 bags

hence facings required = 329.6/20 = 16.48

we round up to next whole number since fractional facing not possible: 17 facings

option E 17