Question

Alex Tuber, store manager of Edgeway Grocery Store in Washingtown, is worried about allocating enough shelf space to a new breakfast cereal, Rice Krimpies. The cereal will be restocked from the distributor once a week, at noon on each Thursday. At that time, the delivery person will arrive with ample stock to fill the shelf area that is reserved for Rice Krimpies, thereby replenishing the packages that were sold during the previous week rather than some set amount ordered in advance. As the week progresses, and the stock of Rice Krimpies drops, the space reserved can not be used for any other product.

Each package of Rice Krimpies costs Alex $2 to purchase. Alex sells a package of Rice Krimpies for $5. The opportunity cost of the shelf space that Alex must reserve for Rice Krimpies is $2.50 per week per foot of shelf space. Ten packages of Rice Krimpies can be stored and displayed per foot of shelf space. (Assume any shelf length in feet is viable and that the number of Rice Krimpies boxes is ten times this length.) Other carrying costs (i.e., other than shelf space) of the Rice Krimpies are so small that they can be safely neglected in this problem.

Based on his past experience, Alex estimates that the weekly demand for cereal will be normally distributed with a mean of 140 packages and a standard deviation of 40 packages. Alex also figures that if his store runs out of the new cereal during the week, customers will go elsewhere to buy the cereal that week, but will hold no permanent grudges against the Edgeway store. In particular, the stockout will have no effect on sales of other products in the store or on sales of the cereal in the future.

How many feet of shelf space should Alex reserve for Rice Krimpies?

Answer 1

Cost per package = $2
Selling price for each package = $5
Carrying cost per week per foot of shelf space = $2.5
So, Carrying cost per week per package = $0.25 (since 10 packages are kept per foot of shelf space)

So,

Cu = underage cost = 5 - 2 = 3
Co = carrying cost = 0.25

Critical ratio = Cu / (Co + Cu) = 3 / (0.25+3) = 0.923

So, z = normsinv(0.923) = 1.426

The review period, p=1 week and the replenishment lead time is negligible i.e. l=0

Order up to level, S = d*(l+p) + z*σ * sqrt(l+p) = 140*(0+1) + 1.426*40*sqrt(0+1) = 197

So, foot reserved should be = 197/10 = 19.7 feet.