Problem 1

The Penn Bookstore sells several magazines. A single stocking quantity is ordered for each issue. When a new issue arrives, any remaining copies of the old issue are returned to the publisher. If a magazine sells out, then it remains unavailable until the next issue arrives.

Consider the following data on Bits and Bytes magazine at the Penn Bookstore:

The forecast column lists their forecast of demand for that issue (when they ordered copies for that issue). It is generated by an internal computer system that accounts for seasonality and other events in the store (which is why the forecast varies from issue to issue). The quantity column is the actual number of issues stocked that week and the sales column provides the number of units actually sold. The estimated demand column provides an estimate of what sales could have been had there been no stockouts. (If sales is less than or equal to the order quantity, the estimated demand equals sales, otherwise it can be greater.)

a) The system forecasts that week 37 demand at this location will be for 25 copies. Suppose they were to choose a normal distribution to represent demand in week 37. What mean and standard deviation should they choose?

b) Suppose the week 39 forecast is for 20 copies. What would be the coefficient of variation of demand (σ/μ)? Again, assume a normal distribution is chosen to model demand.