solution

Case indicates that 97 rental requests arrived over a 26 week span. Assume no variation in rental times (i.e. the standard deviation of rental times is zero) and that inter-arrival times are exponentially distributed (i.e. the coefficient of variation is 1). Suppose REI has decided to set up a subscription-based rental ski business. In this model, customers pay a flat subscription fee on a monthly basis and can rent skis for one weekend at a time whenever they want at no additional charge. With this model REI is focused on ensuring sufficient inventory availability to their customers who subscribe. Assume the same data as discussed in the REI Rentals case.

•From exhibit 8 see that 97 requests came in over 26 weeks

Arrival rate is 97 requests/26 weeks (1/a) = 3.73 requests per week,

•Inter-arrival time (a) = 1/3.73 = .268 weeks/request

Assume everyone rents for one weekend, p = 1

Also, assume no variation in rental time (standard deviation)

Suppose they keep 3 pairs of skis in Salt Lake City. What is the probability one of their subscribers WILL be able to rent a pair of skis on a given weekend?

A. 78% B. 58% C. 88% D. 68%

What’s the smallest number of skis they would need to stock at Salt Lake City?

A. 8 B. 10 C. 7 D. 9