Question

TABLE 13.10 The Distribution Function, F(O), and Expected Leftover Inventory, I(Q), for the Number of Slots Larry Needs F(O) 0183 0916 -2381 4335 6288 .7851 8893 9489 9786 9919 9972 9991 .9997 0.00 0.02 0.11 0.35 0.78 1.41 2.20 3.08 4.03 5.01 6.00 7.00 8.00 9.00 10.00 0 2 3 4 5 6 7 8 9 10 12 13 1.0000

Share&Care is a nonprofit car share company that rents cars. When a customer makes a reservation, they specify their pick up time and the number of time slots they will hold the vehicle, where each time slot equals 15 minutes. For example, if the pick up time is 1pm, then possible drop off times are 1:15 (1 slot), 1:30 (2 slots), etc. Share&Care charges $1.25 for each time slot in the reservation. To discourage customers from returning the rented cars beyond their drop off time, they charge $15 per time slot used beyond the drop off time. For example, if a customer’s drop off time is 2:30 and he returns the vehicle at 2:47, then he is charged $30 for the 2 time slots he used beyond his reservation (and of course, $1.25 per slot that he reserved). Larry runs a small business that makes deliveries on Fridays. To ensure availability of a car, he books his car 2 days in advance. However he doesn’t know his exact needs when he books. Table 13.10 provides information regarding Larry’s demand (in terms of slots). For example, if he needs 5 slots but booked 4 slots, then he uses the car for 5 slots – for a total charge of 4 x $1.25 + $15 = $20. If he ends up booking the car for more time than he needs, the extra time on the car has no value to him. a. Suppose he books the car for 2 time slots. How likely is he to pay $15 or more in late fees? Use Table 13.10. 0.6520 (Round your answer to 4 decimal places.) b. To minimize his rental costs, how many time slots should Larry reserve? Use Table 13.10 and round-up rule. c. Suppose he books the car for 6 time slots. How many time slots can he expect to waste (i.e., they end up being of no use to him)? Use Table 13.10. (Round your answer to 2 decimal places.) d. Larry hates paying any late penalty fee. Suppose he wants to be 99.0% sure that he will not have to pay a late fee. How many slots should he book? Use Table 13.10 and round-up rule. 4 decimal places required.

Answer 1

60 ov more ir) (ak fee acn hen the actuol dewond iR of 4 slot ore b) cost of aesevving i slot les than achual dewand. eu -22P Cost ofeing 1slo mete than acal de Theve fare, Larry d) for 99% service level, imes