Question
The Country Rose Truck Stop at the crossroads of Interstates 64 and 57 near Mt. Vernon, Illinois is a full-service stop serving cross-country truckers with
The Country Rose Truck Stop at the crossroads of Interstates 64 and 57 near Mt. Vernon, Illinois is a full-service stop serving cross-country truckers with fuel, ample overnight parking with wireless internet access, showers, a game room with pool tables and a 24/7 restaurant. The restaurant serves a simple but wide menu including burgers, club and Reuben sandwiches, catfish, and breakfast anytime. Scheduling wait staff in the restaurant has long been a challenge due to the hour-by-hour change in restaurant traffic. Mae Allen, the restaurant manager, has looked at her typical customer traffic over a 24-hour period. Reviewing traffic in two-hour increments Mae came up with the following table showing how many persons should generally be scheduled to wait tables through the day.
Mae employs both full- and part-time staffers. Full-timers work 8 hour shifts and part-timers work shifts of 2, 4, or 6 hours. For either class of wait staff those shifts may begin at any time of the day Mae chooses. For example, a full-time staffer waiting tables may work from midnight to 8 AM, from 2:00 AM to 10:00 AM, 4:00 AM to noon, etc. Full-time wait staff are paid $7.25 per hour, with every hour worked from 10:00 PM to 6:00 AM paying an additional $2.50 premium. Part-timers are paid a base rate of $6.25 per hour with the same shift premium scheme for late night work.
Mae recognizes part time staff save Country Rose on wages, but she prefers full-timers. Them part-time peoples just a pain in the neck! she says with exasperation in a perfect southern Illinois drawl. They dont know the job as well, and they dont show up to work, and theyll quit without tellin you! You can count on full-timers better.
a. Formulate and solve the mathematical programming model which will show Mae how to schedule the restaurant in the truck stop such that she meets her minimum staffing levels in each 2-hour block of time while minimizing daily wage expense. Mae would like no part-time staff on duty at any time.
b. Youd like to convince Mae to use up to six part-time staffers, but she only agrees to having them on the premises between 6 AM and 8 PM when she can watch them. Following Maes stipulation, how much could be saved in daily wage expense if part-time staffers were used?
| From | To | Staff |
| From | To | Staff |
| 00:00 | 02:00 | 3 |
| 12:00 | 14:00 | 16 |
| 02:00 | 04:00 | 3 |
| 14:00 | 16:00 | 8 |
| 04:00 | 06:00 | 6 |
| 16:00 | 18:00 | 4 |
| 06:00 | 08:00 | 14 |
| 18:00 | 20:00 | 13 |
| 08:00 | 10:00 | 11 |
| 20:00 | 22:00 | 5 |
| 10:00 | 12:00 | 8 |
| 22:00 | 24:00 | 4 |
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