Maurice Tutor
$15/per page/Negotiable
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 Ac€A?breakfast anytimeAc€??. 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. Ac€A?Them part-time peopleAc€?cs just a pain in the neck!Ac€?? she says with exasperation in a perfect southern Illinois drawl. Ac€A?They donAc€?ct know the job as well, and they donAc€?ct show up to work, and theyAc€?cll quit without tellinAc€?c you! You can count on full-timers better.Ac€??
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.  YouAc€?cd 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 MaeAc€?cs 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 |
Â