The Northshore Bank is working to develop an efficient work schedule for full-time and part-time tellers. The schedule must provide for efficient operation of the bank including adequate customer service, employee breaks, and so on. On Fridays the bank is open from 9:00 A.M. to 7:00 P.M. The number of tellers necessary to provide adequate customer ser- vice during each hour of operation is summarized here.
|
Time
|
Number of Tellers
|
Time
|
Number of Tellers
|
|
9:00 a.m.-10:00 a.m.
|
6
|
2:00 p.m.-3:00 p.m.
|
6
|
|
10:00 a.m.-11:00 a.m.
|
4
|
3:00 p.m.-4:00 p.m.
|
4
|
|
11:00 a.m.-Noon
|
8
|
4:00 p.m.-5:00 p.m.
|
7
|
|
Noon-1:00 p.m.
|
10
|
5:00 p.m.-6:00 p.m.
|
6
|
|
1:00 p.m.-2:00 p.m.
|
9
|
6:00 p.m.-7:00 p.m.
|
6
|
Each full-time employee starts on the hour and works a 4-hour shift, followed by 1 hour for lunch and then a 3-hour shift. Part-time employees work one 4-hour shift beginning on the hour. Considering salary and fringe benefits, full-time employees cost the bank $15 per hour ($105 a day), and part-time employees cost the bank $8 per hour ($32 per day).
a. Formulate an integer programming model that can be used to develop a schedule that will satisfy customer service needs at a minimum employee cost. (Hint: Let xi = number of full-time employees coming on duty at the beginning of hour i and yi = num- ber of part-time employees coming on duty at the beginning of hour i.)
b. Solve the LP Relaxation of your model in part (a).
c. Solve for the optimal schedule of tellers. Comment on the solution.
d. After reviewing the solution to part (c), the bank manager realized that some additional requirements must be specified. Specifically, she wants to ensure that one full- time employee is on duty at all times and that there is a staff of at least five full-time employees. Revise your model to incorporate these additional requirements and solve for the optimal solution.