Operator Assignment

Oxford University maintains a powerful mainframe computer research use by its faculty, Ph.D. students, and research associates. During all working hours, an operator must be available to operate and maintain the computer, as well as to perform some programming services. Beryl Ingram, the director of the computer facility, oversees the operation.

It is now the beginning of the fall semester and Beryl is confronted with the problem of assigning different working hours to her operators. Because all the operators are currently enrolled in the university, they are available to work only a limited number of hours each day.

There are six operators (four undergraduate students and two graduate students). They all have different wage rates because of differences in their experience with computers and in their programming ability. The following table shows their wage rates, along with the maximum number of hours that each can work each day.

Each operator is guaranteed a certain minimum number of hours per week that will maintain an adequate knowledge of the operation. This level is set arbitrarily at 8 hours per week for the undergraduate students (KC, DH, HB, and SC) and 7 hours per week for the graduate students (KS and NK).

The computer facility is to be open for operation from 8am to 10pm Monday through Friday with exactly one operator on duty during these hours. Therefore, for each weekday, the total number of operator hours available should be exactly equal to 14 hours. On Saturdays and Sundays, the computer is to be operated by other stuff. It is assumed that operators can work their hours during any period of time in a given day (that is, for instance, Beryl decides to have KC work 6 hours on Monday and HB for 3.2 hours on Monday and SC for 4.8 hours on Monday, scheduling them is not of interest because they can work anytime during 8am-10pm on Monday given that their time is not exceeding their available time on Monday).

Because of a tight budget, Beryl has to minimize the total operating cost. She wishes to determine the number of hours she should assign to each operator on each day.

a) Mathematically formulate a linear programming model for this problem. Define decision variables, and then define your constraints and objective function accordingly. Combine everything to get the final model.

b) Formulate and solve this problem on a spreadsheet using Excel.