Problem:
Linear Programming: Assignment of students to classes
In the MBA program at a prestigious university in the Pacific Northwest, student bid for electives in their second year of their program. Each student has 100 points to bid (total) and must take two electives. There are four electives available: Management Science, Finance, Operations Management, and Marketing. Each class is limited to 5 students. The bids submitted for each of the 10 students are shown in the table below.
|
|
|
Student |
Bids |
for |
Classes |
|
|
|
|
Management |
|
|
Operations |
|
| Student |
|
Science |
|
Finance |
|
Management |
Marketing |
| George |
|
60 |
|
10 |
|
10 |
|
20 |
| Fred |
|
20 |
|
20 |
|
40 |
|
20 |
| Ann |
|
45 |
|
45 |
|
5 |
|
5 |
| Eric |
|
50 |
|
20 |
|
5 |
|
25 |
| Susan |
|
30 |
|
30 |
|
30 |
|
10 |
| Liz |
|
50 |
|
50 |
|
0 |
|
0 |
| Ed |
|
70 |
|
20 |
|
10 |
|
0 |
| David |
|
25 |
|
25 |
|
35 |
|
15 |
| Tony |
|
35 |
|
15 |
|
35 |
|
15 |
| Jennifer |
|
60 |
|
10 |
|
10 |
|
20 |
Solve problem and discuss the associated questions.
a. Formulate and solve a spreadsheet model to determine an assignment of students to classes so as to maximize the total bid points of the assignments.
b. Does the resulting solution seem like a fair assignment?
c. Which alternative objectives might lead to a fairer assignment?