Bidding for Classes

In the MBA program at a prestigious university in the Pacific Northwest, students bid for electives in the 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 Management

Science

Finance Operations

Management

Marketing

Hyun $60101020$

Fred $20204020$

Alicia $454555$

Eric $5020525$

Susan $30303010$

Liz $505000$

Carlos $7020100$

Haresh $25253515$

Tony $35153515$

Jasmine $60101020$

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.

What category of problem is this?

What decisions are you expected to make?

What goal are you expected to reach?

Use solver to provide the solution to the problem

b$.$Does the resulting solution seem like a fair assignment?

No$.$ For example, Eric did not get into Management Science despite bidding $50$ points, while Alicia got in with only $45$ points. Also, Eric got into classes worth only $45$ total bid points to him while Liz got classes worth $100$ bid points to her.

c$.$ which alternative objectives might lead to a fairer assignment?

Perhaps maximizing the minimum total number of bid points achieved by each student.