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Linear Programming: Assignment of students to classes

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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

MS Fin OM Mar
Student Management Science Finance Operations 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?

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Solution Summary

Formulates and solves a spreadsheet model to determine an assignment of students to classes so as to maximize the total bid points of the assignments. EXCEL solver has been used to solve the problem.

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Quantitative Methods (Linear Programming Model) : Optimizing a Teaching Schedule

The Department of Management Science and Information Technology at Tech

The management science and information technology department at tech offers between 36 and 40 three-hour course sections each semester. Some of the courses are taught by graduate student instructors, whereas 20 of the course sections are taught by the 10 regular tenured, faculty in the department. Before the beginning of each year the department head sends the faculty a questionnaire asking them to rate their preference for each course using a scale from 1 to 5, where 1 is "strongly preferred, 2 is "preferred but not as strongly as 1", 3 is "neutral," 4 is "prefer but not to teach but not strongly," and 5 is "strongly prefer not to teach this course." The faculty have returned their preferences as follows.

Course
______________________________________________________

Faculty Member 3424 3434 3444 3454 4434 4444 4454 4464

Clayton 2 4 1 3 2 5 5 5
Houck 3 3 4 1 2 5 5 4
Huang 2 3 2 1 3 4 4 4
Major 1 4 2 5 1 3 2 2
Moore 1 1 4 4 2 3 3 5
Ragsdale 1 3 1 5 4 1 1 2
Rakes 3 1 2 5 3 1 1 1
Rees 3 4 3 5 5 1 1 3
Russell 4 1 3 2 2 5 5 5
Sumichrast 4 3 1 5 2 3 3 1

For the fall semester the department will offer two sections each of 3424 and 4464; three sections of 3434, 3444, 4434, 4444, and 4454; and one section of 3454.

The normal semester teaching load for a regular faculty member is two sections. (Once the department head determines the courses, he will assign the faculty he schedules the course times so they will not conflict.) Help the department head determine a teach schedule that will satisfy faculty teach preferences to the greatest degree possible.
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