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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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#### Solution Preview

Hello!
I've included the solution in the Excel file I'm attaching.

In order to solve this, I used the Excel Solver function. The objective was to maximize the total utility of the faculty. I assumed that the utility of each professor was (here's an example for professor Clayton):

Utility = 2*(Number of 3424 sections assigned) + 4*(Number of 3434 sections assigned) + ...

Since some sections are offered more than once, and that each professor takes on two sections, it's possible that a professor gets assigned two ...

#### Solution Summary

A teaching schedule is optimized using LP methods. The solution is detailed and well presented.

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