Operations Research

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EGMT 410 (Fall 2014) –Operations Research

Final Exam

Problem

Suppose the Dean of the Engineering Technology Department at BSC is trying to create a course schedule for the upcoming semester. Instead of trying to randomly assign courses to professors he thinks each would like to teach each course, he gives a survey that asks each of the professors to give their preference for each course that is offered. He asks them to rank each course on a scale of 0-10. A zero represents they do not want to teach a course at all, whereas a 10 represents that they very much want to teach the course. Values between 0-10 represent their “happiness” if they have to teach the course. He also asks each professor to give a preference on what day of the week they would like to teach, following the same ranking logic of 0-10. Below is the information matrix of the course rankings and day rankings. Courses a professor has to teach and the day that they teach on carry the same weight. (i.e. a professor’s course-day ranking is just as important as the course they are assigned to teach.) Also included are requirements for the number of sections that must be taught for each course, the number of courses each professor is required to teach, and the number of sections that are available for each day.

Preference                    
Instructor\Course 1 2 3 4 5 6 7 8 9 10
A 0 8 3 0 0 10 0 6 0 9
B 10 0 0 0 0 10 9 0 6 0
C 9 4 0 8 5 0 0 0 3 10
D 0 0 0 0 10 6 0 0 0 0
E 6 7 9 10 6 0 3 8 7 8
F 0 0 9 10 9 0 0 0 5 0
G 8 7 7 6 9 0 8 0 0 0
H 0 0 10 0 0 0 10 0 0 0
I 10 9 0 0 0 0 0 0 0 0
J 0 0 0 0 0 0 0 0 10 0
Instructor\Day Monday Tuesday Wednesday Thursday Friday Saturday
A 10 9 9 8 6 0
B 8 10 7 6 5 6
C 6 10 7 8 3 0
D 10 7 6 8 0 9
E 8 9 8 10 7 0
F 9 10 10 7 6 0
G 0 10 10 8 0 0
H 10 8 0 8 5 10
I 10 10 10 0 0 0
J 9 8 10 8 7 0
Course # Sections
1 2
2 1
3 2
4 1
5 2
6 1
7 3
8 2
9 1
10 1
Instructor # of Courses Required to teach
A 1
B 1
C 2
D 2
E 2
F 1
G 2
H 1
I 2
J 2
Day Slots Available
Monday 2
Tuesday 4
Wednesday 3
Thursday 3
Friday 2
Saturday 2

A. Formulate the problem as an assignment model, show all decision variables and constraints. Formulate the problem such that the average “happiness” of the department is maximized.

B. What is the average “happiness” of each professor in terms of their course load? What is the average “happiness” of each professor in terms of the day of the week that they teach? What is the average total “happiness” (e.g. courses and days) of each professor? What is average “happiness” of the entire department? What professor has the lowest average total “happiness” and what is that value?

C. Create a schedule that gives the maximum average “happiness” of the department.