Question

You are thinking about registering three courses in Fall 2018. There are three courses that you are interested in, which will be taught by three professors. Based on prior experiences and conversations with your colleagues with these courses, you have work a “complexity table” (shown below) that illustrated your expectation on the complexity of each course (the higher the number, the more complex you expect the course to be with that professor.)

Course ?	Professor 1	Professor 2	Professor 3
1	70	90	90
2	80	80	90
3	80	70	65

Based on your linear programming model to optimize the total complexity of all three courses, which of the courses and professors should you register?

Answer 1

Let A11, A12 & A13 be the binary variable determining if the Course 1 is taken under Professor 1, Professor 2 & Professor 3 respectively.

Similarly, A21, A22 & A23 be the binary variable determining if the Course 2 is taken under Professor 1, Professor 2 & Professor 3 respectively.

Similarly, A31, A32 & A33 be the binary variable determining if the Course 3 is taken under Professor 1, Professor 2 & Professor 3 respectively.

Our Objective is to minimize the overall complexity. Hence our objective function is-

Min(70*A11+90*A12+90*A13+80*A21+80*22+90*A23+80*A31+70*A32+65*A33)

Constraints-

Each Course can be undertaken under 1 professor only.

A11+A12+A13 = 1

A21+A22+A23 = 1

A31+A32+A33 = 1

Each Professor can take only one course.

A11+A21+A31 = 1

A12+A22+A32 = 1

A13+A23+A33 = 1

The Solver output is as shown-

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