Classroom Scheduling Optimization

This project formulates the university classroom scheduling problem as a binary integer linear program (ILP).

The goal is to assign each course to a professor, classroom, and time slot while maximizing preference scores and satisfying operational constraints.

Problem Overview

Creating a course schedule is a constrained optimization problem.

Each course must be assigned to:

• One qualified professor
• One available classroom
• One valid time slot

At the same time, the schedule must satisfy several constraints:

• A professor cannot teach two courses at the same time.
• A classroom cannot host two courses at the same time.
• Professor availability must be respected.
• Room availability must be respected.
• Courses should be assigned to professors who prefer to teach them.

The model converts these requirements into a mathematical optimization problem and uses an integer programming solver to find the highest-scoring feasible schedule.

Mathematical Formulation

Decision Variables

For every valid combination of:

• Course c
• Professor p
• Room r
• Time slot t

a binary variable is created:

x(c, p, r, t) = 1 if the course is assigned to that combination, and 0 otherwise.

Objective Function

The model maximizes:

• Professor-course preference scores
• Professor time-slot preference scores
• Minus penalties for unassigned courses

Constraints

1. Each course is assigned exactly once or marked unassigned.
2. Professors may teach at most one course in any time slot.
3. Rooms may host at most one course in any time slot.
4. Only available rooms and professors are considered.

Technologies Used

• Python
• pandas
• PuLP
• Excel
• CBC Solver

Input Data

The model reads data from data.xlsx, which contains:

• Courses
• Professors
• Rooms

Output

The program generates Output.xlsx containing:

• Assigned courses
• Unassigned courses

It also prints:

• Total objective score
• Number of assigned courses

Example Result

Result - Optimal solution found
Total Objective Score: 26.0
Courses Assigned: 3/3