Solving the University Class Scheduling Problem Using Advanced ILP Techniques

The University Class Scheduling Problem (UCSP) is concerned with assigning a number of courses to classrooms taking into consideration constraints like classroom capacities and university regulations. The problem also attempts to optimize the performance criteria and distribute the courses fairly to classrooms depending on the ratio of classroom capacities to course enrollments. The problem is a classical scheduling problem and considered to be NP-complete. It has received some research during the past few years given its wide use in colleges and universities. Several formulations and algorithms have been proposed to solve scheduling problems, most of which are based on local search techniques. In this paper, we propose a complete approach using integer linear programming (ILP) to solve the problem. The ILP model of interest is developed and solved using the three advanced ILP solvers based on generic algorithms and Boolean Satisfiability (SAT) techniques. SAT has been heavily researched in the past few years and has lead to the development of powerful 0-1 ILP solvers that can compete with the best available generic ILP solvers. Experimental results indicate that the proposed model is tractable for reasonable-sized UCSP problems. Index Terms — University Class Scheduling, Optimization, Integer Linear Programming (ILP), Boolean Satisfiability.