A novel two-stage optimization scheme for solving university class scheduling problem using binary integer linear programming

University Class Scheduling Problem (UCSP) is an inevitable task every university must go through prior to the commencement of a semester. The problem studied in this paper is decomposed into two stages - lab scheduling and theoretical class scheduling. This novel technique of decomposition of the problem not only allowed maximum number of free variables to stricter constraints found in lab scheduling, but also reduced the overall computational cost and combinatorial complexity. The mathematical model for the problem is formulated via Binary Integer Linear Programming (BILP) structure using data collected from the department considered in the study. Part of the contribution of this work also includes developing ways to recognize only the true variables while formulating the model. The model is then optimized using the simplex method with the objectives to optimize classroom utilization and faculty preferences while fulfilling additional constraints. Furthermore, the proposed method is compared to the traditional technique in which the model is optimized in a single stage with both true variables recognized and not recognized.