Allocation of Classrooms by Linear Programming

A procedure for allocating classrooms in an educational institution is presented. It is based on a linear programming model in which a penalty function is minimized. With the default values of some parameters provided by the procedure, the model first assigns as many real rooms to the requests as possible. It also seeks to do so with the most preferred rooms. Finally, when it is necessary to depart from the most preferred rooms to satisfy the first objective, the model attempts to spread this departure uniformly among requests. By altering the default values in the penalty function, the user may also favour some requests in the attribution of rooms. Constraints are concerned with the availability of rooms at various hours of the day, and with the requests for these rooms. Since this approach implicitly explores all possible assignments, it should produce better results than manual allocation. Results of empirical applications confirm these expectations, taking the number of demands that can be met as the main criterion. Moreover, an automated procedure to prepare the problem and decode its solution has made it possible to decrease substantially the time spent on this task.