Aplicação da teoria dos jogos na resolução do problema de Alocação de professores em disciplinas

Abstract

There are several formulae for allocating teachers to different classes. In this work the problem will consist of allocating a set of professors at the Quixadá campus of the Federal University of Ceará to a set of classes offered, according to restrictions of professor availability and preferences on different subjects. The objective of this work is to model the problem according to the concepts of the Game Theory. The Game Theory allows us to create models to represent real-life situations in which rational agents interact in the search for objectives. These models are called games. With these models as starting points, solution concepts such as Sub-game Perfect Equilibrium, used in extensive-form games, can be applied to obtain a solution. The Game Theory and game logics are strictly related in such a way that a model created in the former can be directly translated into the latter, in the same way that solution concepts can be represented by formulae. In this work we will use this relationship to find the solutions to the games (allocation) through Game Analysis Logic. We present step-by-step mapping of an instance of the problem of allocating professors in an extensive game model. We developed a tool that receives the problem data and communicates with the Game Analysis Logic Verifier, where the concept of Sub-game Perfect Equilibrium will be applied to offer the best proposal of professor allocation. We show the results of experiments conducted with the proposed tool. In the tests undertaken with real offers in the Information Systems course, the resulting solution met both professor availability and subject preferences.