Alocação de professores com foco em ganho de desempenho, conforme critérios avaliativos do Ministério da Educação

Abstract

In higher education institutions, the management of faculty is a fundamental issue to ensure the quality of the courses and to grant positive gures against the Education Ministry (MEC). In the particular case of private institutions, a higher exibility to dene the composition of faculty enforces the challenge of assigning the appropriated instructors to each course for each class, considering that every decision will impact in the quality of the institution against the MEC evaluation criteria. Nowadays, we have a shortage of master and doctor teachers, besides it they are not available to occupy full or partial time positions, which lets choice of academic sta much more complex, considering the size of the institution and the quantity of courses involved. Based on the characeristics of the teacher allocation problem, we propose a nolinear formulation with integer variables. This formulation aims to maximize the courses general index (IGC) which is linked to faculty. However, the computational costs to solve real problems may exclude the application of this formulation in a practical context. Although, we present strategies of linearization based on the use of parameters by the inclusion of teachers according to their academic background and work regime (characteristics valued by MEC). Through the use of these strategies, we introduce an integer linear formulation able to solving the teacher allocation problem, increasing the performance indicators valued by MEC. The performance of these two formulations were tested and compared through computational experiments using instances randomly generated and obtained from the real context. The nonlinearized formulation with integer variables was not able to presenting optimal solutions to the problems, even after two hours of processing and only returned integer solutions for instances with up to 16 courses. The linearized formulation presented, on average, better results with computational times always less than or equal to 5 seconds. Other computational tests were performed with instances obtained from real data from a private educational institution where the study was conducted and also with larger random instances (up to 105 courses). In all cases, the results demonstrate the applicability of the linearized formulation to solve the teacher allocation problem focusing on improving quality indicators of higher education institutions.