Optimization Methods Applied to ENCE's Schedule

The problem of scheduling is a classic challenge of combinatorial optimization, often dealt with manually, which limits the quality of the solutions obtained. This paper analyzes a real case study of ENCE, reinterpreting it as a problem of matching with constraints. Three approaches are explored: Integer Linear Programming, a Backtracking algorithm, and a VNS-based heuristic. The formulations produce overall optimum in a few seconds, with emphasis on the reduction of the dispersion of the teaching load (from 51 to 47 days). VNS heuristics combine rapid achievement of viable solutions with progressive refinement, while Backtracking enables efficient enumeration of multiple global optimal solutions. The results show relevant gains in the quality of solutions and decision support, with validation in real data.