AbstractThe improvement in the performance of computers and mathematical programming techniques has led to the development of a new class of algorithms called matheuristics. Associated with an improvement of Mixed Integer Programming (MIP) solvers, these methods have successfully solved plenty of combinatorial optimization problems. This paper presents a matheuristic approach that hybridizes local search based metaheuristics and mathematical programming techniques to solve the capacitated p‐median problem. The proposal considers reduced mathematical models obtained by a heuristic elimination of variables that are unlikely to belong to a good or optimal solution. In addition, a partial optimization algorithm based on the reduction is proposed. All mathematical models are solved by an MIP solver. Computational experiments on five sets of instances confirm the good performance of our approach.