A Math-Heuristic for the Multi-Level Capacitated Lot Sizing Problem with Carryover

We present a math-heuristic algorithm for the lot sizing problem with carryover. The proposed algorithm uses mathematical programming techniques in a metaheuristic fashion to iteratively solve smaller portions of the original problem. More specifically; we draw ideas from the corridor method to design and impose exogenous constraints on the original problem and, subsequently, we solve to optimality the constrained problem using a MIP solver. The algorithm iteratively builds new corridors around the best solution found within each corridor and, therefore, explores adjacent portions of the search space. In the attempt of fostering diversification while exploring the original search space, we generate a pool of incumbent solutions for the corridor method and, therefore, we reapply the corridor method using different starting points. The algorithm has been tested on instances of a standard benchmark library and the reported results show the robustness and effectiveness of the proposed scheme.