Variable neighborhood search for the economic lot sizing problem with product returns and recovery

The economic lot sizing problem with product returns and recovery is an important problem that appears in reverse logistics, and has recently been proved to be NP-hard. In this paper, we suggest a variable neighborhood search (VNS) metaheuristic algorithm for solving this problem. It is the first time that such an approach has been used for this problem in the literature. Our research contributions are threefold: first, we propose two novel VNS variants to tackle this problem efficiently. Second, we present several new neighborhoods for this combinatorial optimization problem, and an efficient local search method for exploring them. The computational results, obtained on a recent set of benchmark problems with 6480 instances, demonstrate that our approach outperforms the state-of-the-art heuristic methods from the literature, and that it achieved an average optimality gap equal to 0.283% within average 8.3 s. Third, we also present a new benchmark set with the largest instances in the literature. We demonstrate the robustness of the proposed VNS approach in this new benchmark set compared with Gurobi optimizer.