A computational comparison of formulations for the economic lot-sizing with remanufacturing

• We consider the economic lot-sizing with remanufacturing (ELSR).
• A multicommodity formulation and a strengthened Wagner–Whitin formulation are presented.
• A novel dynamic heuristic to determine the size of a partial formulation is proposed.
• Our novel approach could solve more than 96% of the tested instances for the ELSRs.

An important way to try reducing environmental damage in the manufacture of industrialized goods is through the use of production systems which deal with the reuse of returned materials such as reverse logistics. In this paper, we consider a production planning problem arising in the context of reverse logistics, namely the economic lot-sizing with remanufacturing (ELSR). In the ELSR, deterministic demand for a single item over a finite time horizon has to be satisfied, which can be performed from either newly produced or remanufactured items, and the goal consists in minimizing the total production costs. Our objective is to devise approaches to solve larger (more difficult) instances of the problem available in the literature to optimality using a standard mixed-integer programming (MIP) solver. We present a multicommodity extended formulation and a strengthened Wagner–Whitin based formulation, which makes use of a priori addition of newly described valid inequalities in the space of original variables. We also propose a novel dynamic heuristic measure based on the cost structure to automatically determine the size of a partial version of the Wagner–Whitin based formulation. Computational results show that the novel partial Wagner–Whitin based formulation with the size automatically determined in a heuristic way outperforms all the other tested approaches, including a best performing shortest path formulation available in the literature, when we consider the number of instances solved to proven optimality using a standard MIP solver. This new approach allowed to solve to optimality more than 96% of the tested instances for the ELSR with separate setups, including several instances that could not be solved otherwise.