Solving Multi-Level Capacitated Lot Sizing Problems via a Fix-and-Optimize Approach

Abstract

We present a solution approach for the dynamic multi-level capacitated lot sizing problem (MLCLSP) and its extensions. The objective is to determine a cost minimizing production plan for discrete products on multiple resources. The time-varying demand is assumed to be given for each product in each period and has to be completely fulfilled. The production is located on capacity constrained resources for the different production stages. In an iterative fashion, our Fix-and-Optimize approach solves a series of mixed-integer programs. In each of these programs all real-valued variables are treated, but only a small and iteration-specific subset of binary setup variables is optimized. All remaining binary variables are fixed. A numerical study shows that the algorithm provides high-quality results and that the computational effort is moderate.