A comparative analysis of mixed-integer linear formulations for the multi-family capacitated lot-sizing problem

Despite having a very broad spectrum of applicability in practice, the multi-family capacitated lot-sizing problem (MFCLSP) has been scarcely studied. The MFCLSP is an extension of the capacitated lot-sizing problem with setup times (CLST) in which items are organized into families based on similar setup structures. In this paper, we propose three formulations for the MFCLSP (MF-TRAD, MF-ARBNET, and MF-EXREQ), and develop a comprehensive comparative analysis to evaluate their performance using a generic solver (CPLEX). Solving large-scale problems to optimality has been shown to consume a great amount of computational time, which is very impractical for real-life applications. Because of that, this study focuses on analyzing the performance of these formulations in a limited, and reasonable, amount of time. The results show the MF-EXREQ model outperforms the other two models in both the time to the first feasible solution and the quality of the solutions generated throughout the solving process.