Capacitated lot-sizing with extensions: a review

The capacitated lot-sizing problem (CLSP) is a standard formulation for big bucket lot-sizing problems with a discrete period segmentation and deterministic demands. We present a literature review on problems that incorporate one of the following extensions in the CLSP: back-orders, setup carry-over, sequencing, and parallel machines. We illustrate model formulations for each of the extensions and also mention the inclusion of setup times, multi-level product structures and overtime in a study. For practitioners, this overview allows to check the availability of successful solution procedures for a specific problem. For scientists, it identifies areas that are open for future research.