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.

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Abstract:We address the capacitated lot-sizing and scheduling problem with setup times, setup carry-over, back-orders, and parallel machines as it appears in a semiconductor assembly facility. The problem can be formulated as an extension of the capacitated lot-sizing problem with linked lot-sizes (CLSPL). We present a mixed integer (MIP) formulation of the problem and a new solution procedure. The solution procedure is based on a novel "aggregate model," which uses integer instead of binary variables. The model is embedded in a period-by-period heuristic and is solved to optimality or near-optimality in each iteration using standard procedures (CPLEX). A subsequent scheduling routine loads and sequences the products on the parallel machines. Six variants of the heuristic are presented and tested in an extensive computational study.

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