Abstract
In this chapter, we develop two lot-sizing models for multi-level production with flexible BOMs: The Multi-Level Capacitated Lot-Sizing Problem with Substitution (MLCLSP-S), which is an extension of the MLCLSP (see Sect. 2.1.6) and uses hypergraphs to model substitution General Lot-sizing and Scheduling Problem for Multiple production Stages with Flexible Production Sequences (GLSPMS-FPS), which is an extension of the GLSPMS (see Sect. 2.1.7) that uses STN (see Sect. 3.2.4) to model flexible production sequences and flexible BOMs
The purpose of the former model, the MLCLSP-S, is to show how flexible BOMs modeled by hypergraphs can be integrated in multi-level lot-sizing models. The MLCLSP-S would be suitable for applications with discrete products and assembly structures, but is less appropriate for flexible production structures as they can be found in the process industries. The model cannot map flexible production sequences.
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Notes
- 1.
Analogously to 2.60 (see footnote 5 on p. 50), 7.27 is more restrictive than required for ensuring temporal feasibility. It can be reformulated by introducing variables y rabs b and y rabs e that denote the setup time consumed by a changeover from task a to b on resource r at the beginning and end of micro-period s, respectively.
- 2.
References
Begnaud, J., Miller, L., & Benjaafar, S. (2006). The multilevel lot sizing problem with flexible production sequences (Working paper). Minnesota: Industrial and Systems Engineering Department of Mechanical Engineering, University of Minnesota, MN.
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Lang, J.C. (2010). Multi-Level Lot-Sizing Models with Flexible Bills-of-Materials. In: Production and Inventory Management with Substitutions. Lecture Notes in Economics and Mathematical Systems, vol 636. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04247-8_7
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DOI: https://doi.org/10.1007/978-3-642-04247-8_7
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