Abstract
Determining lot sizes is an essential step during the material requirements planning phase influencing total production cost and total throughput time of a production system. It is well-known that lot-sizing and scheduling decisions are intertwined. Neglecting this relation, as it is done in the classical hierarchical planning approach, leads to inefficient and sometimes infeasible plans. In this work we compare different approaches for integrating the lot-sizing and the scheduling decisions in multi-stage systems. We show their abilities and limitations in describing relevant aspects of a production environment. By applying the models to benchmark instances we analyze their computational behavior. The structural and numerical comparisons show that there are considerable differences between the approaches although all models aim to describe the same planning problem. The results provide a guideline for selecting the right modeling approach for different planning situations.
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Notes
- 1.
The actual processing time of a lot usually takes only a small fraction of a macro-period.
References
Almeder, C., Klabjan, D., Traxler, R., & Almada-Lobo, B. (2015). Lead time considerations for the multi-level capacitated lot-sizing problem. European Journal of Operational Research, 241(3), 727–738.
Billington, P. J., McClain, J. O., & Thomas, L. J. (1983). Mathematical programming approaches to capacity-constrained MRP systems: Review, formulation and problem reduction. Management Science, 29(10), 1126–1141.
Bitran, G. R., & Yanasse, H. H. (1982). Computational complexity of the capacitated lot size problem. Management Science, 28(10), 1174–1186.
Buschkühl, L., Sahling, F., Helber, S., & Tempelmeier, H. (2010). Dynamic capacitated lot-sizing problems: A classification and review of solution approaches. OR Spectrum, 32(2), 231–261.
Dauzère-Pérès, S., & Lasserre, J.-B. (2002). On the importance of sequencing decisions in production planning and scheduling. International Transactions in Operational Research, 9, 779–793.
Drexl, A., & Kimms, A. (1997). Lot sizing and scheduling - survey and extensions. European Journal of Operational Research, 99(2), 221–235.
Fandel, G., & Stammen-Hegene, C. (2006, December). Simultaneous lot sizing and scheduling for multi-product multi-level production. International Journal of Production Economics, 104(2), 308–316.
Fleischmann, B., & Meyr, H. (1997). The general lotsizing and scheduling problem. OR Spektrum, 19, 11–21.
Haase, K. (1994). Lotsizing and scheduling for production planning. Lecture notes in economics and mathematical systems (Vol. 408). Berlin, Heidelberg: Springer.
Kim, H., Jeong, H.-I., & Park, J. (2008). Integrated model for production planning and scheduling in a supply chain using benchmarked genetic algorithm. International Journal of Advanced Manufacturing Technology, 39, 1207–1226.
Kimms, A., & Drexl, A. (1998). Some insights into proportional lot sizing and scheduling. Journal of the Operational Research Society, 49(11), 1196–1205.
Sahling, F., Buschkühl, L., Tempelmeier, H., & Helber, S. (2009). Solving a multi-level capacitated lot sizing problem with multi-period setup carry-over via a fix-and-optimize heuristic. Computers & Operations Research, 36, 2546–2553.
Seeanner, F., & Meyr, H. (2013). Multi-stage simultaneous lot-sizing and scheduling for flow line production. OR Spectrum, 35(1), 33–73.
Stadtler, H. (2011). Multi-level single machine lot-sizing and scheduling with zero lead times. European Journal of Operational Research, 209, 241–252.
Suerie, C., & Stadtler, H. (2003). The capacitated lot-sizing problem with linked lot sizes. Management Science, 49(8), 1039–1054.
Tempelmeier, H., & Buschkühl, L. (2009). A heuristic for the dynamic multi-level capacitated lotsizing problem with linked lotsizes for general product structures. OR Spectrum, 31, 385–404.
Wagner, H. M., & Whitin, T. M. (1958). Dynamic version of the economic lot size model. Management Science, 5, 89–96.
Acknowledgement
The author wants to thank Renate Traxler for performing the numerical experiments.
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Almeder, C. (2016). Comparing Modeling Approaches for the Multi-Level Capacitated Lot-Sizing and Scheduling Problem. In: Dawid, H., Doerner, K., Feichtinger, G., Kort, P., Seidl, A. (eds) Dynamic Perspectives on Managerial Decision Making. Dynamic Modeling and Econometrics in Economics and Finance, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-39120-5_19
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DOI: https://doi.org/10.1007/978-3-319-39120-5_19
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