Practical Tips for Modelling Lot-Sizing and Scheduling Problems
DOI:
https://doi.org/10.7494/dmms.2009.3.2.37Keywords:
production, lot-sizing and scheduling, mixed integer programmingAbstract
This paper presents some important alternatives for modelling Lot-Sizing and Scheduling Problems. First, the accuracy of models can improved by using short time buckets, which allow more detailed planning but lead to higher computational effort. Next, valid inequalities make the models tighter but increase their size. Sometimes it is possible to find a good balance between the size and tightness of a model by limiting a priori the number of valid inequalities. Finally, a special normalization of the variables simplifies the presentation of results and validation of models.
References
Belvaux G. & Wolsey L.A. (2001). Modelling practical lot-sizing problems as mixed-integer programs. Management Science, 47(7), pp. 993–1007. DOI: https://doi.org/10.1287/mnsc.47.7.993.9800.
Drexl A. & Haase K. (1995). Proportional lotsizing and scheduling. International Journal of Production Economics, 40(1), pp. 73–87. DOI: https://doi.org/10.1016/0925-5273(95)00040-U.
Drexl A. & Kimms A. (1997). Lot sizing and scheduling – Survey and extensions. European Journal of Operational Research, 99(2), pp. 221–235. DOI: https://doi.org/10.1016/S0377-2217(97)00030-1.
Fleischmann B. (1990). The discrete lot-sizing and scheduling problem. European Journal of Operational Research, 44(3), pp. 337–348. DOI: https://doi.org/10.1016/0377-2217(90)90245-7.
Fleischmann B. (1994). The discrete lot-sizing and scheduling problem with sequence-dependent setup costs. European Journal of Operational Research, 75(2), pp. 395–404. DOI: https://doi.org/10.1016/0377-2217(94)90083-3.
Haase K. (1994). Lotsizing and Scheduling for Production Planning. Lecture Notes in Economics and Mathematical Systems, 408. Berlin–Heidelberg: Springer. DOI: https://doi.org/10.1007/978-3-642-45735-7.
Haase K. (1998). Capacitated lot-sizing with linked production quantities of adjacent periods. In: Drexl A. & Kimms A. (Eds.), Beyond Manufacturing Resource Planning (MRP II): Advanced Models and Methods for Production Planning. Berlin–Heidelberg: Springer, pp. 127–146. DOI: https://doi.org/10.1007/978-3-662-03742-3_6.
Jans R. & Degraeve Z. (2008). Modeling industrial lot sizing problems: A review. International Journal of Production Research, 46(6), pp. 1619–1643. DOI: https://doi.org/10.1080/00207540600902262.
Kaczmarczyk W. (2011). Proportional lot-sizing and scheduling problem with identical parallel machines. International Journal of Production Research, 49(9), pp. 2605–2623. DOI: https://doi.org/10.1080/00207543.2010.532929.
Pochet Y. & Wolsey L.A. (2006). Production Planning by Mixed Integer Programming. Springer Series in Operations Research and Financial Engineering. New York: Springer. DOI: https://doi.org/10.1007/0-387-33477-7.
Sox C.R. & Gao Y. (1999). The capacitated lot sizing problem with setup carry-over. IIE Transactions, 31(2), pp. 173–181. DOI: https://doi.org/10.1023/A:1007520703382.
Suerie C. (2005). Time Continuity in Discrete Time Models: New Approaches for Production Planning in Process Industries. Lecture Notes in Economics and Mathematical Systems, 552. Berlin–Heidelberg: Springer. DOI: https://doi.org/10.1007/b138843.
Suerie C. & Stadtler H. (2003). The capacitated lot-sizing problem with linked lot sizes. Management Science, 49(8), pp. 1039–1054. DOI: https://doi.org/10.1287/mnsc.49.8.1039.16406.
Wagner H.M. & Whitin T.M. (1958). Dynamic version of the economic lot size model. Management Science, 5(1), pp. 89–96. DOI: https://doi.org/10.1287/mnsc.5.1.89.
Wolsey L.A. (2002). Solving multi-item lot-sizing problems with an MIP solver using classification and reformulation. Management Science, 48(12), pp. 1587–1602. DOI: https://doi.org/10.1287/mnsc.48.12.1587.442.
