Abstract
We present a math-heuristic algorithm for the lot sizing problem with carryover. The proposed algorithm uses mathematical programming techniques in a metaheuristic fashion to iteratively solve smaller portions of the original problem. More specifically, we draw ideas from the corridor method to design and impose exogenous constraints on the original problem and, subsequently, we solve to optimality the constrained problem using a MIP solver. The algorithm iteratively builds new corridors around the best solution found within each corridor and, therefore, explores adjacent portions of the search space. In the attempt of fostering diversification while exploring the original search space, we generate a pool of incumbent solutions for the corridor method and, therefore, we reapply the corridor method using different starting points. The algorithm has been tested on instances of a standard benchmark library and the reported results show the robustness and effectiveness of the proposed scheme.
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References
Box, G., Wilson, K.: On the Experimental Attainment of Optimum Conditions. Journal of the Royal Statistical Society B-13, 1–45 (1951)
Buschkühl, L., Sahling, F., Helber, S., Tempelmeier, H.: Dynamic capacitated lot-sizing problems: a clasification and review of solution approaches. OR Spectrum (2008), doi:10.1007/s00291-008-0150-7
Caserta, M., Ramirez, A., Voß, S., Moreno, R.: A hybrid algorithm for the multi level capacitated lot sizing problem with setup carryover. In: Voß, S., Pahl, J., Schwarze, S. (eds.) Logistik Management, pp. 123–138. Physica, Heidelberg (2009)
Caserta, M., Quiñonez, E.: A Cross Entropy-Lagrangean Hybrid Algorithm for the Multi-Item Capacitated Lot-Sizing Problem with Setups. Computers and Operations Research 36(2), 530–548 (2009)
Caserta, M., Voß, S., Sniedovich, M.: Applying the corridor method to a block relocation problem. OR Spectrum (2009), doi:10.1007/s00291-009-0176-5
Caserta, M., Voß, S.: A corridor method-based algorithm for the pre-marshalling problem. In: Giacobini, M., et al. (eds.) EvoWorkshops 2009. LNCS, vol. 5484, pp. 788–797. Springer, Heidelberg (2009)
De Boer, P., Kroese, D.P., Mannor, S., Rubinstein, R.Y.: A tutorial on the cross-entropy method. Annals of Operations Research 134(1), 19–67 (2005)
Maes, J., McClain, J., Van Wassenhove, L.: Multilevel capacitated lotsizing complexity and LP-based heuristics. European Journal of Operational Research 53, 131–148 (1991)
Quadt, D., Kuhn, H.: Capacitated lot-sizing with extensions: a review. 4OR: A Quarterly Journal of Operations Research 6(1), 61–83 (2008)
Sahling, F., Buschkühl, L., Tempelmeier, H., Helber, S.: Solving a multi-level capacitated lot sizing problem with multi-period setup carry-over via a fix-and-optimize heuristic. Computers and Operations Research 36(9), 2546–2553 (2009)
Sniedovich, M., Voß, S.: The Corridor Method: a Dynamic Programming Inspired Metaheuristic. Control and Cybernetics 35(3), 551–578 (2006)
Suerie, C., Stadtler, H.: The capacitated lot-sizing problem with linked lot sizes. Management Science 49(8), 1039–1054 (2003)
Tempelmeier, H., Destroff, M.: A lagrangian-based heuristic for dynamic multilevel multiitem constrained lotsizing with setup times. Management Science 42(5), 738–757 (1996)
Tempelmeier, H., Buschkühl, L.: A heuristic for the dynamic multi-level capacitated lotsizing problem with linked lotsizes for general product structures. OR Spectrum 31, 385–404 (2009)
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Caserta, M., Ramirez, A., Voß, S. (2010). A Math-Heuristic for the Multi-Level Capacitated Lot Sizing Problem with Carryover. In: Di Chio, C., et al. Applications of Evolutionary Computation. EvoApplications 2010. Lecture Notes in Computer Science, vol 6025. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12242-2_47
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DOI: https://doi.org/10.1007/978-3-642-12242-2_47
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