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A hybrid heuristic for the multi-plant capacitated lot sizing problem with setup carry-over
Journal of the Brazilian Computer Society volume 14, pages 7–15 (2008)
This paper addresses the capacitated lot sizing problem (CLSP) with a single stage composed of multiple plants, items and periods with setup carry-over among the periods. The CLSP is well studied and many heuristics have been proposed to solve it. Nevertheless, few researches explored the multi-plant capacitated lot sizing problem (MPCLSP), which means that few solution methods were proposed to solve it. Furthermore, to our knowledge, no study of the MPCLSP with setup carry-over was found in the literature. This paper presents a mathematical model and a GRASP (Greedy Randomized Adaptive Search Procedure) with path relinking to the MPCLSP with setup carry-over. This solution method is an extension and adaptation of a previously adopted methodology without the setup carry-over. Computational tests showed that the improvement of the setup carry-over is significant in terms of the solution value with a low increase in computational time.
A. Aggarwal, J. K. Park. Improved algorithms for economic lot size problems.Operations Research. 41: 549–571, 1993.
V. A. Armentano, P. M. França, F. M. B. de Toledo. A network flow model for the capacitated lot-sizing problem.Omega. 27: 275–284, 1999.
D. Briskorn. A note on capacitated lot sizing with setup carry over.IIE Transactions. 38: 1045–1047, 2006.
M. Diaby, H. C. Bahl, M. H. Karwan, S. Zionts. Capacitated lot-sizing and scheduling by lagrangean relaxation.European Journal of Operational Research. 59: 444–458, 1992.
M. Diaby, H. C. Bahl, M. H. Karwan, S. Zionts. A lagrangean relaxation approach for very-largescale capacitated lot-sizing.Management Science. 59: 1329–1340, 1992.
A. Federgruen, M. Tzur. A simple forward algorithm to solve general dynamic lot sizing models with n periods in o(nlogn) or o(n) time.Management Science. 37: 909–925, 1991.
T. A. Feo, M. G. C. Resende. A probabilistic heuristic for a computationally difficult set covering problem.Operations Research Letters. 8: 67–71, 1989.
F. Glover. A template for scatter search and path relinking. In Proceedings of AE ’97:Selected Papers from the Third European Conference on Artificial Evolution, London, UK, pages 3-54, 1998.
M. Gopalakrishnan, K. Ding, J. M. Bourjolly, S. Mohan. A tabu-search heuristic for the capacitated lotsizing problem with set-up carryover.Management Science. 47: 851–863, 2001.
M. Gopalakrishnan, D. M. Miller, C. P. Schmidt. A framework for modelling setup carryover in the capacitated lot sizing problem.International Journal of Production Research. 33(7): 1973–1988, 1995.
M. Laguna, R. Martí. Grasp and path relinking for 2-layer straight line crossing minimization.Informs Journal on Computing. 11(1): 44–52, 1999.
S. Lozano, J. Larraneta, L. Onieva. Primal-dual approach to the single level capacitated lot-sizing problem.European Journal of Operational Research. 51: 354–366, 1991.
J. Maes, J. O. McClain, L. N. Van Wassenhove. Multilevel capacitated lotsizing complexity and lpbased heuristics.European Journal of Operational Research. 53: 131–148, 1991.
M. C. V. Nascimento, M. C. G. Resende, F. M. B. Toledo. GRASP with path-relinking for the multiplant capacitated lot sizing problem. EuropeanJournal of Operational Research, accepted for publication, 2008.
L. S. Pitsoulis, M. G. C. Resende. Greedy randomized adaptive search procedures.Journal of Global Optimization. 6: 109–133, 1995.
P. Porkka, A. P. J. Vepsäläinen, M. Kuula. Multiperiod production planning carrying over set-up time.International Journal of Production Research. 41(6): 1133–1148, 2003.
M. Sambasivan, C. P. Schimidt. A heuristic procedure for solving multi-plant, multi-item, multi-period capacitated lot-sizing problems.Asia Pacific Journal of Operational Research. 19: 87–105, 2002.
M. Sambasivan, S. Yahya. A Lagrangean-based heuristic for multi-plant, multi-item, multi-period capacitated lot-sizing problems with inter-plant transfers.Computers and Operations Research. 32: 537–555, 2005.
K. X. S. Souza, V. A. Armentano. Multi-item capacitated lot-sizing by a cross decomposition based algorithm.Annals of Operations Research. 50: 557–574, 1994.
C. R. Sox, Y. B. Gao. The capacitated lot sizing problem with setup carry-over.IEE Transactions. 31: 173–181, 1999.
C. Suerie, H. Stadtler. The capacitated lot-sizing problem with linked lot sizes.Management Science. 49: 1039–1054, 2003.
C. S. Sung. A single-product parallel-facilities production-planning model.International Journal of Systems Science. 17: 983–989, 1986.
F. M. B. Toledo, V. A. Armentano. A lagrangean-based heuristic for the capacitated lot-sizing problem in parallel machines.European Journal of Operational Research. 175: 1070–1083, 2006.
W. W. Trigeiro, L. J. Thomas, J. O. McClain. Capacitated lot sizing with setup times.Management Science. 35: 353–366, 1989.
A. Wagelmans, S. Van Hoesel, A. Kolen. Economic lot sizing: an o(nlogn) algorithm that runs in linear time in the wagner-whitin case.Operations Research. 40: 145–156, 1992.
H. M. Wagner, T. M. Whitin. Dynamic version of the economic lot size mode.Management Science. 5: 89–96, 1958.
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Nascimento, M.C.V., Toledo, F.M.B. A hybrid heuristic for the multi-plant capacitated lot sizing problem with setup carry-over. J Braz Comp Soc 14, 7–15 (2008). https://doi.org/10.1007/BF03192568
- path relinking
- lot sizing