M. Maldonado1, S. Rangel*1 and D. Ferreira2
1 Departamento de Matemática Aplicada, UNESP-Univ Estadual Paulista, IBILCE São José do Rio Preto, São Paulo, Brazil. * socorro@ibilce.unesp.br
2 Departamento de Física, Química e Matemática, UFSCAR-Univ Federal de São Carlos Sorocaba, São Paulo, Brazil.
ABSTRACT
The production of soft drinks involves two main stages: syrup preparation and bottling. To obtain the lots sequence in the bottling stage, three approaches are studied. They are based on the sub-tour elimination constraints used in mathematical models for the Asymmetric Traveling Salesman Problem. Two of the mathematical models are from the literature and use classical constraints. The third model includes multi-commodity flow constraints to eliminate disconnected subsequences. The computational behavior of the three models is studied using instances generated with data from the literature. The numerical results show that there are considerable differences among the three models and indicates that the multi-commodity formulation provides good results but it requires far more computational effort when the instances are solved by a commercial software.
]]> Keywords: Production planning, integrated lot sizing and scheduling models, asymmetric travelling salesman problem, multi-commodity flow.
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Acknowledgment
This research was partly supported by the Brazilian research agencies CNPQ (306194/2012-0) and FAPESP (2010/19006-0, 2013/07375-0, 2010/10133-0).
References
[1] Y.S.P. Chiu, et al., "Reexamination of 'Combining an alternative multi-delivery policy into economic production lot size problem with partial rework" Using an Alternative Approach", Journal of Applied Research and Technology, Vol. 11, no. 13, pp. 317-323, 2013. [ Links ]
]]>[2] M. Vanzela, et al., "The Integrated Lot Sizing and Cutting Stock Problem in a Furniture Factory", In: 11th IFAC Workshop on Intelligent Manufacturing Systems, vol. 11, pp. 390-395, 2013. [ Links ]
[3] A. Clark et al., "Lot sizing and scheduling: industrial extensions and research opportunities", International Journal of Production Research, vol. 49, no. 9, pp. 2457-2461, 2011. [ Links ]
[4] B. Almada-Lobo et al., "Single machine multi-product capacitated lot sizing with sequence-dependent setups", International Journal of Production Research, vol. 45, no. 20, pp. 4873-4894, 2007. [ Links ]
[5] E. Toso, et al., "Lot sizing and sequencing optimization at an animal-feed plant", Computers & Industrial Engineering, vol. 57, no. 3, pp. 813-821, 2009. [ Links ]
[6] H. Rezazadeh, et al., "Linear programming embedded particle swarm optimization for solving an extended model of dynamic virtual cellular manufacturing systems", Journal of Applied Research and Technology, vol. 7, no. 1, pp. 83-108, 2009. [ Links ]
]]>[7] B. Fleischmann and H. Meyr, "The general lot sizing and scheduling problem", Operation Research Spectrum, vol. 19, no. 1, pp. 11-21, 1997. [ Links ]
[8] C.F.M. Toledo, et al., "Um modelo de otimização para o problema integrado de dimensionamento de lotes e programação da produção em fábricas de refrigerantes", Pesquisa Operacional, vol. 27, no. 1, pp. 155-186, 2007. [ Links ]
[9] D. Ferreira et al., "Solution approaches for the soft drink integrated production lot sizing and scheduling problem", European Journal of Operational Research, vol. 196, no. 2, pp. 697-706, 2009. [ Links ]
[10] C. Defalque, et al., "Usando o ATSP na Modelagem do Problema Integrado de Produçâo de Bebidas", TEMA - Tend. Mat. Apl. Comput., vol. 12, no. 3, pp. 195-209, 2011. [ Links ]
[11] D. Ferreira, et al., "Single-stage formulations for synchronized two-stage lot sizing and scheduling in soft drink production", International Journal of Production Economics, vol. 136, no. 2, pp. 255-265, 2012. [ Links ]
]]>[12] B. Karimi, et al., "The capacitated lot sizing problem: a review of models and algorithms", Omega, vol. 31, no. 5, pp. 365-378, 2003. [ Links ]
[13] C.E. Miller, et al., "Integer Programming Formulations of Traveling Salesman Problem", JACM-Journal of the ACM, vol. 7, no. 4, pp. 326-329, 1960. [ Links ]
[14] T. Oncan et al., "A comparative analysis of several asymmetric traveling salesman problem formulations", Computer & Operation Research, vol. 36, no. 3, pp. 637-654, 2009. [ Links ]
[15] A. Claus, "A new formulation for the traveling salesman problem", Journal on Algebraic and Discrete Methods, vol. 5, no. 1, pp. 21-25, 1984. [ Links ]
[16] A. Clark, et al., "Production Lot Sizing and Scheduling with Non-Triangular Sequence-Dependent Setup Times", International Journal of Production Research, to print, 2014. [ Links ]
]]>[17] S. Rangel and M. Maldonado, "Strategies to Model Scheduling Decisions to Plan the Soft Drink Production Process", In Proceedings of the 1st International Conference on Operations Research and Enterprise Systems, Copyrigth 2012©, ScitePress. doi: 10.5220/0003761801810185. [ Links ]
[18] G. Dantzig, et al., "Solution of a Large-Scale Traveling Salesman Problem", Journal of the Operations Research Society of America, vol 2, no. 4, pp. 393-410, 1954. [ Links ]
[19] AMPL, A Modeling Language for Mathematical Programming. Available from www.ampl.com [ Links ]
[20] IBM ILOG-CPLEX - Mathematical Programming Optimizers. Available form www.ibm.com [ Links ] ]]>