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Lagrangian relaxation of the generic materials and operations planning model

Author

Listed:
  • G. Rius-Sorolla

    (Universitat Politècnica de València)

  • J. Maheut

    (Universitat Politècnica de València)

  • Jairo R. Coronado-Hernandez

    (Universidad de la Costa)

  • J. P. Garcia-Sabater

    (Universitat Politècnica de València)

Abstract

The supply chain management requires increasingly proposals for the production programming planning that brings together its special singularities. Solving coexisting products and alternative processes or by-products must be allowed by the mathematical programming models. The generic materials and operations planning (GMOP) formulation allows operating with different materials and process lists. The paper presents a procedure to solve the versatile GMOP model by the Lagrange Relaxation. The subgradient update method of the lagrangian multiplier is compared with a linear update method. Obtaining lower bound faster compared to the linear method is allowed by the subgradient method, but the linear method provides better solutions after certain iterations.

Suggested Citation

  • G. Rius-Sorolla & J. Maheut & Jairo R. Coronado-Hernandez & J. P. Garcia-Sabater, 2020. "Lagrangian relaxation of the generic materials and operations planning model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 105-123, March.
  • Handle: RePEc:spr:cejnor:v:28:y:2020:i:1:d:10.1007_s10100-018-0593-0
    DOI: 10.1007/s10100-018-0593-0
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    1. James H. Lorie & Leonard J. Savage, 1955. "Three Problems in Rationing Capital," The Journal of Business, University of Chicago Press, vol. 28, pages 229-229.
    2. Monique Guignard, 2003. "Lagrangean relaxation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 151-200, December.
    3. Marshall L. Fisher, 2004. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 50(12_supple), pages 1861-1871, December.
    4. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2009. "On solving the Lagrangian dual of integer programs via an incremental approach," Computational Optimization and Applications, Springer, vol. 44(1), pages 117-138, October.
    5. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    6. Michael Held & Richard M. Karp, 1970. "The Traveling-Salesman Problem and Minimum Spanning Trees," Operations Research, INFORMS, vol. 18(6), pages 1138-1162, December.
    7. Zhang, Zhi-Hai & Jiang, Hai & Pan, Xunzhang, 2012. "A Lagrangian relaxation based approach for the capacitated lot sizing problem in closed-loop supply chain," International Journal of Production Economics, Elsevier, vol. 140(1), pages 249-255.
    8. Roberto D. Galvão & Vladimir Marianov, 2011. "Lagrangean Relaxation-Based Techniques for Solving Facility Location Problems," International Series in Operations Research & Management Science, in: H. A. Eiselt & Vladimir Marianov (ed.), Foundations of Location Analysis, chapter 0, pages 391-420, Springer.
    9. Marshall L. Fisher, 1985. "An Applications Oriented Guide to Lagrangian Relaxation," Interfaces, INFORMS, vol. 15(2), pages 10-21, April.
    10. Jeet, V. & Kutanoglu, E., 2007. "Lagrangian relaxation guided problem space search heuristics for generalized assignment problems," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1039-1056, November.
    11. Vidal-Carreras, Pilar I. & Garcia-Sabater, Jose P. & Coronado-Hernandez, Jairo R., 2012. "Economic lot scheduling with deliberated and controlled coproduction," European Journal of Operational Research, Elsevier, vol. 219(2), pages 396-404.
    12. Gabriel R. Bitran & Horacio H. Yanasse, 1982. "Computational Complexity of the Capacitated Lot Size Problem," Management Science, INFORMS, vol. 28(10), pages 1174-1186, October.
    13. X. Zhao & P. B. Luh & J. Wang, 1999. "Surrogate Gradient Algorithm for Lagrangian Relaxation," Journal of Optimization Theory and Applications, Springer, vol. 100(3), pages 699-712, March.
    14. C. Beltran & F. J. Heredia, 2002. "Unit Commitment by Augmented Lagrangian Relaxation: Testing Two Decomposition Approaches," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 295-314, February.
    15. T. S. Chang, 2008. "Comments on “Surrogate Gradient Algorithm for Lagrangian Relaxation”," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 691-697, June.
    16. Narciso, Marcelo G. & Lorena, Luiz Antonio N., 1999. "Lagrangean/surrogate relaxation for generalized assignment problems," European Journal of Operational Research, Elsevier, vol. 114(1), pages 165-177, April.
    17. Jose P. Garcia-Sabater & Julien Maheut & Juan A. Marin-Garcia, 2013. "A new formulation technique to model materials and operations planning: the generic materials and operations planning (GMOP) problem," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 7(2), pages 119-147.
    18. Walther, Grit & Schmid, Eberhard & Spengler, Thomas S., 2008. "Negotiation-based coordination in product recovery networks," International Journal of Production Economics, Elsevier, vol. 111(2), pages 334-350, February.
    19. Mao, Kun & Pan, Quan-ke & Pang, Xinfu & Chai, Tianyou, 2014. "A novel Lagrangian relaxation approach for a hybrid flowshop scheduling problem in the steelmaking-continuous casting process," European Journal of Operational Research, Elsevier, vol. 236(1), pages 51-60.
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