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Primal-Dual Simplex Method for Multiobjective Linear Programming

Author

Listed:
  • M. Ehrgott

    (University of Auckland)

  • J. Puerto

    (Universidad de Sevilla)

  • A. M. Rodríguez-Chía

    (Universidad de Cádiz)

Abstract

We develop a primal-dual simplex algorithm for multicriteria linear programming. It is based on the scalarization theorem of Pareto optimal solutions of multicriteria linear programs and the single objective primal-dual simplex algorithm. We illustrate the algorithm by an example, present some numerical results, give some further details on special cases and point out future research.

Suggested Citation

  • M. Ehrgott & J. Puerto & A. M. Rodríguez-Chía, 2007. "Primal-Dual Simplex Method for Multiobjective Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 483-497, September.
    • Handle: RePEc:spr:joptap:v:134:y:2007:i:3:d:10.1007_s10957-007-9232-y
    DOI: 10.1007/s10957-007-9232-y
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    References listed on IDEAS

    as
    1. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, December.
    2. Matthias Ehrgott & Xavier Gandibleux, 2004. "Approximative solution methods for multiobjective combinatorial optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 1-63, June.
    3. H. P. Benson & E. Sun, 2000. "Outcome Space Partition of the Weight Set in Multiobjective Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 17-36, April.
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    Cited by:

    1. Jornada, Daniel & Leon, V. Jorge, 2016. "Robustness methodology to aid multiobjective decision making in the electricity generation capacity expansion problem to minimize cost and water withdrawal," Applied Energy, Elsevier, vol. 162(C), pages 1089-1108.
    2. S. Rivaz & M. A. Yaghoobi & M. Hladík, 2016. "Using modified maximum regret for finding a necessarily efficient solution in an interval MOLP problem," Fuzzy Optimization and Decision Making, Springer, vol. 15(3), pages 237-253, September.
    3. Moradi, Siamak & Raith, Andrea & Ehrgott, Matthias, 2015. "A bi-objective column generation algorithm for the multi-commodity minimum cost flow problem," European Journal of Operational Research, Elsevier, vol. 244(2), pages 369-378.

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