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Linear Multiparametric Programming by Multicriteria Simplex Method

Author

Listed:
  • P. L. Yuf

    (University of Texas)

  • M. Zeleny

    (Columbia University)

Abstract

A recently derived Multicriteria Simplex Method [Yu, P. L., M. Zeleny. 1975. The set of all nondominated solutions in linear cases and a multicriteria simplex method. J. Math. Anal. Appl. 49 (2, February) 430-468.] is used to study some basic properties in the decomposition of parametric space. A new type of parametric space, which arises naturally in its formulation, is used. Two computational methods are discussed. The first one is an indirect algebraic method which locates the corresponding set of all nondominated extreme points. The second one is a direct geometric decomposition method which is similar to that discussed by Gal and Nedoma [Gal, T., J. Nedoma. 1972 Multiparametric linear programming. Management Sci.. 18 406-421.]. The difficulties of such a geometric method are discussed through an example.

Suggested Citation

  • P. L. Yuf & M. Zeleny, 1976. "Linear Multiparametric Programming by Multicriteria Simplex Method," Management Science, INFORMS, vol. 23(2), pages 159-170, October.
    • Handle: RePEc:inm:ormnsc:v:23:y:1976:i:2:p:159-170
    DOI: 10.1287/mnsc.23.2.159
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    Cited by:

    1. Iosif Pappas & Nikolaos A. Diangelakis & Efstratios N. Pistikopoulos, 2021. "The exact solution of multiparametric quadratically constrained quadratic programming problems," Journal of Global Optimization, Springer, vol. 79(1), pages 59-85, January.
    2. Soylu, Banu, 2015. "Heuristic approaches for biobjective mixed 0–1 integer linear programming problems," European Journal of Operational Research, Elsevier, vol. 245(3), pages 690-703.
    3. Sedeno-Noda, A. & Gonzalez-Martin, C., 2000. "The biobjective minimum cost flow problem," European Journal of Operational Research, Elsevier, vol. 124(3), pages 591-600, August.
    4. Osman Ou{g}uz, 2000. "Bounds on the Opportunity Cost of Neglecting Reoptimization in Mathematical Programming," Management Science, INFORMS, vol. 46(7), pages 1009-1012, July.
    5. Alves, Maria João & Costa, João Paulo, 2016. "Graphical exploration of the weight space in three-objective mixed integer linear programs," European Journal of Operational Research, Elsevier, vol. 248(1), pages 72-83.
    6. Inuiguchi, Masahiro & Sakawa, Masatoshi, 1995. "Minimax regret solution to linear programming problems with an interval objective function," European Journal of Operational Research, Elsevier, vol. 86(3), pages 526-536, November.
    7. Charitopoulos, Vassilis M. & Dua, Vivek, 2017. "A unified framework for model-based multi-objective linear process and energy optimisation under uncertainty," Applied Energy, Elsevier, vol. 186(P3), pages 539-548.

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