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On Efficient Solutions to Multiple Objective Mathematical Programs

Author

Listed:
  • T. J. Lowe

    (Krannert Graduate School of Management, Purdue University, West Lafayette, Indiana 47907)

  • J.-F. Thisse

    (SPUR, Universite Catholique de Louvain, Louvain-la-Neuve, Belgium)

  • J. E. Ward

    (Krannert Graduate School of Management, Purdue University, West Lafayette, Indiana 47907)

  • R. E. Wendell

    (Graduate School of Business, University of Pittsburgh, Pittsburgh, Pennsylvania 15260)

Abstract

This note develops properties of quasi-efficient solutions and explores interrelationships to the classical concept of efficiency. In particular, a point is a quasi-efficient solution to a multiple objective mathematical program if and only if it is an optimal solution to a scalar maximum problem for some set of nonnegative weights on the objectives. This result is then used to characterize the set of quasi-efficient solutions as the union of efficient solutions to a multiple objective problem over all nonempty subsets of the objectives.

Suggested Citation

  • T. J. Lowe & J.-F. Thisse & J. E. Ward & R. E. Wendell, 1984. "On Efficient Solutions to Multiple Objective Mathematical Programs," Management Science, INFORMS, vol. 30(11), pages 1346-1349, November.
  • Handle: RePEc:inm:ormnsc:v:30:y:1984:i:11:p:1346-1349
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    File URL: http://dx.doi.org/10.1287/mnsc.30.11.1346
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    References listed on IDEAS

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    1. Ian I. Mitroff, 1972. "The Myth of Objectivity OR Why Science Needs a New Psychology of Science," Management Science, INFORMS, vol. 18(10), pages 613-618, June.
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    Cited by:

    1. Alzorba, Shaghaf & Günther, Christian & Popovici, Nicolae & Tammer, Christiane, 2017. "A new algorithm for solving planar multiobjective location problems involving the Manhattan norm," European Journal of Operational Research, Elsevier, vol. 258(1), pages 35-46.
    2. Jornada, Daniel & Leon, V. Jorge, 2016. "Biobjective robust optimization over the efficient set for Pareto set reduction," European Journal of Operational Research, Elsevier, vol. 252(2), pages 573-586.
    3. Lindroth, Peter & Patriksson, Michael & Strömberg, Ann-Brith, 2010. "Approximating the Pareto optimal set using a reduced set of objective functions," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1519-1534, December.
    4. Alexander Engau & Margaret M. Wiecek, 2008. "Interactive Coordination of Objective Decompositions in Multiobjective Programming," Management Science, INFORMS, pages 1350-1363.
    5. Psarras, J. & Capros, P. & Samouilidis, J.-E., 1990. "4.5. Multiobjective programming," Energy, Elsevier, vol. 15(7), pages 583-605.
    6. Nicolae Popovici & Matteo Rocca, 2010. "Pareto reducibility of vector variational inequalities," Economics and Quantitative Methods qf1004, Department of Economics, University of Insubria.

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