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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
    DOI: 10.1287/mnsc.30.11.1346
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    Cited by:

    1. Bennet Gebken & Sebastian Peitz & Michael Dellnitz, 2019. "On the hierarchical structure of Pareto critical sets," Journal of Global Optimization, Springer, vol. 73(4), pages 891-913, April.
    2. 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.
    3. 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.
    4. Naoki Hamada & Shunsuke Ichiki, 2022. "Free Disposal Hull Condition to Verify When Efficiency Coincides with Weak Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 248-270, January.
    5. 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.
    6. Francisco Ruiz & Lourdes Rey & María Muñoz, 2008. "A graphical characterization of the efficient set for convex multiobjective problems," Annals of Operations Research, Springer, vol. 164(1), pages 115-126, November.
    7. Alexander Engau & Margaret M. Wiecek, 2008. "Interactive Coordination of Objective Decompositions in Multiobjective Programming," Management Science, INFORMS, vol. 54(7), pages 1350-1363, July.
    8. Psarras, J. & Capros, P. & Samouilidis, J.-E., 1990. "4.5. Multiobjective programming," Energy, Elsevier, vol. 15(7), pages 583-605.
    9. Nicolae Popovici, 2017. "A decomposition approach to vector equilibrium problems," Annals of Operations Research, Springer, vol. 251(1), pages 105-115, April.
    10. 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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