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On the equivalence between compromise programming and the use of composite compromise metrics

Author

Listed:
  • Francisco J. André

    (Department of Economics, Universidad Pablo de Olavide)

  • Carlos Romero

    (Departamento de Economía y Gestión Forestal, Escuela Tecnica Superior de Ingenieros de Montes, Universidad Politécnica de Madrid.)

Abstract

This paper analyzes the relationship between Compromise Programming and a close relative called Composite Programming that is based on the use of composite metrics. More specifically, it focuses on the possibility that the results of Compromise Programming are equivalent to those obtained with a particular case of Composite Programming in which a linear combination between the two bounds of the compromise set is established. Several situations, depending on the number of criteria involved and the mathematical structure of the efficient set, are studied. The most relevant result is obtained when two criteria are involved and the efficient set is continuously differentiable. In this case, it is possible to find a unique equivalent value of the control parameter in Composite Programming for each metric in Compromise Programming. It is remarked that this particular case is very relevant in many economic scenarios. On the other hand, it turns out that the equivalence between both approaches can not be extended to the case with more than two criteria.

Suggested Citation

  • Francisco J. André & Carlos Romero, 2006. "On the equivalence between compromise programming and the use of composite compromise metrics," Working Papers 06.33, Universidad Pablo de Olavide, Department of Economics.
    • Handle: RePEc:pab:wpaper:06.33
    as

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    File URL: http://www.upo.es/serv/bib/wps/econ0633.pdf
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    References listed on IDEAS

    as
    1. P. L. Yu, 1973. "A Class of Solutions for Group Decision Problems," Management Science, INFORMS, vol. 19(8), pages 936-946, April.
    2. Nakayama, Hirotaka, 1992. "Trade-off analysis using parametric optimization techniques," European Journal of Operational Research, Elsevier, vol. 60(1), pages 87-98, July.
    3. M. Freimer & P. L. Yu, 1976. "Some New Results on Compromise Solutions for Group Decision Problems," Management Science, INFORMS, vol. 22(6), pages 688-693, February.
    4. F J André & M A Cardenete & C Romero, 2008. "Using compromise programming for macroeconomic policy making in a general equilibrium framework: theory and application to the Spanish economy," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(7), pages 875-883, July.
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    Cited by:

    1. B. Domenech & L. Ferrer-Martí & R. Pastor, 2022. "Multicriteria analysis of renewable-based electrification projects in developing countries," Annals of Operations Research, Springer, vol. 312(2), pages 1375-1401, May.

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    More about this item

    Keywords

    Compromise programming; composite metric; p-norms; economic optimization.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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