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Axial solutions for multiple objective linear problems. An application to target setting in DEA models with preferences

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  • Hinojosa, M.A.
  • Mármol, A.M.
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    Abstract

    In this paper we introduce the class of axial solutions for multiple objective optimization problems in contexts in which partial information on preference weights is available. These solutions combine the use of an improvement axis to direct the search of the most preferred result with the concept of efficiency with respect to preference information. In addition, we show how this solution is used in data envelopment analysis in order to set realistic targets in accordance with either the partially specified preferences of a single decision maker, or the different individual preference information provided by the members of a group of decision makers.

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    Bibliographic Info

    Article provided by Elsevier in its journal Omega.

    Volume (Year): 39 (2011)
    Issue (Month): 2 (April)
    Pages: 159-167

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    Handle: RePEc:eee:jomega:v:39:y:2011:i:2:p:159-167

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    Keywords: Multiple objective linear problems Partial information DEA;

    References

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    1. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
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    5. M. Halme & P. Korhonen, 1998. "Restricting Weights in Value Efficiency Analysis," Working Papers ir98104, International Institute for Applied Systems Analysis.
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    7. André, Francisco J., 2009. "Indirect elicitation of non-linear multi-attribute utility functions. A dual procedure combined with DEA," Omega, Elsevier, vol. 37(4), pages 883-895, August.
    8. Charnes, A. & Cooper, W. W. & Huang, Z. M. & Sun, D. B., 1990. "Polyhedral Cone-Ratio DEA Models with an illustrative application to large commercial banks," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 73-91.
    9. Doyle, J & Green, R, 1993. "Data envelopment analysis and multiple criteria decision making," Omega, Elsevier, vol. 21(6), pages 713-715, November.
    10. Ehud Kalai, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Discussion Papers 179, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Richard E. Wendell, 2004. "Tolerance Sensitivity and Optimality Bounds in Linear Programming," Management Science, INFORMS, vol. 50(6), pages 797-803, June.
    12. Stewart, Theodor J., 2010. "Goal directed benchmarking for organizational efficiency," Omega, Elsevier, vol. 38(6), pages 534-539, December.
    13. Weber, Martin, 1987. "Decision making with incomplete information," European Journal of Operational Research, Elsevier, vol. 28(1), pages 44-57, January.
    14. Richard E. Wendell, 1985. "The Tolerance Approach to Sensitivity Analysis in Linear Programming," Management Science, INFORMS, vol. 31(5), pages 564-578, May.
    15. Merja Halme & Tarja Joro & Pekka Korhonen & Seppo Salo & Jyrki Wallenius, 1999. "A Value Efficiency Approach to Incorporating Preference Information in Data Envelopment Analysis," Management Science, INFORMS, vol. 45(1), pages 103-115, January.
    16. Hansen, Pierre & Labbe, Martine & Wendell, Richard E., 1989. "Sensitivity analysis in multiple objective linear programming: The tolerance approach," European Journal of Operational Research, Elsevier, vol. 38(1), pages 63-69, January.
    17. André, Francisco J. & Herrero, Inés & Riesgo, Laura, 2010. "A modified DEA model to estimate the importance of objectives with an application to agricultural economics," Omega, Elsevier, vol. 38(5), pages 371-382, October.
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    Cited by:
    1. Hatami-Marbini, Adel & Tavana, Madjid, 2011. "An extension of the Electre I method for group decision-making under a fuzzy environment," Omega, Elsevier, vol. 39(4), pages 373-386, August.
    2. Ahn, Heinz & Neumann, Ludmila & Vazquez Novoa, Nadia, 2012. "Measuring the relative balance of DMUs," European Journal of Operational Research, Elsevier, vol. 221(2), pages 417-423.
    3. Aparicio, Juan & Pastor, Jesus T., 2014. "Closest targets and strong monotonicity on the strongly efficient frontier in DEA," Omega, Elsevier, vol. 44(C), pages 51-57.

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