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Using convex preference cones in multiple criteria decision making and related fields

Author

Listed:
  • Nasim Nasrabadi

    (University of Birjand)

  • Akram Dehnokhalaji

    (Aston University)

  • Pekka Korhonen

    (Aalto University School of Business)

  • Jyrki Wallenius

    (Aalto University School of Business)

Abstract

This paper reviews our own and colleagues’ research on using convex preference cones in multiple criteria decision making and related fields. The original paper by Korhonen, Wallenius, and Zionts was published in Management Science in 1984. We first present the underlying theory, concepts, and method. Then we discuss applications of the theory, particularly for finding the most preferred alternative, finding a partial and total rank ordering of alternatives, as well as developing algorithms for solving multi-objective integer and other optimization problems.

Suggested Citation

  • Nasim Nasrabadi & Akram Dehnokhalaji & Pekka Korhonen & Jyrki Wallenius, 2019. "Using convex preference cones in multiple criteria decision making and related fields," Journal of Business Economics, Springer, vol. 89(6), pages 699-717, August.
    • Handle: RePEc:spr:jbecon:v:89:y:2019:i:6:d:10.1007_s11573-019-00935-4
    DOI: 10.1007/s11573-019-00935-4
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    References listed on IDEAS

    as
    1. Canan Ulu & Murat Köksalan, 2001. "An interactive procedure for selecting acceptable alternatives in the presence of multiple criteria," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(7), pages 592-606, October.
    2. Korhonen, Pekka & Soleimani-damaneh, Majid & Wallenius, Jyrki, 2016. "Dual cone approach to convex-cone dominance in multiple criteria decision making," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1139-1143.
    3. Canan Ulu & Murat Köksalan, 2014. "An interactive approach to multicriteria sorting for quasiconcave value functions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(6), pages 447-457, September.
    4. Gülşah Karakaya & Murat Köksalan, 2016. "An interactive approach for Bi-attribute multi-item auctions," Annals of Operations Research, Springer, vol. 245(1), pages 97-119, October.
    5. Karakaya, G. & Köksalan, M. & Ahipaşaoğlu, S.D., 2018. "Interactive algorithms for a broad underlying family of preference functions," European Journal of Operational Research, Elsevier, vol. 265(1), pages 248-262.
    6. Halme, Merja & Korhonen, Pekka & Eskelinen, Juha, 2014. "Non-convex value efficiency analysis and its application to bank branch sales evaluation," Omega, Elsevier, vol. 48(C), pages 10-18.
    7. R. Ramesh & Mark H. Karwan & Stanley Zionts, 1989. "Preference Structure Representation Using Convex Cones in Multicriteria Integer Programming," Management Science, INFORMS, vol. 35(9), pages 1092-1105, September.
    8. Pekka Korhonen & Jyrki Wallenius & Stanley Zionts, 1984. "Solving the Discrete Multiple Criteria Problem using Convex Cones," Management Science, INFORMS, vol. 30(11), pages 1336-1345, November.
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    12. Banu Lokman & Murat Köksalan & Pekka J. Korhonen & Jyrki Wallenius, 2016. "An interactive algorithm to find the most preferred solution of multi-objective integer programs," Annals of Operations Research, Springer, vol. 245(1), pages 67-95, October.
    13. Diclehan Tezcaner & Murat Köksalan, 2011. "An Interactive Algorithm for Multi-objective Route Planning," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 379-394, August.
    14. Murat Köksalan & Mark H. Karwan & Stanley Zionts, 1988. "An approach for solving discrete alternative multiple criteria problems involving ordinal criteria," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(6), pages 625-641, December.
    15. Fowler, John W. & Gel, Esma S. & Köksalan, Murat M. & Korhonen, Pekka & Marquis, Jon L. & Wallenius, Jyrki, 2010. "Interactive evolutionary multi-objective optimization for quasi-concave preference functions," European Journal of Operational Research, Elsevier, vol. 206(2), pages 417-425, October.
    16. Murat Koksalan, M. & Taner, Orhan V., 1992. "An approach for finding the most preferred alternative in the presence of multiple criteria," European Journal of Operational Research, Elsevier, vol. 60(1), pages 52-60, July.
    17. Srinivas Y. Prasad & Mark H. Karwan & Stanley Zionts, 1997. "Use of Convex Cones in Interactive Multiple Objective Decision Making," Management Science, INFORMS, vol. 43(5), pages 723-734, May.
    18. 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.
    19. Pekka Korhonen & Majid Soleimani-damaneh & Jyrki Wallenius, 2017. "The use of quasi-concave value functions in MCDM: some theoretical results," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(2), pages 367-375, October.
    20. Karsu, Özlem & Morton, Alec & Argyris, Nikos, 2018. "Capturing preferences for inequality aversion in decision support," European Journal of Operational Research, Elsevier, vol. 264(2), pages 686-706.
    21. Stanley Zionts & Jyrki Wallenius, 1976. "An Interactive Programming Method for Solving the Multiple Criteria Problem," Management Science, INFORMS, vol. 22(6), pages 652-663, February.
    22. Pekka Korhonen & Herbert Moskowitz & Jyrki Wallenius, 1986. "A Progressive Algorithm for Modeling and Solving Multiple-Criteria Decision Problems," Operations Research, INFORMS, vol. 34(5), pages 726-731, October.
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    Cited by:

    1. Soleimani-damaneh, Majid & Pourkarimi, Latif & Korhonen, Pekka J. & Wallenius, Jyrki, 2021. "An operational test for the existence of a consistent increasing quasi-concave value function," European Journal of Operational Research, Elsevier, vol. 289(1), pages 232-239.
    2. Selin Özpeynirci & Özgür Özpeynirci & Vincent Mousseau, 2021. "An interactive algorithm for resource allocation with balance concerns," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(4), pages 983-1005, December.

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    More about this item

    Keywords

    Multiple criteria decision making; Discrete; Convex preference cones; Data envelopment analysis; Integer programming;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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