IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v212y2011i3p535-551.html
   My bibliography  Save this article

Generalized equitable preference in multiobjective programming

Author

Listed:
  • Mut, Murat
  • Wiecek, Margaret M.

Abstract

The concept of equitability in multiobjective programming is generalized within a framework of convex cones. Two models are presented. First, more general polyhedral cones are assumed to determine the equitable preference. Second, the Pareto cone appearing in the monotonicity axiom of equitability is replaced with a permutation-invariant polyhedral cone. The conditions under which the new models are related and satisfy original and modified axioms of the equitable preference are developed. Relationships between generalized equitability and relative importance of criteria and stochastic dominance are revealed.

Suggested Citation

  • Mut, Murat & Wiecek, Margaret M., 2011. "Generalized equitable preference in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 212(3), pages 535-551, August.
    • Handle: RePEc:eee:ejores:v:212:y:2011:i:3:p:535-551
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(11)00136-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Patrice Perny & Olivier Spanjaard & Louis-Xavier Storme, 2006. "A decision-theoretic approach to robust optimization in multivalued graphs," Annals of Operations Research, Springer, vol. 147(1), pages 317-341, October.
    2. Włodzimierz Ogryczak, 2000. "Multiple criteria linear programming model for portfolio selection," Annals of Operations Research, Springer, vol. 97(1), pages 143-162, December.
    3. Kostreva, Michael M. & Ogryczak, Wlodzimierz & Wierzbicki, Adam, 2004. "Equitable aggregations and multiple criteria analysis," European Journal of Operational Research, Elsevier, vol. 158(2), pages 362-377, October.
    4. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
    5. Ogryczak, Wlodzimierz & Wierzbicki, Adam & Milewski, Marcin, 2008. "A multi-criteria approach to fair and efficient bandwidth allocation," Omega, Elsevier, vol. 36(3), pages 451-463, June.
    6. Ogryczak, Wlodzimierz & Sliwinski, Tomasz, 2003. "On solving linear programs with the ordered weighted averaging objective," European Journal of Operational Research, Elsevier, vol. 148(1), pages 80-91, July.
    7. Marmol, Amparo M. & Puerto, Justo & Fernandez, Francisco R., 2002. "Sequential incorporation of imprecise information in multiple criteria decision processes," European Journal of Operational Research, Elsevier, vol. 137(1), pages 123-133, February.
    8. Ogryczak, Wlodzimierz, 2000. "Inequality measures and equitable approaches to location problems," European Journal of Operational Research, Elsevier, vol. 122(2), pages 374-391, April.
    9. Włodzimierz Ogryczak & Mariusz Zawadzki, 2002. "Conditional Median: A Parametric Solution Concept for Location Problems," Annals of Operations Research, Springer, vol. 110(1), pages 167-181, February.
    10. Hunt, Brian J. & Wiecek, Margaret M. & Hughes, Colleen S., 2010. "Relative importance of criteria in multiobjective programming: A cone-based approach," European Journal of Operational Research, Elsevier, vol. 207(2), pages 936-945, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
    2. Argyris, Nikolaos & Karsu, Özlem & Yavuz, Mirel, 2022. "Fair resource allocation: Using welfare-based dominance constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 560-578.
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
    3. Kaynar, Nur & Karsu, Özlem, 2018. "Equitable decision making approaches over allocations of multiple benefits to multiple entities," Omega, Elsevier, vol. 81(C), pages 85-98.
    4. Bashir Bashir & Özlem Karsu, 2022. "Solution approaches for equitable multiobjective integer programming problems," Annals of Operations Research, Springer, vol. 311(2), pages 967-995, April.
    5. Argyris, Nikolaos & Karsu, Özlem & Yavuz, Mirel, 2022. "Fair resource allocation: Using welfare-based dominance constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 560-578.
    6. Virginie Gabrel & Cécile Murat & Aurélie Thiele, 2018. "Portfolio optimization with pw-robustness," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(3), pages 267-290, September.
    7. Chassein, André & Goerigk, Marc & Kasperski, Adam & Zieliński, Paweł, 2020. "Approximating combinatorial optimization problems with the ordered weighted averaging criterion," European Journal of Operational Research, Elsevier, vol. 286(3), pages 828-838.
    8. Włodzimierz Ogryczak, 2009. "Inequality measures and equitable locations," Annals of Operations Research, Springer, vol. 167(1), pages 61-86, March.
    9. Kostreva, Michael M. & Ogryczak, Wlodzimierz & Wierzbicki, Adam, 2004. "Equitable aggregations and multiple criteria analysis," European Journal of Operational Research, Elsevier, vol. 158(2), pages 362-377, October.
    10. Klamroth, Kathrin & Köbis, Elisabeth & Schöbel, Anita & Tammer, Christiane, 2017. "A unified approach to uncertain optimization," European Journal of Operational Research, Elsevier, vol. 260(2), pages 403-420.
    11. Medernach, Emmanuel & Sanlaville, Eric, 2012. "Fair resource allocation for different scenarios of demands," European Journal of Operational Research, Elsevier, vol. 218(2), pages 339-350.
    12. Rafael Rodríguez & Mariano Luque & Mercedes González, 2011. "Portfolio selection in the Spanish stock market by interactive multiobjective programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 213-231, July.
    13. Kasin Ransikarbum & Scott J. Mason, 2016. "Multiple-objective analysis of integrated relief supply and network restoration in humanitarian logistics operations," International Journal of Production Research, Taylor & Francis Journals, vol. 54(1), pages 49-68, January.
    14. Violet Xinying Chen & J. N. Hooker, 2023. "A guide to formulating fairness in an optimization model," Annals of Operations Research, Springer, vol. 326(1), pages 581-619, July.
    15. Galand, Lucie & Perny, Patrice & Spanjaard, Olivier, 2010. "Choquet-based optimisation in multiobjective shortest path and spanning tree problems," European Journal of Operational Research, Elsevier, vol. 204(2), pages 303-315, July.
    16. Bouyssou, Denis & Marchant, Thierry, 2014. "An axiomatic approach to bibliometric rankings and indices," Journal of Informetrics, Elsevier, vol. 8(3), pages 449-477.
    17. Jesús Sánchez-Oro & Ana D. López-Sánchez & Anna Martínez-Gavara & Alfredo G. Hernández-Díaz & Abraham Duarte, 2021. "A Hybrid Strategic Oscillation with Path Relinking Algorithm for the Multiobjective k -Balanced Center Location Problem," Mathematics, MDPI, vol. 9(8), pages 1-21, April.
    18. Mansini, Renata & Ogryczak, Wlodzimierz & Speranza, M. Grazia, 2014. "Twenty years of linear programming based portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 518-535.
    19. Li, Linda & Firouz, Mohammad & Ahmed, Abdulaziz & Delen, Dursun, 2023. "On the Egalitarian–Utilitarian spectrum in stochastic capacitated resource allocation problems," International Journal of Production Economics, Elsevier, vol. 262(C).
    20. Dugardin, Frédéric & Yalaoui, Farouk & Amodeo, Lionel, 2010. "New multi-objective method to solve reentrant hybrid flow shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 203(1), pages 22-31, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:212:y:2011:i:3:p:535-551. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.