IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v40y1992i2p247-258.html
   My bibliography  Save this article

A Bi-Reference Procedure for Interactive Multiple Criteria Programming

Author

Listed:
  • Wojtek Michalowski

    (Carleton University, Ottawa, Ontario, Canada)

  • Tomek Szapiro

    (Central School of Planning and Statistics, Warsaw, Poland)

Abstract

The paper presents an interactive procedure to search the set of nondominated outcomes of a multiple criteria linear programming problem. The procedure requires the decision maker to specify the worst outcome. Then, the ideal outcome is identified, and the improvement direction from the worst to ideal outcomes is constructed. A trial solution is found by moving from a current solution along the improvement direction, while maximizing the step size. For a trial solution, the decision maker is requested to partition the set of objective functions into three categories: those to be improved, those which may remain unchanged, those which may be relaxed. Based on this partition, the procedure displaces the worst and ideal outcomes, calculates the new improvement direction, and the entire process is repeated. The method terminates when two successive trial solutions are reasonably similar.

Suggested Citation

  • Wojtek Michalowski & Tomek Szapiro, 1992. "A Bi-Reference Procedure for Interactive Multiple Criteria Programming," Operations Research, INFORMS, vol. 40(2), pages 247-258, April.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:2:p:247-258
    DOI: 10.1287/opre.40.2.247
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.40.2.247
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.40.2.247?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

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


    Cited by:

    1. Kaliszewski, Ignacy & Michalowski, Wojtek, 1999. "Searching for psychologically stable solutions of multiple criteria decision problems," European Journal of Operational Research, Elsevier, vol. 118(3), pages 549-562, November.
    2. Nowak, Maciej, 2007. "Aspiration level approach in stochastic MCDM problems," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1626-1640, March.
    3. Tadeusz Trzaskalik, 2023. "Vectors of indicators and pointer function in the Multistage Bipolar Method," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(3), pages 791-816, September.
    4. Tomasz Szapiro & Przemysław Szufel, 2014. "Simulated Negotiation Outcomes Through Recommendation Crowding," Group Decision and Negotiation, Springer, vol. 23(3), pages 443-461, May.
    5. Tadeusz Trzaskalik, 2022. "Multiobjective dynamic programming in bipolar multistage method," Annals of Operations Research, Springer, vol. 311(2), pages 1259-1279, April.
    6. Sun, Minghe, 2005. "Some issues in measuring and reporting solution quality of interactive multiple objective programming procedures," European Journal of Operational Research, Elsevier, vol. 162(2), pages 468-483, April.
    7. Buchanan, John & Gardiner, Lorraine, 2003. "A comparison of two reference point methods in multiple objective mathematical programming," European Journal of Operational Research, Elsevier, vol. 149(1), pages 17-34, August.
    8. Piotr Wojewnik & Tomasz Szapiro, 2010. "Bireference Procedure fBIP for Interactive Multicriteria Optimization with Fuzzy Coefficients," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 2(3), pages 169-193, June.
    9. Tadeusz Trzaskalik & Sebastian Sitarz & Cezary Dominiak, 2019. "Bipolar method and its modifications," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(3), pages 625-651, September.
    10. Roszkowska, Ewa & Wachowicz, Tomasz, 2015. "Application of fuzzy TOPSIS to scoring the negotiation offers in ill-structured negotiation problems," European Journal of Operational Research, Elsevier, vol. 242(3), pages 920-932.
    11. Aksoy, Yasemin & Butler, Timothy W. & Minor, Elliott D., 1996. "Comparative studies in interactive multiple objective mathematical programming," European Journal of Operational Research, Elsevier, vol. 89(2), pages 408-422, March.
    12. I. Kaliszewski & W. Michalowski, 1998. "Establishing Regret Attitude of a Decision Maker within the MCDM Modeling Framework," Working Papers ir98070, International Institute for Applied Systems Analysis.
    13. Koronakos, Gregory & Sotiros, Dimitris & Despotis, Dimitris K. & Kritikos, Manolis N., 2022. "Fair efficiency decomposition in network DEA: A compromise programming approach," Socio-Economic Planning Sciences, Elsevier, vol. 79(C).
    14. P. Korhonen, 1998. "Multiple Objective Programming Support," Working Papers ir98010, International Institute for Applied Systems Analysis.
    15. Kaliszewski, Ignacy, 2004. "Out of the mist--towards decision-maker-friendly multiple criteria decision making support," European Journal of Operational Research, Elsevier, vol. 158(2), pages 293-307, October.

    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:inm:oropre:v:40:y:1992:i:2:p:247-258. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.