IDEAS home Printed from https://ideas.repec.org/a/spr/cejnor/v29y2021i3d10.1007_s10100-020-00718-1.html
   My bibliography  Save this article

Which efficient solution in multi objective programming problem should be taken?

Author

Listed:
  • Josip Matejaš

    (Faculty of Economics and Business Zagreb)

  • Tunjo Perić

    (Faculty of Economics and Business Zagreb)

  • Danijel Mlinarić

    (Faculty of Economics and Business Zagreb)

Abstract

In practical problems, which can be stated in the form of multi objective programming problem, we have usually a large set of efficient solutions. So, which solution from this set should be taken, appears as a natural question here. In the paper we propose some sustainable principles and simple numerical method for such choice. The method respects aspirations and priorities of decision makers and enables iterations for possible improvement of the solution. In this way decision makers can clearly understand why a particular solution is obtained and when and how it can be improved. The features of the method are explained by a practical example. An applications to bilevel programming problems are also presented, where the both side mapping, between the set of efficient solutions and the set of all possible priorities, is shown. It is illustrated in detail through several linear and nonlinear examples.

Suggested Citation

  • Josip Matejaš & Tunjo Perić & Danijel Mlinarić, 2021. "Which efficient solution in multi objective programming problem should be taken?," 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. 29(3), pages 967-987, September.
    • Handle: RePEc:spr:cejnor:v:29:y:2021:i:3:d:10.1007_s10100-020-00718-1
    DOI: 10.1007/s10100-020-00718-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10100-020-00718-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10100-020-00718-1?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
    ---><---

    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. Mishra, Savita, 2007. "Weighting method for bi-level linear fractional programming problems," European Journal of Operational Research, Elsevier, vol. 183(1), pages 296-302, November.
    2. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, September.
    3. Tunjo Perić & Zoran Babić & Josip Matejaš, 2018. "Comparative analysis of application efficiency of two iterative multi objective linear programming methods (MP method and STEM 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. 26(3), pages 565-583, September.
    4. Peter C. Fishburn, 1974. "Exceptional Paper--Lexicographic Orders, Utilities and Decision Rules: A Survey," Management Science, INFORMS, vol. 20(11), pages 1442-1471, July.
    5. Pramanik, Surapati & Roy, Tapan Kumar, 2007. "Fuzzy goal programming approach to multilevel programming problems," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1151-1166, January.
    6. Ernestas Filatovas & Algirdas Lančinskas & Olga Kurasova & Julius Žilinskas, 2017. "A preference-based multi-objective evolutionary algorithm R-NSGA-II with stochastic local search," 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. 25(4), pages 859-878, 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. Andrej Kastrin & Janez Povh & Lidija Zadnik Stirn & Janez Žerovnik, 2021. "Methodologies and applications for resilient global development from the aspect of SDI-SOR special issues of CJOR," 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. 29(3), pages 773-790, September.

    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. Angilella, Silvia & Giarlotta, Alfio, 2009. "Implementations of PACMAN," European Journal of Operational Research, Elsevier, vol. 194(2), pages 474-495, April.
    2. Tunjo Perić & Zoran Babić & Josip Matejaš, 2018. "Comparative analysis of application efficiency of two iterative multi objective linear programming methods (MP method and STEM 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. 26(3), pages 565-583, September.
    3. Tunjo Perić & Josip Matejaš & Zoran Babić, 2023. "Advantages, sensitivity and application efficiency of the new iterative method to solve multi-objective linear fractional programming problem," 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 751-767, September.
    4. Corrente, Salvatore & Figueira, José Rui & Greco, Salvatore, 2014. "The SMAA-PROMETHEE method," European Journal of Operational Research, Elsevier, vol. 239(2), pages 514-522.
    5. Comino, E. & Ferretti, V., 2016. "Indicators-based spatial SWOT analysis: supporting the strategic planning and management of complex territorial systems," LSE Research Online Documents on Economics 64142, London School of Economics and Political Science, LSE Library.
    6. Kaveh Madani & Laura Read & Laleh Shalikarian, 2014. "Voting Under Uncertainty: A Stochastic Framework for Analyzing Group Decision Making Problems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(7), pages 1839-1856, May.
    7. Kadziński, MiŁosz & Greco, Salvatore & SŁowiński, Roman, 2012. "Extreme ranking analysis in robust ordinal regression," Omega, Elsevier, vol. 40(4), pages 488-501.
    8. Petri, Henrik & Voorneveld, Mark, 2016. "Characterizing lexicographic preferences," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 54-61.
    9. Haurant, P. & Oberti, P. & Muselli, M., 2011. "Multicriteria selection aiding related to photovoltaic plants on farming fields on Corsica island: A real case study using the ELECTRE outranking framework," Energy Policy, Elsevier, vol. 39(2), pages 676-688, February.
    10. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, II: More than two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 246-276, April.
    11. Juan Candeal, 2013. "Invariance axioms for preferences: applications to social choice theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 453-471, September.
    12. Juliana Martins Ruzante & Valerie J. Davidson & Julie Caswell & Aamir Fazil & John A. L. Cranfield & Spencer J. Henson & Sven M. Anders & Claudia Schmidt & Jeffrey M. Farber, 2010. "A Multifactorial Risk Prioritization Framework for Foodborne Pathogens," Risk Analysis, John Wiley & Sons, vol. 30(5), pages 724-742, May.
    13. Morgenroth, Edgar & FitzGerald, John & FitzGerald, John, 2006. "Summary and Conclusions," Book Chapters, in: Morgenroth, Edgar (ed.),Ex-Ante Evaluation of the Investment Priorities for the National Development Plan 2007-2013, chapter 24, pages 317-333, Economic and Social Research Institute (ESRI).
      • Baker, Terence J. & FitzGerald, John & Honohan, Patrick & FitzGerald, John & Honohan, Patrick, 1996. "Summary and Conclusions," Book Chapters, in: Baker, Terence J. (ed.),Economic Implications for Ireland of EMU, chapter 12, pages 339-352, Economic and Social Research Institute (ESRI).
    14. Fernandez, Eduardo & Navarro, Jorge & Bernal, Sergio, 2010. "Handling multicriteria preferences in cluster analysis," European Journal of Operational Research, Elsevier, vol. 202(3), pages 819-827, May.
    15. Pawel Lezanski & Maria Pilacinska, 2018. "The dominance-based rough set approach to cylindrical plunge grinding process diagnosis," Journal of Intelligent Manufacturing, Springer, vol. 29(5), pages 989-1004, June.
    16. repec:cup:judgdm:v:8:y:2013:i:5:p:552-560 is not listed on IDEAS
    17. García Cáceres, Rafael Guillermo & Aráoz Durand, Julián Arturo & Gómez, Fernando Palacios, 2009. "Integral analysis method - IAM," European Journal of Operational Research, Elsevier, vol. 192(3), pages 891-903, February.
    18. 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.
    19. Mahmoud A. Abo-Sinna & Ibrahim A. Baky, 2010. "Fuzzy Goal Programming Procedure to Bilevel Multiobjective Linear Fractional Programming Problems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2010, pages 1-15, March.
    20. Sward, Jeffrey A. & Nilson, Roberta S. & Katkar, Venktesh V. & Stedman, Richard C. & Kay, David L. & Ifft, Jennifer E. & Zhang, K. Max, 2021. "Integrating social considerations in multicriteria decision analysis for utility-scale solar photovoltaic siting," Applied Energy, Elsevier, vol. 288(C).
    21. Amir Noori & Hossein Bonakdari & Khosro Morovati & Bahram Gharabaghi, 2018. "The optimal dam site selection using a group decision-making method through fuzzy TOPSIS model," Environment Systems and Decisions, Springer, vol. 38(4), pages 471-488, December.

    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:spr:cejnor:v:29:y:2021:i:3:d:10.1007_s10100-020-00718-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.