IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v311y2022i2d10.1007_s10479-020-03911-2.html
   My bibliography  Save this article

Multiobjective dynamic programming in bipolar multistage method

Author

Listed:
  • Tadeusz Trzaskalik

    (University of Economics)

Abstract

The multicriteria Bipolar method can be extended and used to control multicriteria, multistage decision processes. In this extension, at each stage of the given multistage process two sets of reference points are determined, constituting a reference system for the evaluation of stage alternatives. Multistage alternatives, which are compositions of stage alternatives, are assigned to one of six predefined hierarchical classes and then ranked. The aim of this paper is to show the possibility of finding the best multistage alternative, using Bellman’s optimality principle and optimality equations. Of particular importance is a theorem on the non-dominance of the best multistage alternative, proven here. The methodology proposed allows to avoid reviewing each multistage alternative, which is important in large-size problems. The method is illustrated by a numerical example and a brief description of the sustainable regional development problem. The problem can be solved by means of the proposed procedure.

Suggested Citation

  • Tadeusz Trzaskalik, 2022. "Multiobjective dynamic programming in bipolar multistage method," Annals of Operations Research, Springer, vol. 311(2), pages 1259-1279, April.
    • Handle: RePEc:spr:annopr:v:311:y:2022:i:2:d:10.1007_s10479-020-03911-2
    DOI: 10.1007/s10479-020-03911-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-020-03911-2
    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/s10479-020-03911-2?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. Diakoulaki, D. & Koumoutsos, N., 1991. "Cardinal ranking of alternative actions: extension of the method," European Journal of Operational Research, Elsevier, vol. 53(3), pages 337-347, August.
    2. C. West Churchman & Russell L. Ackoff, 1954. "An Approximate Measure of Value," Operations Research, INFORMS, vol. 2(2), pages 172-187, May.
    3. Wojtek Michalowski & Tomek Szapiro, 1992. "A Bi-Reference Procedure for Interactive Multiple Criteria Programming," Operations Research, INFORMS, vol. 40(2), pages 247-258, April.
    4. 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.
    5. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    6. Larichev, Oleg I., 2001. "Ranking multicriteria alternatives: The method ZAPROS III," European Journal of Operational Research, Elsevier, vol. 131(3), pages 550-558, June.
    7. Larichev, O. I. & Moshkovich, H. M., 1995. "ZAPROS-LM -- A method and system for ordering multiattribute alternatives," European Journal of Operational Research, Elsevier, vol. 82(3), pages 503-521, May.
    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. 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.

    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. 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.
    2. Dorota Górecka & Ewa Roszkowska & Tomasz Wachowicz, 2016. "The MARS Approach in the Verbal and Holistic Evaluation of the Negotiation Template," Group Decision and Negotiation, Springer, vol. 25(6), pages 1097-1136, November.
    3. Dorota Górecka, 2012. "Applying Multi-Criteria Decision Aiding techniques in the process of project management within the wedding planning business," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 22(4), pages 41-67.
    4. P P Sutton & R H Green, 2007. "Choice is a value statement. On inferring optimal multiple attribute portfolios from non-optimal nominations," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(11), pages 1526-1533, November.
    5. 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.
    6. Wu-E Yang & Chao-Qun Ma & Zhi-Qiu Han & Wen-Jun Chen, 2016. "Checking and adjusting order-consistency of linguistic pairwise comparison matrices for getting transitive preference relations," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(3), pages 769-787, July.
    7. Thomas L. Saaty & Daji Ergu, 2015. "When is a Decision-Making Method Trustworthy? Criteria for Evaluating Multi-Criteria Decision-Making Methods," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 1171-1187, November.
    8. Ewa Roszkowska, 2020. "The extention rank ordering criteria weighting methods in fuzzy enviroment," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 30(2), pages 91-114.
    9. Agata Sielska, 2020. "Stability of hospital rankings," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 30(4), pages 95-112.
    10. Eun-Sung Chung & Kil Lee, 2009. "Identification of Spatial Ranking of Hydrological Vulnerability Using Multi-Criteria Decision Making Techniques: Case Study of Korea," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(12), pages 2395-2416, September.
    11. Nejc Trdin & Marko Bohanec, 2018. "Extending the multi-criteria decision making method DEX with numeric attributes, value distributions and relational models," 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(1), pages 1-41, March.
    12. Guitouni, Adel & Martel, Jean-Marc, 1998. "Tentative guidelines to help choosing an appropriate MCDA method," European Journal of Operational Research, Elsevier, vol. 109(2), pages 501-521, September.
    13. Banai, Reza, 2010. "Evaluation of land use-transportation systems with the Analytic Network Process," The Journal of Transport and Land Use, Center for Transportation Studies, University of Minnesota, vol. 3(1), pages 85-112.
    14. Fatih Yiğit & Şakir Esnaf, 2021. "A new Fuzzy C-Means and AHP-based three-phased approach for multiple criteria ABC inventory classification," Journal of Intelligent Manufacturing, Springer, vol. 32(6), pages 1517-1528, August.
    15. Rachele Corticelli & Margherita Pazzini & Cecilia Mazzoli & Claudio Lantieri & Annarita Ferrante & Valeria Vignali, 2022. "Urban Regeneration and Soft Mobility: The Case Study of the Rimini Canal Port in Italy," Sustainability, MDPI, vol. 14(21), pages 1-27, November.
    16. Lin, Sheng-Hau & Zhao, Xiaofeng & Wu, Jiuxing & Liang, Fachao & Li, Jia-Hsuan & Lai, Ren-Ji & Hsieh, Jing-Chzi & Tzeng, Gwo-Hshiung, 2021. "An evaluation framework for developing green infrastructure by using a new hybrid multiple attribute decision-making model for promoting environmental sustainability," Socio-Economic Planning Sciences, Elsevier, vol. 75(C).
    17. Pishchulov, Grigory & Trautrims, Alexander & Chesney, Thomas & Gold, Stefan & Schwab, Leila, 2019. "The Voting Analytic Hierarchy Process revisited: A revised method with application to sustainable supplier selection," International Journal of Production Economics, Elsevier, vol. 211(C), pages 166-179.
    18. Seung-Jin Han & Won-Jae Lee & So-Hee Kim & Sang-Hoon Yoon & Hyunwoong Pyun, 2022. "Assessing Expected Long-term Benefits for the Olympic Games: Delphi-AHP Approach from Korean Olympic Experts," SAGE Open, , vol. 12(4), pages 21582440221, December.
    19. Denys Yemshanov & Frank H. Koch & Yakov Ben‐Haim & Marla Downing & Frank Sapio & Marty Siltanen, 2013. "A New Multicriteria Risk Mapping Approach Based on a Multiattribute Frontier Concept," Risk Analysis, John Wiley & Sons, vol. 33(9), pages 1694-1709, September.
    20. 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.

    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:annopr:v:311:y:2022:i:2:d:10.1007_s10479-020-03911-2. 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.