IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v80y2018icp166-174.html
   My bibliography  Save this article

An alternative weight sensitivity analysis for PROMETHEE II rankings

Author

Listed:
  • Doan, N.A.V.
  • De Smet, Y.

Abstract

Most strategic decision problems involve the simultaneous optimization of several conflicting criteria. Among multicriteria decision aid methods, PROMETHEE II has earned some attention during the past decades. This method outputs a complete ranking of a set of alternatives, given some parameters provided by a decision maker, such as the weights of the criteria. In order to assess the stability of the ranking, weight stability intervals (WSI) have been developed. However, this method only focuses on one criterion at a time (changes are assumed to be applied uniformly to the other criteria in order to remain normalized). In this work, we analyze how weight stability intervals can be redefined while allowing any modifications on any criterion weight, by applying inverse optimization based on mixed integer linear programming (MILP). The problem formulation can be stated as follows: what would be the minimum modification on the weights such that a given alternative ai of rank n > 1 becomes first? This methodology has been applied on two case studies, and compared to the WSI. The results show that it is always possible to find narrower intervals while it is never required to modify all the weights simultaneously. Additionally, when using the WSI, only few alternatives can be ranked first. By taking the inverse optimization point of view, all (non-dominated) alternatives can be placed at the first position (at the price of large deviations). It is therefore possible to apply this methodology for a consensus search when different decision makers are involved.

Suggested Citation

  • Doan, N.A.V. & De Smet, Y., 2018. "An alternative weight sensitivity analysis for PROMETHEE II rankings," Omega, Elsevier, vol. 80(C), pages 166-174.
    • Handle: RePEc:eee:jomega:v:80:y:2018:i:c:p:166-174
    DOI: 10.1016/j.omega.2017.08.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048316308921
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2017.08.017?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. Shirland, Larry E. & Jesse, Richard R. & Thompson, Ronald L. & Iacovou, Charalambos L., 2003. "Determining attribute weights using mathematical programming," Omega, Elsevier, vol. 31(6), pages 423-437, December.
    2. Gong, Zaiwu & Xu, Xiaoxia & Zhang, Huanhuan & Aytun Ozturk, U. & Herrera-Viedma, Enrique & Xu, Chao, 2015. "The consensus models with interval preference opinions and their economic interpretation," Omega, Elsevier, vol. 55(C), pages 81-90.
    3. Stefan Eppe & Yves De Smet, 2014. "An adaptive questioning procedure for eliciting PROMETHEE II's weight parameters," International Journal of Multicriteria Decision Making, Inderscience Enterprises Ltd, vol. 4(1), pages 1-30.
    4. Mareschal, Bertrand, 1988. "Weight stability intervals in multicriteria decision aid," European Journal of Operational Research, Elsevier, vol. 33(1), pages 54-64, January.
    5. James S. Dyer, 2016. "Multiattribute Utility Theory (MAUT)," International Series in Operations Research & Management Science, in: Salvatore Greco & Matthias Ehrgott & José Rui Figueira (ed.), Multiple Criteria Decision Analysis, edition 2, chapter 0, pages 285-314, Springer.
    6. Quantin Hayez & Yves De Smet & Jimmy Bonney, 2012. "D-Sight: A New Decision Making Software to Address Multi-Criteria Problems," International Journal of Decision Support System Technology (IJDSST), IGI Global, vol. 4(4), pages 1-23, October.
    7. J. P. Brans & Ph. Vincke, 1985. "Note---A Preference Ranking Organisation Method," Management Science, INFORMS, vol. 31(6), pages 647-656, June.
    8. Ramanathan, Ramakrishnan & Ramanathan, Usha, 2010. "A qualitative perspective to deriving weights from pairwise comparison matrices," Omega, Elsevier, vol. 38(3-4), pages 228-232, June.
    9. Mareschal, Bertrand & Brans, Jean-Pierre, 1988. "Geometrical representations for MCDA," European Journal of Operational Research, Elsevier, vol. 34(1), pages 69-77, February.
    10. Insua, David Rios & French, Simon, 1991. "A framework for sensitivity analysis in discrete multi-objective decision-making," European Journal of Operational Research, Elsevier, vol. 54(2), pages 176-190, September.
    11. Corrente, Salvatore & Figueira, José Rui & Greco, Salvatore, 2014. "The SMAA-PROMETHEE method," European Journal of Operational Research, Elsevier, vol. 239(2), pages 514-522.
    12. Thomas L. Saaty, 2016. "The Analytic Hierarchy and Analytic Network Processes for the Measurement of Intangible Criteria and for Decision-Making," International Series in Operations Research & Management Science, in: Salvatore Greco & Matthias Ehrgott & José Rui Figueira (ed.), Multiple Criteria Decision Analysis, edition 2, chapter 0, pages 363-419, Springer.
    13. Behzadian, Majid & Kazemzadeh, R.B. & Albadvi, A. & Aghdasi, M., 2010. "PROMETHEE: A comprehensive literature review on methodologies and applications," European Journal of Operational Research, Elsevier, vol. 200(1), pages 198-215, January.
    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. Prabha Bhola & Alexandros-Georgios Chronis & Panos Kotsampopoulos & Nikos Hatziargyriou, 2023. "Business Model Selection for Community Energy Storage: A Multi Criteria Decision Making Approach," Energies, MDPI, vol. 16(18), pages 1-30, September.
    2. Marta Bottero & Chiara D’Alpaos & Alessandra Oppio, 2019. "Ranking of Adaptive Reuse Strategies for Abandoned Industrial Heritage in Vulnerable Contexts: A Multiple Criteria Decision Aiding Approach," Sustainability, MDPI, vol. 11(3), pages 1-18, February.
    3. Sebastian Schär & Jutta Geldermann, 2021. "Adopting Multiactor Multicriteria Analysis for the Evaluation of Energy Scenarios," Sustainability, MDPI, vol. 13(5), pages 1-19, March.
    4. Jônatas Augusto Manzolli & André Oliveira & Miguel de Castro Neto, 2021. "Evaluating Walkability through a Multi-Criteria Decision Analysis Approach: A Lisbon Case Study," Sustainability, MDPI, vol. 13(3), pages 1-20, January.
    5. Henry Huang & Yves De Smet & Cathy Macharis & Nguyen Anh Vu Doan, 2020. "Collaborative decision-making in sustainable mobility: identifying possible consensuses in the multi-actor multi-criteria analysis based on inverse mixed-integer linear optimization," ULB Institutional Repository 2013/311571, ULB -- Universite Libre de Bruxelles.

    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. de Almeida Filho, Adiel T. & Clemente, Thárcylla R.N. & Morais, Danielle Costa & de Almeida, Adiel Teixeira, 2018. "Preference modeling experiments with surrogate weighting procedures for the PROMETHEE method," European Journal of Operational Research, Elsevier, vol. 264(2), pages 453-461.
    2. Alessio Ishizaka & Philippe Nemery, 2013. "A Multi-Criteria Group Decision Framework for Partner Grouping When Sharing Facilities," Group Decision and Negotiation, Springer, vol. 22(4), pages 773-799, July.
    3. Tobias Witt & Matthias Klumpp, 2021. "Multi-Period Multi-Criteria Decision Making under Uncertainty: A Renewable Energy Transition Case from Germany," Sustainability, MDPI, vol. 13(11), pages 1-20, June.
    4. Cinelli, Marco & Kadziński, Miłosz & Miebs, Grzegorz & Gonzalez, Michael & Słowiński, Roman, 2022. "Recommending multiple criteria decision analysis methods with a new taxonomy-based decision support system," European Journal of Operational Research, Elsevier, vol. 302(2), pages 633-651.
    5. Behzadian, Majid & Kazemzadeh, R.B. & Albadvi, A. & Aghdasi, M., 2010. "PROMETHEE: A comprehensive literature review on methodologies and applications," European Journal of Operational Research, Elsevier, vol. 200(1), pages 198-215, January.
    6. Arcidiacono, Sally Giuseppe & Corrente, Salvatore & Greco, Salvatore, 2018. "GAIA-SMAA-PROMETHEE for a hierarchy of interacting criteria," European Journal of Operational Research, Elsevier, vol. 270(2), pages 606-624.
    7. Anjali Singh & Anjana Gupta & Aparna Mehra, 2021. "Best criteria selection based PROMETHEE II method," OPSEARCH, Springer;Operational Research Society of India, vol. 58(1), pages 160-180, March.
    8. Majid Behzadian & Seyyed-Mahdi Hosseini-Motlagh & Joshua Ignatius & Mark Goh & Mohammad Mehdi Sepehri, 2013. "PROMETHEE Group Decision Support System and the House of Quality," Group Decision and Negotiation, Springer, vol. 22(2), pages 189-205, March.
    9. Greco, Salvatore & Ishizaka, Alessio & Tasiou, Menelaos & Torrisi, Gianpiero, 2021. "The ordinal input for cardinal output approach of non-compensatory composite indicators: the PROMETHEE scoring method," European Journal of Operational Research, Elsevier, vol. 288(1), pages 225-246.
    10. Chrysovalantis Gaganis & Panagiota Papadimitri & Menelaos Tasiou, 2021. "A multicriteria decision support tool for modelling bank credit ratings," Annals of Operations Research, Springer, vol. 306(1), pages 27-56, November.
    11. Ishizaka, Alessio & Lokman, Banu & Tasiou, Menelaos, 2021. "A Stochastic Multi-criteria divisive hierarchical clustering algorithm," Omega, Elsevier, vol. 103(C).
    12. Corrente, Salvatore & Figueira, José Rui & Greco, Salvatore, 2014. "The SMAA-PROMETHEE method," European Journal of Operational Research, Elsevier, vol. 239(2), pages 514-522.
    13. Podinovski, Vladislav V., 2020. "Maximum likelihood solutions for multicriterial choice problems," European Journal of Operational Research, Elsevier, vol. 286(1), pages 299-308.
    14. Thies, Christian & Kieckhäfer, Karsten & Spengler, Thomas S. & Sodhi, Manbir S., 2019. "Operations research for sustainability assessment of products: A review," European Journal of Operational Research, Elsevier, vol. 274(1), pages 1-21.
    15. Wulf, David & Bertsch, Valentin, 2016. "A natural language generation approach to support understanding and traceability of multi-dimensional preferential sensitivity analysis in multi-criteria decision making," MPRA Paper 75025, University Library of Munich, Germany.
    16. G Özerol & E Karasakal, 2008. "Interactive outranking approaches for multicriteria decision-making problems with imprecise information," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(9), pages 1253-1268, September.
    17. Calders, Toon & Van Assche, Dimitri, 2018. "PROMETHEE is not quadratic: An O(qnlog(n)) algorithm," Omega, Elsevier, vol. 76(C), pages 63-69.
    18. Arcidiacono, Sally Giuseppe & Corrente, Salvatore & Greco, Salvatore, 2021. "Robust stochastic sorting with interacting criteria hierarchically structured," European Journal of Operational Research, Elsevier, vol. 292(2), pages 735-754.
    19. Khalid Aljohani & Russell G. Thompson, 2018. "A Stakeholder-Based Evaluation of the Most Suitable and Sustainable Delivery Fleet for Freight Consolidation Policies in the Inner-City Area," Sustainability, MDPI, vol. 11(1), pages 1-27, December.
    20. Silvia Angilella & Maria Rosaria Pappalardo, 2022. "Performance assessment of energy companies employing Hierarchy Stochastic Multi-Attribute Acceptability Analysis," Operational Research, Springer, vol. 22(1), pages 299-370, March.

    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:jomega:v:80:y:2018:i:c:p:166-174. 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/wps/find/journaldescription.cws_home/375/description#description .

    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.