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A Concentration Ratio for Nonlinear Best Worst Method

Author

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  • Jafar Rezaei

    (Faculty of Technology, Policy and Management, Delft University of Technology, 2628 BX Delft, the Netherlands)

Abstract

Best Worst Method (BWM) is a multi-criteria decision-making method that is based on a structured pairwise comparison system. It uses two pairwise comparison vectors (best-to-others and others-to-worst) as input for an optimization model to get the optimal weights of the criteria (or alternatives). The original BWM involves a nonlinear model that sometimes results in multiple optimal weights meaning that the weight of each criterion is presented as an interval. The aim of this paper is to introduce a ratio, called concentration ratio, to check the concentration of the optimal intervals obtained from the nonlinear BWM. The relationship between the concentration ratio and the consistency ratio is investigated and it is found that the concentration ratio along with the consistency ratio of the model provides enhanced insights into the reliability and flexibility of the results of BWM.

Suggested Citation

  • Jafar Rezaei, 2020. "A Concentration Ratio for Nonlinear Best Worst Method," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 891-907, May.
    • Handle: RePEc:wsi:ijitdm:v:19:y:2020:i:03:n:s0219622020500170
    DOI: 10.1142/S0219622020500170
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    Cited by:

    1. Li, Qinglin & Rezaei, Jafar & Tavasszy, Lori & Wiegmans, Bart & Guo, Jingwei & Tang, Yinying & Peng, Qiyuan, 2020. "Customers’ preferences for freight service attributes of China Railway Express," Transportation Research Part A: Policy and Practice, Elsevier, vol. 142(C), pages 225-236.
    2. Wu, Qun & Liu, Xinwang & Zhou, Ligang & Qin, Jindong & Rezaei, Jafar, 2024. "An analytical framework for the best–worst method," Omega, Elsevier, vol. 123(C).
    3. Murad, C.A. & Bellinello, M.M. & Silva, A.J. & Netto, A. Caminada & de Souza, G.F.M. & Nabeta, S.I., 2022. "A novel methodology employed for ranking and consolidating performance indicators in holding companies with multiple power plants based on multi-criteria decision-making method," Operations Research Perspectives, Elsevier, vol. 9(C).
    4. Tseng, Ming-Lang & Bui, Tat-Dat & Lim, Ming K. & Fujii, Minoru & Mishra, Umakanta, 2022. "Assessing data-driven sustainable supply chain management indicators for the textile industry under industrial disruption and ambidexterity," International Journal of Production Economics, Elsevier, vol. 245(C).
    5. Shashank Bansal & Mohul Mukhopadhyay & Shipra Maurya, 2023. "Strategic drivers for sustainable implementation of carbon trading in India," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 25(5), pages 4411-4435, May.
    6. Siamak Kheybari & Mohammad Reza Mehrpour & Paul Bauer & Alessio Ishizaka, 2024. "How Can Risk-Averse and Risk-Taking Approaches be Considered in a Group Multi-Criteria Decision-Making Problem?," Group Decision and Negotiation, Springer, vol. 33(4), pages 883-909, August.
    7. Alireza Parsa Rad & Mohammad Khalilzadeh & Sayyid Ali Banihashemi & Darko Božanić & Aleksandar Milić & Goran Ćirović, 2024. "Supplier Selection in Downstream Oil and Gas and Petrochemicals with the Fuzzy BWM and Gray COCOSO Methods Considering Sustainability Criteria and Uncertainty Conditions," Sustainability, MDPI, vol. 16(2), pages 1-18, January.
    8. Md. Abdul Moktadir & Anil Kumar & Syed Mithun Ali & Sanjoy Kumar Paul & Razia Sultana & Jafar Rezaei, 2020. "Critical success factors for a circular economy: Implications for business strategy and the environment," Business Strategy and the Environment, Wiley Blackwell, vol. 29(8), pages 3611-3635, December.
    9. Kheybari, Siamak & Javdanmehr, Mahsa & Rezaie, Fariba Mahdi & Rezaei, Jafar, 2021. "Corn cultivation location selection for bioethanol production: An application of BWM and extended PROMETHEE II," Energy, Elsevier, vol. 228(C).
    10. Silke van der Burg & Maarten F. M. Jurg & Flore M. Tadema & Linda M. Kamp & Geerten van de Kaa, 2022. "Dominant Designs for Wings of Airborne Wind Energy Systems," Energies, MDPI, vol. 15(19), pages 1-11, October.
    11. Sisto, Roberta & Fernández-Portillo, Luis A. & Yazdani, Morteza & Estepa-Mohedano, Lorenzo & Torkayesh, Ali Ebadi, 2022. "Strategic planning of rural areas: Integrating participatory backcasting and multiple criteria decision analysis tools," Socio-Economic Planning Sciences, Elsevier, vol. 82(PA).
    12. Shashank Bansal & Satya Prakash Mani & Himanshu Gupta & Shipra Maurya, 2023. "Sustainable development of the green bond markets in India: Challenges and strategies," Sustainable Development, John Wiley & Sons, Ltd., vol. 31(1), pages 237-252, February.
    13. Tushar, Saifur Rahman & Alam, Md. Fahim Bin & Bari, A.B.M. Mainul & Karmaker, Chitra Lekha, 2023. "Assessing the challenges to medical waste management during the COVID-19 pandemic: Implications for the environmental sustainability in the emerging economies," Socio-Economic Planning Sciences, Elsevier, vol. 87(PA).
    14. Mir Seyed Mohammad Mohsen Emamat & Caroline Maria de Miranda Mota & Mohammad Reza Mehregan & Mohammad Reza Sadeghi Moghadam & Philippe Nemery, 2022. "Using ELECTRE-TRI and FlowSort methods in a stock portfolio selection context," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-35, December.
    15. Vieira, Fabiana C. & Ferreira, Fernando A.F. & Govindan, Kannan & Ferreira, Neuza C.M.Q.F. & Banaitis, Audrius, 2022. "Measuring urban digitalization using cognitive mapping and the best worst method (BWM)," Technology in Society, Elsevier, vol. 71(C).
    16. Karmaker, Chitra Lekha & Bari, A.B.M. Mainul & Anam, Md. Zahidul & Ahmed, Tazim & Ali, Syed Mithun & de Jesus Pacheco, Diego Augusto & Moktadir, Md. Abdul, 2023. "Industry 5.0 challenges for post-pandemic supply chain sustainability in an emerging economy," International Journal of Production Economics, Elsevier, vol. 258(C).
    17. Driss El Kadiri Boutchich, 2024. "Tourism performance evaluation and analysis from composite index and slack based method," OPSEARCH, Springer;Operational Research Society of India, vol. 61(2), pages 501-523, June.
    18. Fahim, Patrick B.M. & Rezaei, Jafar & Montreuil, Benoit & Tavasszy, Lorant, 2022. "Port performance evaluation and selection in the Physical Internet," Transport Policy, Elsevier, vol. 124(C), pages 83-94.
    19. Alessio Ishizaka & Sharfuddin Ahmed Khan & Siamak Kheybari & Syed Imran Zaman, 2023. "Supplier selection in closed loop pharma supply chain: a novel BWM–GAIA framework," Annals of Operations Research, Springer, vol. 324(1), pages 13-36, May.

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