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Modeling the minimum cost consensus problem in an asymmetric costs context

Author

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  • Cheng, Dong
  • Zhou, Zhili
  • Cheng, Faxin
  • Zhou, Yanfang
  • Xie, Yujing

Abstract

The unit costs of up- and down-adjustments are not equal in some real-life minimum cost consensus (MCC) problems, such as when each individual has two different cost coefficients that depend on the adjustment direction of his/her opinion. To solve these problems, the MCC model with directional constraints (MCCM-DC) is constructed on the basis of goal programming theory and the rectilinear distance function. To analyse the impact of individuals’ limited compromises and tolerance behaviors on the consensus modeling, we further develop the ε-MCCM-DC and the threshold-based (TB)-MCCM-DC. Then, the relationships and transformation conditions of these models are investigated. Furthermore, the validity of the proposed models is demonstrated by the case of trans-boundary pollution control negotiations in China’s Taihu Lake Basin. The analysis results show the following: First, the consensus opinion obtained from MCCM-DC is more inclined to the lower cost direction, and its total consensus costs will no longer ascend after reaching a critical point with the increase of unit adjustment costs. Second, the optimal solution of MCCM-DC is the lower bound of ε-MCCM-DC and the upper bound of TB-MCCM-DC. Compared with consensus models without directional constraints, the proposed models can obtain a better consensus opinion at lower costs due to the flexibility in adjusting individual opinions and can also characterize the MCC problems in a more realistic way.

Suggested Citation

  • Cheng, Dong & Zhou, Zhili & Cheng, Faxin & Zhou, Yanfang & Xie, Yujing, 2018. "Modeling the minimum cost consensus problem in an asymmetric costs context," European Journal of Operational Research, Elsevier, vol. 270(3), pages 1122-1137.
    • Handle: RePEc:eee:ejores:v:270:y:2018:i:3:p:1122-1137
    DOI: 10.1016/j.ejor.2018.04.041
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    Cited by:

    1. Zhang, Bowen & Dong, Yucheng & Zhang, Hengjie & Pedrycz, Witold, 2020. "Consensus mechanism with maximum-return modifications and minimum-cost feedback: A perspective of game theory," European Journal of Operational Research, Elsevier, vol. 287(2), pages 546-559.
    2. Tang, Ming & Liao, Huchang, 2024. "Group efficiency and individual fairness tradeoff in making wise decisions," Omega, Elsevier, vol. 124(C).
    3. Tang, Ming & Liao, Huchang, 2021. "From conventional group decision making to large-scale group decision making: What are the challenges and how to meet them in big data era? A state-of-the-art survey," Omega, Elsevier, vol. 100(C).
    4. Ying Ji & Huanhuan Li & Huijie Zhang, 2022. "Risk-Averse Two-Stage Stochastic Minimum Cost Consensus Models with Asymmetric Adjustment Cost," Group Decision and Negotiation, Springer, vol. 31(2), pages 261-291, April.
    5. Tang, Ming & Liao, Huchang & Xu, Jiuping & Streimikiene, Dalia & Zheng, Xiaosong, 2020. "Adaptive consensus reaching process with hybrid strategies for large-scale group decision making," European Journal of Operational Research, Elsevier, vol. 282(3), pages 957-971.
    6. Cheng, Dong & Yuan, Yuxiang & Wu, Yong & Hao, Tiantian & Cheng, Faxin, 2022. "Maximum satisfaction consensus with budget constraints considering individual tolerance and compromise limit behaviors," European Journal of Operational Research, Elsevier, vol. 297(1), pages 221-238.
    7. Shaojian Qu & Yefan Han & Zhong Wu & Hassan Raza, 2021. "Consensus Modeling with Asymmetric Cost Based on Data-Driven Robust Optimization," Group Decision and Negotiation, Springer, vol. 30(6), pages 1395-1432, December.
    8. Mingwei Wang & Decui Liang & Zeshui Xu & Wen Cao, 2022. "Consensus reaching with the externality effect of social network for three-way group decisions," Annals of Operations Research, Springer, vol. 315(2), pages 707-745, August.
    9. Yuanming Li & Ying Ji & Shaojian Qu, 2022. "Consensus Building for Uncertain Large-Scale Group Decision-Making Based on the Clustering Algorithm and Robust Discrete Optimization," Group Decision and Negotiation, Springer, vol. 31(2), pages 453-489, April.
    10. Meng, Fan-Yong & Gong, Zai-Wu & Pedrycz, Witold & Chu, Jun-Fei, 2023. "Selfish-dilemma consensus analysis for group decision making in the perspective of cooperative game theory," European Journal of Operational Research, Elsevier, vol. 308(1), pages 290-305.
    11. Labella, Álvaro & Liu, Hongbin & Rodríguez, Rosa M. & Martínez, Luis, 2020. "A Cost Consensus Metric for Consensus Reaching Processes based on a comprehensive minimum cost model," European Journal of Operational Research, Elsevier, vol. 281(2), pages 316-331.
    12. Zhang, Huanhuan & Kou, Gang & Peng, Yi, 2019. "Soft consensus cost models for group decision making and economic interpretations," European Journal of Operational Research, Elsevier, vol. 277(3), pages 964-980.
    13. Zhang, Hengjie & Dong, Yucheng & Chiclana, Francisco & Yu, Shui, 2019. "Consensus efficiency in group decision making: A comprehensive comparative study and its optimal design," European Journal of Operational Research, Elsevier, vol. 275(2), pages 580-598.
    14. Weijun Xu & Xin Chen & Yucheng Dong & Francisco Chiclana, 2021. "Impact of Decision Rules and Non-cooperative Behaviors on Minimum Consensus Cost in Group Decision Making," Group Decision and Negotiation, Springer, vol. 30(6), pages 1239-1260, December.
    15. Ziqi Wu & Kai Zhu & Shaojian Qu, 2022. "Distributionally Robust Optimization Model for a Minimum Cost Consensus with Asymmetric Adjustment Costs Based on the Wasserstein Metric," Mathematics, MDPI, vol. 10(22), pages 1-21, November.
    16. Li, Ying & Liu, Peide & Li, Gang, 2023. "An asymmetric cost consensus based failure mode and effect analysis method with personalized risk attitude information," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    17. Rodríguez, Rosa M. & Labella, Álvaro & Nuñez-Cacho, Pedro & Molina-Moreno, Valentin & Martínez, Luis, 2022. "A comprehensive minimum cost consensus model for large scale group decision making for circular economy measurement," Technological Forecasting and Social Change, Elsevier, vol. 175(C).
    18. Guo, Weiwei & Gong, Zaiwu & Zhang, Wei-Guo & Xu, Yanxin, 2023. "Minimum cost consensus modeling under dynamic feedback regulation mechanism considering consensus principle and tolerance level," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1279-1295.
    19. Gong, Zaiwu & Guo, Weiwei & Słowiński, Roman, 2021. "Transaction and interaction behavior-based consensus model and its application to optimal carbon emission reduction," Omega, Elsevier, vol. 104(C).
    20. Wenfeng Zhu & Hengjie Zhang & Jing Xiao, 2023. "Coming to Consensus on Classification in Flexible Linguistic Preference Relations: The Role of Personalized Individual Semantics," Group Decision and Negotiation, Springer, vol. 32(5), pages 1237-1271, October.

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