Water Resources Management

, Volume 33, Issue 10, pp 3633–3653 | Cite as

A Fair Approach for Multi-Objective Water Resources Allocation

  • Jing Tian
  • Shenglian GuoEmail author
  • Dedi Liu
  • Zhengke Pan
  • Xingjun Hong


Due to the effect of climate change, rapid population growth and widespread water pollution, fresh water becomes an increasingly scarce natural resource. Optimal allocation of water resources is one of the most effective resolutions to deal with rising water demand and insufficient freshwater resources. This study proposes a fair approach for water resources allocation by employing the Sperner’s lemma to solve the conflicts of different objectives and those of competing regions. A multi-objective optimal allocation model is firstly formulated to generate the Pareto frontier surface, which maximizes the economic interest while minimizing the amount of organic pollutants. Subsequently, the approach searches for acceptable allocation schemes over the Pareto frontier surfaces through the total water quantity and envy-free constraints. The proposed model is applied to the middle and lower reaches of Hanjiang river basin in China. Results indicate that water allocation between multi-region can achieve Nash equilibrium by using the water conflict resolution method to select fair water allocation schemes, in which each region obtains its preferred water quantity. The proposed approach is proved effective for water resources management in the case study and demonstrates the potential for effective application in other basins.


Water resources Fair allocation Multi-objective Conflicts resolution Sperner’s lemma Pareto frontier surface 



This study is financially supported by the National Key Research and Development Project of China (Grant NO. 2016YFC0402206), the National Natural Science Foundation of China (Grant NO. 51539009, 91647106, 51579183). The authors would like to thank the editor and anonymous reviewers for their comments, and Prof. Chong-Yu Xu for proofreading the final version, that helped improve the quality of the paper.

Compliance with Ethical Standards

Conflict of Interest



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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Jing Tian
    • 1
  • Shenglian Guo
    • 1
    Email author
  • Dedi Liu
    • 1
  • Zhengke Pan
    • 1
  • Xingjun Hong
    • 1
  1. 1.State Key Laboratory of Water Resources and Hydropower Engineering ScienceWuhan UniversityWuhanChina

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