Environmental Science and Pollution Research

, Volume 24, Issue 21, pp 17741–17759 | Cite as

Integrated waste load allocation for river water pollution control under uncertainty: a case study of Tuojiang River, China

  • Jiuping XuEmail author
  • Shuhua Hou
  • Liming Yao
  • Chaozhi Li
Research Article


This paper presents a bi-level optimization waste load allocation programming model under a fuzzy random environment to assist integrated river pollution control. Taking account of the leader-follower decision-making in the water function zones framework, the proposed approach examines the decision making feedback relationships and conflict coordination between the river basin authority and the regional Environmental Protection Agency (EPA) based on the Stackelberg-Nash equilibrium strategy. In the pollution control system, the river basin authority, as the leader, allocates equitable emissions rights to different subareas, and the then subarea EPA, as the followers, reallocates the limited resources to various functional zones to minimize pollution costs. This research also considers the uncertainty in the water pollution management, and the uncertain input information is expressed as fuzzy random variables. The proposed methodological approach is then applied to Tuojiang River in China and the bi-level linear programming model solutions are achieved using the Karush-Kuhn-Tucker condition. Based on the waste load allocation scheme results and various scenario analyses and discussion, some operational policies are proposed to assist decision makers (DMs) cope with waste load allocation problem for integrated river pollution control for the overall benefits.


Waste load allocation Bi-level optimization model Stackelberg-Nash game Uncertainty Integrated 



The work is supported by the National Natural Science Foundation for Young Scholars of China (Grant No. 71301109), Soft Science Program of Sichuan Province (Grant No. 2017ZR0154), the Research Foundation of Ministry of Education for the Doctoral Program of Higher Education of China (Grant No. 20130181110063), and Key Program of National Natural Science Foundation of China (Grant No. 70831005).

Compliance with ethical standards

The authors state the sources of funding of compliance with ethical standards and ensure that there is no potential conflicts of interest (financial or non-financial).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Jiuping Xu
    • 1
    • 2
    Email author
  • Shuhua Hou
    • 2
  • Liming Yao
    • 1
    • 2
  • Chaozhi Li
    • 3
  1. 1.State Key & Laboratory of Hydraulics and Mountain River EngineeringSichuan UniversityChengduPeople’s Republic of China
  2. 2.Uncertainty Decision-Making LaboratorySichuan UniversityChengduPeople’s Republic of China
  3. 3.Neijiang Survey and Design Institute of Water Conservancy and HydropowerNeijiangPeople’s Republic of China

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