Optimizing Multiple-Pollutant Waste Load Allocation in Rivers: An Interval Parameter Game Theoretic Model

Mohammad Reza Nikoo, Pouyan Hatami Bahman Beiglou, Najmeh Mahjouri*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)


In this paper, a new methodology is developed for optimal multiple-pollutant waste load allocation (MPWLA) in rivers considering the main existing uncertainties. An interval optimization method is used to solve the MPWLA problem. Different possible scenarios for treatment of pollution loads are defined and corresponding treatment costs are taken into account in an interval parameter optimization model. A QUAL2Kw-based water quality simulation model is developed and calibrated to estimate the concentration of the water quality variables along the river. Two non-cooperative and cooperative multiple-pollutant scenario-based models are proposed for determining waste load allocation policies in rivers. Finally, a new fuzzy interval solution concept for cooperative games, namely, Fuzzy Boundary Interval Variable Least Core (FIVLC), is developed for reallocating the total fuzzy benefit obtained from discharge permit trading among waste load dischargers. The results of applying the proposed methodology to the Zarjub River in Iran illustrate its effectiveness and applicability in multiple-pollutant waste load allocation in rivers.

Original languageEnglish
Pages (from-to)4201-4220
Number of pages20
JournalWater Resources Management
Issue number12
Publication statusPublished - Sept 1 2016


  • Game theory
  • Interval optimization
  • Multiple-pollutant
  • The Zarjub river
  • Waste load allocation

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Water Science and Technology


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