Waste Load Allocation in Rivers using Fallback Bargaining


In this paper, bargaining process between different stakeholders involved in a waste load allocation problem is simulated using the Fallback Bargaining (FB) concept. The paper considers two main parties in a waste load allocation problem. On the one hand, there are wastewater dischargers intending to minimize their treatment costs and on the other hand, there is an environmental protection agency which monitors the river water quality at a checkpoint downstream of the location of dischargers. In this paper, different alternatives which are combinations of dischargers’ treatment scenarios are defined. A water quality simulation model is utilized to estimate the concentration of the water quality indicator along the river based on a selected alternative. If the concentration of water quality indicator in the selected checkpoint violates the water quality standards, a penalty function is used to calculate the amount of penalty assigned to dischargers. The allocated cost to each discharger is computed considering his treatment scenario as well as the penalty allocated to him. Two kinds of Fallback bargaining procedure termed as Unanimity Fallback Bargaining (UFB) and Fallback bargaining with Impasse (FBI), which both aim at minimizing the maximum dissatisfaction of bargainers in a negotiation problem, are utilized for finding a Compromise Set (CS) of alternatives. In this paper, the best alternative (alternatives) among CS members is (are) selected using a social choice theory namely Condorcet winner. The results of these two approaches are compared and the final alternative is selected which shows the initial Tradable Discharge Permits (TDPs) allocated to dischargers. Finally, in order to decrease the total allocated cost to dischargers, initial allocated TDPs are exchanged between them using the Extended Trading Ratio System (ETRS) developed by Mesbah et al. (Environ Model Software 24:238–246, 2009). The applicability and efficiency of the proposed methodology is investigated by applying it to a case study of the Zarjub River in the northern part of Iran.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2


  1. Abed-Elmdoust A, Kerachian R (2012a) Water resources allocation using a cooperative game with fuzzy payoffs and fuzzy coalitions. Water Resour Manag 26(13):3961–3976

    Article  Google Scholar 

  2. Abed-Elmdoust A, Kerachian R (2012b) River water quality management under incomplete information: application of an n-person iterated signaling game. Environ Monit Assess 184(10):5875–5888

    Article  Google Scholar 

  3. Brams SJ, Kilgour DM (2001) Fallback bargaining. Group Decis Negot 10:287–316

    Article  Google Scholar 

  4. Brams SJ, Kilgour DM, Sanver M (2004) A minimax procedure for negotiating multilateral treaties. Department of Politics, New York University Press

  5. Condorcet JAN (1785) An essay on the application of analysis to the probability of decisions rendered by a plurality of voters. Abridged and translated. In: McLean I, Urken AB (eds) Classics of social choice, 1995. University of Michigan Press, Ann Arbor

    Google Scholar 

  6. Hung M, Shaw D (2005) A trading ratio system for trading water pollution discharge permits. J Environ Manag 81:233–246

    Google Scholar 

  7. Iran Department of Environment (2005) Developing pollution discharge permits in the Zarjub river basin. Tech Rep

  8. Madani K, Shalikarian L, Naeeni STO (2011) Resolving hydro-environmental conflicts under uncertainty using fallback bargaining procedures. International Conference on Environment Science and Engineering (IPCBEE). IACSIT Press, Singapore

    Google Scholar 

  9. Malakpour-Estalaki S, Kerachian R, Abed-Elmdoust A (2010) Application of evolutionary games in river water quality management. Proceedings of the Forth Conference and Exhibition of Environmental Engineering, October 23–25, Tehran, Iran

  10. Mesbah SM, Kerachian R, Nikoo MR (2009) Developing real time operating rules for trading discharge permits in rivers: application of Bayesian networks. Environ Model Software 24:238–246

    Article  Google Scholar 

  11. Mesbah SM, Kerachian R, Torabian A (2010) Trading pollutant discharge permits in rivers using fuzzy nonlinear cost functions. Desalination 250(1):313–317

    Article  Google Scholar 

  12. Nikoo MR, Kerachian R, Karimi A (2012) A nonlinear interval model for water and waste load allocation in river basins. Water Resour Manag 26(10):2911–2926

    Article  Google Scholar 

  13. Niksokhan MH, Kerachian R, Karamouz M (2009) A game theoretic approach for trading discharge permits in rivers. Water Sci Technol 60(3):793–804

    Article  Google Scholar 

  14. Poorsepahy-Samian H, Kerachian R, Nikoo MR (2012) A nonlinear interval model for water and waste load allocation in river basins. Water Resour Manag 26(14):4241–4257

    Article  Google Scholar 

  15. Sadegh M, Kerachian R (2011) Water resources allocation using solution concepts of fuzzy cooperative games: fuzzy least core and fuzzy weak least core. Water Resour Manag 25(10):2543–2573

    Article  Google Scholar 

  16. Sheikhmohammady M, Madani K (2008) Bargaining over the Caspian Sea-the largest lake on the earth. Proceeding of the 2008 World Environmental and Water Resources Congress, Honolulu, Hawaii, doi: 10.1061/40976(316)262

  17. Sheikhmohammady M, Kilgour DM, Hipel KW (2010) Modeling the Caspian Sea negotiations. Group Decis Negot 19(2):149–168

    Article  Google Scholar 

  18. Tsagarakis KP, Mara DD, Angelakis AN (2003) Application of cost criteria for selection of municipal wastewater treatment systems. Water Air Soil Pollut 142:187–210

    Article  Google Scholar 

  19. Zhang C, Wang G, Peng Y, Tang G, Liang G (2012) A negotiation-based multi-objective, multi-party decision-making model for inter-basin water transfer scheme optimization. Water Resour Manag 26(14):4029–4038

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Najmeh Mahjouri.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Mahjouri, N., Bizhani-Manzar, M. Waste Load Allocation in Rivers using Fallback Bargaining. Water Resour Manage 27, 2125–2136 (2013). https://doi.org/10.1007/s11269-013-0279-2

Download citation


  • Waste load allocation
  • Fallback bargaining
  • Compromise Set (CS)
  • Tradable Discharge Permits (TDPs)
  • Condorcet winner, the Zarjub River