Water Resources Management

, Volume 27, Issue 7, pp 2125–2136 | Cite as

Waste Load Allocation in Rivers using Fallback Bargaining

  • Najmeh Mahjouri
  • Mohammad Bizhani-Manzar


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.


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


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Faculty of Civil EngineeringK. N. Toosi University of TechnologyTehranIran
  2. 2.Civil EngineeringK. N. Toosi University of TechnologyTehranIran

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