Application of probabilistic bankruptcy method in river water quality management

In this paper, a probabilistic water quality management model is developed to present strategies using bankruptcy rules for solving conflicts between the Environmental Protection Agency and polluters in river systems. The bankruptcy concepts are adapted to the water quality aspect, Dissolved Oxygen as the water quality factor, and the pollutant concentration refers to the asset and stakeholders' claim. Bankruptcy rules are developed to allocate wastewater cooperatively and improve the water quality at the checkpoint. Therefore, a simulation–optimization model, including QUAL2Kw and Particle Swarm Optimization, is used to optimize the bankruptcy method’s waste load allocation. In the probabilistic model, the effect of river flow uncertainty on the optimal solution is investigated by Monte Carlo and Latin Hypercube Sampling. The optimal Dissolved Oxygen values are obtained corresponding to the possibility of river flows under the bankruptcy rules. The results of deterministic and probabilistic models show that the methodology reduces the waste load by 65–94% and increases Dissolved Oxygen from 0.9 to 5 mg/L. However, the streamflow uncertainty benefits polluters and allows them to release pollution more than twice the deterministic model. Analyzing the rules reveals that the Talmud rule outperformed others with higher Dissolved Oxygen and waste load criterion. This reliable probabilistic model can be used when the parties' performance is not cooperative, leading to more adaptability with real situations.