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.

在本文中，建立了概率水质管理模型，以提出使用破产规则解决环境保护局与河流系统污染者之间冲突的策略。破产概念适用于水质方面，溶解氧是水质因子，污染物浓度是指资产和利益相关者的主张。制定破产规则以合作分配废水并改善检查站的水质。因此，使用包括QUAL2Kw和粒子群优化在内的仿真优化模型来优化破产方法的废物负荷分配。在概率模型中，蒙特卡洛和拉丁超立方采样研究了河流流量不确定性对最优解的影响。在破产规则下，获得了与河流流动的可能性相对应的最佳溶解氧值。确定性和概率模型的结果表明，该方法可将废物负荷降低65-94％，并将溶解氧从0.9毫克/升提高至5毫克/升。但是，水流的不确定性使污染者受益，并使他们释放的污染比确定性模型的两倍还多。分析这些规则后发现，Talmud规则在溶解氧和废物负荷标准较高的情况下胜过其他规则。当各方的表现不合作时，可以使用这种可靠的概率模型，从而提高了对实际情况的适应性。确定性和概率模型的结果表明，该方法可将废物负荷减少65-94％，并将溶解氧从0.9毫克/升提高至5毫克/升。但是，水流的不确定性使污染者受益，并使他们释放的污染比确定性模型的两倍还多。分析这些规则后发现，Talmud规则在溶解氧和废物负荷标准较高的情况下胜过其他规则。当各方的表现不合作时，可以使用这种可靠的概率模型，从而提高了对实际情况的适应性。确定性和概率模型的结果表明，该方法可将废物负荷减少65-94％，并将溶解氧从0.9毫克/升提高至5毫克/升。但是，水流的不确定性使污染者受益，并使他们释放的污染比确定性模型的两倍还多。分析这些规则后发现，Talmud规则在溶解氧和废物负荷标准较高的情况下胜过其他规则。当各方的表现不合作时，可以使用这种可靠的概率模型，从而提高了对实际情况的适应性。分析这些规则后发现，Talmud规则在溶解氧和废物负荷标准较高的情况下胜过其他规则。当各方的表现不合作时，可以使用这种可靠的概率模型，从而提高了对实际情况的适应性。分析这些规则后发现，Talmud规则在溶解氧和废物负荷标准较高的情况下胜过其他规则。当各方的表现不合作时，可以使用这种可靠的概率模型，从而提高了对实际情况的适应性。