A novel integration of regret-based methodology and bankruptcy theory for waste load allocation.

Developing a suitable index for Waste Load Allocation (WLA) is essential for both industrial polluters and environmental organizations. Identifying the index that best describes the quality conditions of the river is the main concern of this study. To achieve this purpose, a novel framework incorporating a regret-based index and a bankruptcy-based approach to address the impacts of low water quality and pollutant locations within the WLA are introduced. The framework includes a simulation-optimization model to minimize river quality regret for environmental organizations and total treatment cost for industrial polluters, employing Nash bargaining theory for conflict resolution. Additionally, a new bankruptcy approach, the Namin's rule, is proposed for redistributing the River Quality Regret Index among industrial polluters. Applying this methodology to data from the KhoramAbad River, a sensitivity analysis reveals that while there is no significant difference between the methodology and fuzzy risk when polluters are close, the methodology provides more accurate results as the distance between polluters increases. When the distance between two pollutants was 20 km, the sum of WLA was evaluated to be 300 kg per day higher than that in the compared method, potentially enhancing environmental justice.

A new fuzzy approach and bankruptcy theory in risk estimation in Waste Load Allocation.

In this paper, we developed a simulator-optimizer model based on risk analysis to determine Waste Load Allocation (WLA). A new Fuzzy index as Fuzzy Risk Index (FRI) was linked with multi-objective optimization to minimize FRI for the environmental stakeholder and the total cost of sewage treatment for the polluting industries as the other collective stakeholder. Afterwards, the conflict was resolved with the help of Nash bargaining and bankruptcy approach (Constrained Equal Awards Rule). The model was run using quantitative/qualitative data for the KhoramAbad River. To check the efficiency of FRI, the process followed for WLA was reimplemented by the Monte Carlo simulation (MCS). A comparison between the two approaches revealed that the outcomes derived from Fuzzy arithmetic across all aspects, encompassing river qualitative simulation, nondominated curve, Nash bargaining's agreed point, and bankruptcy output, closely mirrored the results of MCS. The notable distinction lies in the drastic reduction of the model's execution time by a factor of 450.