Waste load allocation in rivers under uncertainty: application of social choice procedures

In this paper, a waste load allocation model is developed which can incorporate uncertainties due to randomness as well as vagueness regarding some variables and parameters. A probabilistic water quality index is also presented and used in the waste load allocation model. For any discharger of the system, different wastewater treatment scenarios are defined. All possible combinations of these scenarios make different wastewater treatment alternatives for the system. An optimization model having the objectives of minimizing total treatment cost as well as water quality violation risk is also developed for finding the optimum treatment alternatives. The uncertainty related to the upstream river flow is addressed through considering probability distribution functions with fuzzy parameters. To deal with fuzzy and random inputs, the fuzzy transformation technique and Monte Carlo analysis are respectively used, and for each alternative, fuzzy membership function of the violation risk is obtained. The optimization model only takes into account the economic and environmental objectives and does not specifically consider the stakeholders satisfaction. To consider this and help the decision maker choose a final alternative among non-dominated solutions, three different social choice procedures which focus on stakeholders priorities are employed. The applicability and effectiveness of the methodology are evaluated by applying it to the Zarjub River in Iran facing serious water quality issues. The results indicate that the presented methodology can effectively take account of priorities of various decision makers as well as economic and environmental considerations, while incorporating multiple forms of uncertainties.