Waste load allocation under uncertainty using game theory approach and simulation-optimization process

Abstract

This article aims to present a new methodology for Waste Load Allocation (WLA) in a riverine system considering the uncertainty and achieve the lowest amount of Inequity Index, Cost, and Fuzzy Risk of Standard Violation. To find a surface of undominated solutions, a new modified PAWN method, initially designed for sensitivity analysis, was developed and coupled with a simulation-optimization process using Multi-Objective Particle Swarm Optimization (MOPSO) algorithm, to consider the uncertainty of all affecting variables and parameters by using their probability distribution. The proposed methodology applied to Sefidrood River in the northern part of Iran. Graph Model for Conflict Resolution (GMCR) as a subset of Game Theory was implemented to attain a compromise on WLA among the stakeholders of a river system's quality in Iran: Department of Environment, Municipal Waste Water, and Private Sector. Some undominated solutions were used in GMCR model and modeling the conflict among Decision Makers reveals that their preferences and the status quo do not lead to a solely stable equilibrium; thus the intervention of a ruler as arbitrator leads them to reach a compromise on a scenario that has a median FRVS and cost. Sensitivity analysis was done using the PAWN method to assess the sensitivity of three intended objectives to all variables and parameters.