A multi-objective optimal allocation of treated wastewater in urban areas using leader-follower game

Abstract This study proposes a new method for optimal allocation of Treated Wastewater (TW), in which different stakeholders, their social position in decision-making, and priority of objectives were attended using the leader-follower game theory. The suggested methodology was applied in a case study in the eastern part of Tehran province in Iran, where the Water and Sewage Department is considered the leader and four TW dependent districts are the followers in the game model. The leader appropriates a certain TW quantity to the system, and the followers compete for the allocated resources in the face of various physical and sociopolitical constraints. The Nash-Harsanyi production function was applied to model the non-cooperative relationships among the followers (i.e., their competition for limited resources) and find a compromise solution. Considering different limitations, such as the location and quantity of the TW allocation, 1569 different allocation scenarios were considered in four districts. Then, the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) based multi-objective optimization model was developed to optimize the main objectives of the leader, including i) minimizing the TW transfer costs, and ii) minimizing the supplied demand deficiency in all districts. A multi-criteria decision-making model was utilized to find the best solution on the achieved Pareto-front space. Nine different weighting scenarios were adopted to assess the model sensitivity to the importance of the selected criteria. Results point to the sensitivity of the framework to weighting scenarios, but provide effective compromise solutions to a complex system that can only partially supply water demands.