Stackelberg strategies for wastewater management

Management of wastewater has become a critical environmental problem during past decades, specially for the particular case of urban areas. In this work we use numerical simulation, and combine optimal control theory of partial differential equations with multi-objective optimization techniques to formulate and solve this type of problems from a new original hierarchical viewpoint with a leader and a follower (Stackelberg strategies). Specifically, the main aim of this paper deals with applying these Stackelberg techniques to the environmental problem related to determining the optimal location and the optimal purification profile when building a new treatment plant in a wastewater depuration system. We analyze the control problem, introduce a numerical algorithm, and show the possibilities of our approach by solving a realistic problem posed in the Estuary of Vigo (NW Spain).