A Multi-Parametric Optimization Approach for Bi-Level Decision-Making Strategies in Energy-Water Nexus Supply Systems

The demands for energy and water continue to increase amid depleting natural resource availability and rising sustainability concerns. To address these exigent challenges, systematic shifts are expected to take place in global energy and water supply systems. Therefore, it is pivotal to understand how these two resource supply systems are interconnected for the generation of synergistic systems solutions based on an energywater nexus (EWN) approach. Effective trade-offs between minimizing cost and maximizing resource utilization, among other objectives, can be identified through this approach for sustainable resource management. In these instances, it is customarily assumed that the decisions made by both systems are dictated at the same level, where there is effectively one single decision-maker to simultaneously satisfy the energy system's water requirements and the water system's energy requirements. However, these systems are typically in competition with one another to meet their respective objectives and true synergy can only be achieved in an ideal case. With these antagonistic objectives, the priorities of the involved systems naturally assume a hierarchical structure. To account for such structured decision-making, we present a bi-level programming framework for EWN supply systems based on a multi-parametric programming approach to optimize system design and operation.