Optimizing bilinear multi-source water supply systems using mixed-integer linear programming approximations: An analysis of the Israeli seawater desalination array

Decision support systems (DSSs) in water resources management often use optimization models to make decisions. Therefore, the quality of these models is crucial for the success of DSSs. However, optimization models can struggle with reaching global optima, resulting in inconsistent and untrustworthy results for decision-makers. Additionally, current solution methods can be slow and inefficient, hindering real-time interaction with the DSS. This study addresses the optimal regional Multisource Water Supply Systems (MWSS) management using efficient global optimization techniques. The MWSS problem is formulated as a nonlinear optimization program due to using bilinear terms, which can result in multiple local optima. To overcome this challenge, four Mixed Integer Linear Program (MILP) formulations are proposed, which can be globally solved in a computationally effective manner using readily available MILP solvers. Our proposed formulations are tested on the Israeli Water Supply System (IWSS), which presents a unique challenge due to the inclusion of the seawater desalination array. In addition, this system must balance conventional and non-conventional water sources with varying qualities and characteristics. The results show that the proposed formulations provide a computationally efficient solution for the IWSS problem, allowing for the optimal utilization of different water sources in the IWSS.