Adjustable Robust Optimization for Water Distribution System Operation Under Uncertainty

The optimal operation of water distribution systems (WDS) is a paramount objective for water utilities due to the substantial energy consumption associated with pumping. A major challenge in optimizing WDS operation is addressing uncertainties such as those related to consumer demands. Real‐time operation under uncertainty necessitates a dynamic approach that can utilize the newly observed information and adjust the operational policy accordingly. This study presents an adjustable robust optimization (ARO) approach to tackle this challenge. Unlike static optimization methods, ARO generates a decision rule policy that is dynamically adjusted as new data becomes available and the operational horizon evolves, thereby ensuring adaptability to changing conditions. Furthermore, the study includes a quantitative analysis of typical demand uncertainty that supports the formulation of the ARO model. The proposed method is evaluated through two case studies and compared with traditional folding horizon approaches. The results indicate that the ARO method is competitive with traditional methods in terms of objective value and surpasses them in terms of robustness. An additional advantage of the method is its offline operation capability which enables it to produce decision rules independent of real‐time programs. This feature facilitates various practical applications such as what‐if analyses, maintenance work planning, and preparation for other special events. The study is focused on developing strategies to optimize the operation of water distribution systems under uncertainty. Pumping and distributing water consumes a lot of energy, therefore water utilities strive to optimize the system's efficiency. This optimization problem involves uncertainties, such as consumer water demands. To address this challenge, a method is developed based on adjustable robust optimization (ARO) theory. Unlike conventional optimization methods that produce a fixed policy for the entire operational horizon, ARO generates an adjustable policy as a decision rule. It creates a dynamic decision‐making policy that can adapt to new data and evolving conditions. The study also includes an analysis to quantify the typical uncertainty associated with water demand which supports the formulation of the ARO model and justifies parts of the theory behind it. The proposed method is tested on two case studies and compared with traditional approaches. Several sensitivity analyses were held to present