Optimal Booster Disinfection Scheduling, Considering Demands and Disinfection Reaction Rate Uncertainty

<p dir="ltr">Ensuring the microbiological safety of drinking water relies heavily on effective disinfection, with chlorine injection serving as the most widely adopted method in water distribution systems. However, determining optimal chlorine injection schedules remains a complex and unresolved challenge. This complexity arises from the need to maintain chlorine residuals within strict regulatory bounds while accounting for the nonlinear interactions of water quality and hydraulics, the scale of the network, and the presence of multiple uncertainties, including variable consumer demands and uncertain chlorine decay kinetics. This study presents a robust and computationally efficient framework that combines Sample Average Approximation (SAA) with Robust Optimization (RO) to address these challenges. The proposed method formulates the chlorine scheduling task as a linear optimization problem that minimizes the expected deviation of chlorine residuals from target levels across a wide range of demand scenarios. The robust optimization formulation uses a box-type uncertainty set to handle uncertainty in chlorine decay, while Monte Carlo sampling addresses uncertainty in consumer demand. The framework is applied to a well-established benchmark water distribution network to evaluate its performance under varying degrees of uncertainty. Comparative analysis with deterministic optimization results reveals that the SAA-RO approach maintains target chlorine levels more consistently and with greater resilience to uncertainty. By combining scenario-based sampling with robust constraint handling, the proposed method offers a practical and scalable solution for real-time, uncertainty-aware disinfection planning.</p><p dir="ltr">This paper was presented at the 21st Computing and Control in the Water Industry Conference (CCWI 2025) at the University of Sheffield (1st - 3rd September 2025).</p>