Restoring water supply after disasters is challenging due to limited resources, uncertain pipe damage, and urgent timelines. This study addresses the water distribution network restoration problem under uncertainty, where pipe damage is initially unknown and gradually inferred from sensor data. The objective is to determine the sequence of pipe restorations to minimize the total weighted delay across all pipes, thereby ensuring the most efficient restoration of water supply. We firstly model this problem as a partially observable Markov decision process (POMDP). Due to the computational complexity of solving large-scale POMDPs, we propose a two-layer open-loop policy that leverages current information, without relying on any assumptions about future observations. The outer layer employs a Bayesian network to update each pipe’s belief state using sensor data, which is then fed into the inner scheduling model to determine a restoration sequence assuming no further observations. We further identify structural properties of the inner scheduling problem and design a heuristic to efficiently generate reasonable sequence. Numerical experiments on randomly generated instances with varying network sizes and information scenarios show that our method significantly improves restoration efficiency compared to benchmark strategies, and achieves the lowest cost.

Peihong Xiao is a Ph.D. candidate in the Department of Industrial Systems Engineering and Management at the National University of Singapore, supervised by Prof. Loon Ching Tang and Prof. Zhisheng Ye. Her research interests include reliability, industrial statistics, and decision analysis. She received her Bachelor’s degree from Tsinghua University in 2021.