The water system minimum-cost flow problem is solved using the successive shortest path (SSP), graph theory algorithm, by representing the network as a directed graph. The graph nodes represent water sources, junctions, tanks and consumers. The edges represent pipes, pumping stations water tanks. The successive shortest path algorithm is applied to the graph ending when max flow limitation is fulfilled between the sources and sink nodes, returning minimal operating costs. A simple 24h water system is examined using the proposed graph representation. The results are compared to the results of numeration and standard linear programing solver.
Price, E., & Ostfeld, A. (2014). Optimal water system operation using graph theory algorithms. In Procedia Engineering (Vol. 89, pp. 502–508). Elsevier Ltd. https://doi.org/10.1016/j.proeng.2014.11.245