Exploring optimal pump scheduling in water distribution networks with branch and bound methods

Water utilities can achieve signi cant savings in operating costs by optimising pump scheduling to improve efficiency and shift electricity consumption to low-tari periods. Due to the complexity of the optimal scheduling problem, heuristic methods that cannot guarantee global optimality are often applied. This paper investigates formulations of the pump scheduling problem solved using a branch and bound method. Piecewise linear component approximations outperform non-linear approximations within application driven accuracy bounds and demand uncertainties. It is shown that the reduction of symmetry through the grouping of pumps signi cantly reduces the computational e ort, whereas loops in the network have the opposite e ect. The computational e ort of including convex, non-linear pump operating, and maintenance cost functions is investigated. Using case studies, it is shown that linear and xed-cost functions can be used to nd schedules which, when simulated in a full hydraulic simulation, have performances that are within the solver optimality gap and the uncertainty of demand forecasts