The global water supply accounts for 7% of worldwide energy consumption. With the increasing energy tariffs, there is a growing need to reduce the energy consumption of water supply systems (WSS). Among the three primary areas for optimization in WSS, pump operation is the most critical one, representing 70% of the energy consumed in WSS. Despite several mathematical formulations and approaches for optimizing pump operation in WSS, there is a lack of comparative studies between them. Moreover, since each WSS system has unique physical characteristics, the performance and solutions generated by each formulation may vary. Therefore, this study aims to conduct a comparative analysis of three WSS optimization approaches, of which one was never implemented. These approaches are applied to two case studies with specific physical characteristics