Centrifugal pumps are widely used in industry with high energy consumption. Operational optimization of pump networks to minimize energy consumption and maximize reliability is necessary for energy saving. In this study, operational optimization of a parallel pump network was investigated. Maximizing reliability and minimizing work consumption were the two objectives which were combined together by multiplication. A mixed-integer linear program (Problem 1) was built with turning on/off as the decision variable, whereas a mixed-integer nonlinear program (Problem 2) with both turning on/off and frequencies of pumps as decision variables was also built. Heuristic rule was proposed to solve Problem 1 for industrial usage. The results obtained by heuristic rules were compared to the global optima of problem 1 by enumeration searching. The results show that optimal solution of heuristic rules is easier to operate manually than the global optima among the total flowrate and head region, while the average work consumption is about 11% higher. Fluctuation of work consumption and reliability of the whole system obtained by heuristic rules were higher as well. When both turning on/off and frequencies were selected as the decision variables, average optimal work consumption of Problem 2 was about 8% lower than that of global optima of Problem 1. Less fluctuation of reliabilities was obtained as well. The minimum work consumption of cooling water was 0.105 kW·h·m~(-3).