This paper presents a modeling and operation approach for tree water supply systems. The network control problem is approximated as a geometric programming (GP) problem. The original nonlinear nonconvex network control problem is transformed into a convex optimization problem. The optimization model can be efficiently solved to optimality using state-of-the-art solvers. Two control schemes are presented: (1) operation of network actuators (pumps and valves) and (2) controlled demand shedding allocation between network consumers with limited resources. The dual of the network control problem is formulated and is used to perform sensitivity analysis with respect to hydraulic constraints. The approach is demonstrated on a small branched-topology network and later extended to a medium-size irrigation network. The results demonstrate an intrinsic trade-off between energy costs and demand shedding policy, providing an efficient decision support tool for active management of water systems.