An optimization model for pump operation based upon minimizing operation and maintenance costs of pumps for a specified demand (load) curve is presented. The purpose of this model is to determine pump operation to meet the known consumer demands as well as to satisfy the pressure requirements in the water distribution system. In addition, constraints on the number of pump ('on-off') switches are included as a surrogate to minimizing the maintenance costs. This model is a mixed integer nonlinear programming (MINLP) problem to consider the uncertainty in demand using a chance constraint formulation of the demand constraint. The optimization model was solved using the LocalSolver option in A Mathematical Programming Language (AMPL). The model was first applied to the operation of the example pumping system for an urban water distribution system (WDS) illustrating a reduction in operation costs using the optimization model. The optimization model with the chance-constraint on meeting demand was applied for a range of demand satisfaction uncertainties. A decrease in the operation costs was observed with an increased uncertainty in demand satisfaction, which shows that the model further optimizes the operations considering the relaxed constraints. Model application could be extended to operations of pumping systems during emergencies and contingencies such as droughts, component failures, etc.