A methodology, based on the concept of Affinely Adjustable Robust Optimization, for optimizing daily operation of pumping stations is proposed, which takes into account the fact that a water distribution system in reality is unavoidably affected by uncertainties. For operation control, the main source of uncertainty is the uncertainty in the demand. Traditional methods for optimizing dynamical systems under uncertainty (Multistage Stochastic Programming) results in computationally intractable models already for small water distribution networks. The most popular optimization method for these problems is Dynamic Programming; however, in practice applications of this approach are restricted to networks with 1-2 pumping stations and/or 1-2 storages, because of severe computational difficulties arising in when state dimension of the controlled dynamical system exceeds 1-2. The approach presented in this paper provides a computationally tractable alternative to the outlined traditional methods in the cases when the problem under consideration, in the absence of uncertainty, can be formulated as a Linear Programming problem.
February 2011, Department of Applied Mathematics, Moscow State University of Printing Arts, Prianishnikova 2a, 127750 Moscow, Russia.