COMPUTATIONAL IMPROVEMENT FOR STOCHASTIC DYNAMIC PROGRAMMING MODELS OF URBAN WATER SUPPLY RESERVOIRS1

ABSTRACT: This paper describes two methods that are introduced to improve the computational effort of stochastic dynamic programming (SDP) as applicable to the operation of multiple urban water supply reservoir systems. The stochastic nature of streamflow is incorporated explicitly by considering it in the form of a multivariate probability distribution. The computationally efficient Gaussian Legendre quadrature method is employed to compute the conditional probabilities of streamflow, which accounts for the serial correlation of streamflow into each storage and the cross correlation between the streamflow into various storages. A realistic assumption of cross correlation of streamflow is introduced to eliminate the need to consider the streamflow combinations which are unlikely to occur in the SDP formulation. A “corridor” approach is devised to eliminate the need to consider the infeasible and/or inferior storage volume combinations in the preceding stage in computing the objective function in the recursive relation. These methods are verified in terms of computational efficiency and accuracy by using a hypothetical example of three interconnected urban water supply reservoirs. Therefore, it can be concluded that these methods allow SDP to be more attractive for deriving optimal operating rules for multiple urban water supply reservoir systems.