Water Resources Management (2005) 19: 655–672 DOI: 10.1007/s11269-005-3275-3 C  Springer 2005 Reservoir Operation Using a Dynamic Programming Fuzzy Rule–Based Approach S. J. MOUSAVI 1 , K. PONNAMBALAM 2,∗ and F. KARRAY 2 1 School of Civil and Environmental Engineering, Amirkabir University of Technology (Tehran Polytechniques), Tehran, Iran; 2 Department of Systems Design Engineering, University of Waterloo, Canada ( ∗ author for correspondence, e-mail: ponnu@uwaterloo.ca) (Received: 27 November 2002; in final form: 8 September 2004) Abstract. A dynamic programming fuzzy rule–based (DPFRB) model for optimal operation of reser- voirs system is presented in this paper. In the first step, a deterministic dynamic programming (DP) model is used to develop the optimal set of inflows, storage volumes, and reservoir releases. These optimal values are then used as inputs to a fuzzy rule–based (FRB) model to establish the general operating policies in the second step. Subsequently, the operating policies are evaluated in a simula- tion model. During the simulation step, the parameters of the FRB model are optimized after which the algorithm gets back to the second step in a feedback loop to establish the new set of operating rules using the optimized parameters. This iterative approach improves the value of the performance function of the simulation model and continues until the satisfaction of predetermined stopping crite- ria. This method results in deriving the operating policies, which are robust against the uncertainty of inflows. These policies are derived by using long-term synthetic inflows and an objective function that minimizes its variance. The DPFRB performance is tested and compared to a model, which uses the commonly used multiple regression–based operating rules. Results show that the DPFRB performs well in terms of satisfying the system target performances and computational requirements. Key words: dynamic programming, fuzzy inference system, reservoir operations 1. Introduction Among the main sources of complexities in optimization models for reservoir oper- ation is the need to account for uncertainties of all sorts. Explicit stochastic methods that consider uncertainties usually do not represent the detailed characteristics of a system under consideration, especially in multiple reservoirs systems. Implicit stochastic methods on the other hand can deal with it. However, one of the important challenges is to combine the large set of results obtained from an implicit stochastic method to derive general operating policies. A summary of different methods used for surface water reservoir management can be found in studies by Yeh (1985) and Ponnambalam (2002). Implicit stochastic programming has been widely used to derive the general operating policies for reservoir systems. Young (1967) proposed the use of linear