Fuzzy-State Stochastic Dynamic Programming for Reservoir Operation

A new way of incorporating fuzzy logic concepts is introduced in order to better capture and manage some uncertainties in applying stochastic dynamic programming (SDP) formulations for reservoir operation. A model called fuzzy-state stochastic dynamic programming (FSDP), which takes into account both uncertainties due to random nature of hydrological variables and imprecision due to variable discretization is introduced in this study. In this model, fuzzy transition probabilities for stochastic hydrologic state variables are calculated by defining a fuzzy Markov chain. These fuzzy probabilities are derived based on fuzzy frequency concept considering different frequencies for different points of a class interval. In order to show how effective the proposed method is, FSDP was applied to the Zayandeh–Rud river–reservoir system in Isfahan, in the central part of Iran, and was compared with a demand driven stochastic dynamic programming model. The results show the robustness of the FSDP solutions with respect to the type of discretization scheme used in calculating the transition probabilities.