17 Water Reservoir Applications of Markov Decision Processes

Decision problems in water resources management are usually stochastic, dynamic and multidimensional. MDP models have been used since the early fties for the planning and operation of reservoir systems because the natural water in ows can be modeled using Markovian stochastic processes and the transition equations of mass conservation for the reservoir storages are akin to those found in inventory theory. However, the \curse of dimensionality" has been a major obstacle to the numerical solution of MDP models for systems with several reservoirs. Also, the use of optimization models for the operation of multipurpose reservoir systems is not so widespread, due to the need for negotiations between di erent users, with dam operators often relying on operating rules obtained by simulation models. In this chapter, we present the basic concepts of reservoir management and we give a brief survey of stochastic in ow models based on statistical hydrology. We also present a stochastic dynamic programming model for the planning and operation of a system of hydroelectric reservoirs, and we discuss some applications and computational issues. We feel many research opportunities exist both in the enhancement of computational methods and in the modeling of reservoir applications.