Management of dam systems via optimal price control

This paper considers an optimal management strategy for a system of linked dams. The level of each dam is approximated by N discrete levels and each dam is then modeled as a continuous-time controlled Markov chain on a finite control period. The inflow processes for each dam are non-stationary as are the customer demands. We also consider non-stationary losses from each dam due to evaporation. The controls are a time and state dependent price control, the bounds of which are prescribed by regulators, and time and state dependent flow controls between dams. The innovation in this model is that the price control is a feedback control that takes into account the active sectoral demands of customers. The general approach to the solution is to consider the solution of this stochastic optimization problem in the average sense and solve it using the dynamic programming method. We consider some issues of the numerical procedures involved in this method and parallelization as a means to deal with higher dimension problems in reasonable time. We show that we can obtain optimal price controls for each joint state of the dam system using numerical methods. The result is illustrated by a numerical example.