Optimal irrigation reservoir operation and simultaneous multi‐crop cultivation area selection using simulated annealing

Abstract

Abstract In this paper, a nonlinear discrete‐time dynamic model is developed to describe the operation of a single‐purpose reservoir during the irrigation season. The impact on crop yield due to water deficit and the effect of soil moisture dynamics on crop water requirements are taken into account by an integrated soil water balance model. The objective function of the model maximizes the total farm income, which is based on crop‐water production functions, production cost and crop prices. The constraints include the state equation of the reservoir, reservoir storage, irrigation requirements of a crop and reservoir release, yield and cultivation area. The decision variables are the optimal allocation of cultivation areas for any number of irrigated crops and the optimal irrigation schedule, which specifies the amount of irrigation to be applied to each crop during its irrigation season. The optimization is performed in two stages. During the first stage the simulated annealing (SA) global optimization stochastic search algorithm is used. In the course of the second stage the solution reached by the SA is refined by a stochastic gradient descent algorithm. The optimization computes the optimal distribution of areas and crops, the water releases to satisfy irrigation requirements and the total farm income. The model can be used as a decision support tool for cropping patterns of an irrigated area and irrigation scheduling. The outputs of this model were compared with the results obtained from a simple model in which the only decision variables are the optimal allocation of cultivation areas. The model was applied on data from a planned reservoir on the Havrias river in northern Greece. Copyright © 2006 John Wiley & Sons, Ltd.