Two-step dynamic programming approach for optimal irrigation water allocation

Abstract

A two-step (deterministic and stochastic) dynamic programming approach has been introduced in this study to solve the complex problem of optimal water allocation in a run-of-the-river-type irrigation project. The complexity of a real-world situation is represented by incorporating in the optimization model the stochasticity of water supply and the nonlinearity of crop production functions. A nonlinear, dated, and multiplicative production function is transformed into a sequentially additive type to replace the usual method of creating an additional ‘state of the plant variable’ which only increases the dimension of the problem. As compared to the explicit stochastic dynamic programming which necessitates, along with its use, an enormous computational complexity due to the so-called ‘curse of dimensionality’, the present model can approximate the theoretical global optimum, at least for the present case study, with a dramatic reduction in computer processing time. It also eliminates the rigidity of the policy derived by the explicit approach, since it provides irrigation planners with alternative decision policies which incorporate intangibles and other nonengineering factors. The traditional method of fixing the cropping pattern based on deterministic estimates of a dependable water supply can likewise be evaluated by the use of the present model. The results of the model's application appear to be practically acceptable.