An inexact programming method for agricultural irrigation systems under parameter uncertainty

Rapid population growth and economy development have led to increasing reliance on water resources. It is even aggravated for agricultural irrigation systems where more water is necessary to support the increasing population. In this study, an inexact programming method based on two-stage stochastic programming and interval-parameter programming is developed to obtain optimal water-allocation strategies for agricultural irrigation systems. It is capable of handling such problems where two-stage decisions need to be suggested under random- and interval-parameter inputs. An interactive solving procedure derived from conventional interval-parameter programming makes it possible for the impact of lower and upper bounds of interval inputs to be well reflected in the resulting solutions. An agricultural irrigation management problem is then provided to demonstrate the applicability, and reasonable solutions are obtained. Compared to the solutions from a representative interval-parameter programming model where only one decision-stage exists, the interval of optimized objective-function value is narrow, indicating more alternatives could be provided when water-allocation targets are rather high. However, chances of obtaining more benefits exist in association with a risk of paying more penalties; such a relationship becomes apparent when the variation of water availability is much intensive.