A coupled random fuzzy two-stage programming model for crop area optimization-A case study of the middle Heihe River basin, China

Crop area optimization is essential for agricultural water management. However, decision makers are challenged by the complexity of fluctuating stream condition and irrigation quota, varying economic profits and crop yield, as well as grayness and errors in the estimated modeling parameters. A random-fuzzy-variable-based inexact two-stage stochastic chance-constrained programming (RFV-ITSCCP) model is developed for crop area optimization in response to such complexities in more efficient and sustainable ways. The model is capable of tackling parameters' dual uncertainties of both randomness and fuzziness and meanwhile reflecting uncertainties expressed as intervals and probability distributions. Moreover, the developed model is helpful for managers in gaining insight into the tradeoffs between the system benefit and the constraint-violation risk. The RFV-ITSCCP model is applied in crop area optimization in the middle reaches of Heihe River basin, northwest of China. The results provide crop area allocation under various flow levels with the maximum system benefit under uncertainty, minimizing the penalty due to water deficit especially in arid and semi-arid area. The results show that the system efficiency (benefit per unit area) increases by 13.2% than conventional linear programming (LP) model with the most credible fuzzy number values under the same condition of water supply, irrigation regimes and socio-economic conditions, which can demonstrate the feasibility and applicability of the developed RFV-ITSCCP model. Sensitivity analysis is also conducted to analyze the impacts of key model parameters on the results. The obtained results are valuable for supporting the adjustment of the existing crop area patterns and identifying desired crop area schemes under complex uncertainties.