Optimization of water use structure and plantation benefit of unit water consumption using fractional programming and conditional value-at-risk model

For optimizing the water-use structure and increasing plantation benefit of unit water consumption, a multi-objective model for water resources utilization was established based on fractional programming (FP). Meanwhile, considering the stochasticity of water availability in the study area, the impact of the risk factor (λ) from a quantitative and qualitative perspective was analyzed. The chance-constrained programming (CCP) and conditional value-at-risk (CVaR) models were introduced into five important major grain production areas in Sanjiang Plain, and the crop planting structure under this condition was optimized. The results showed that, after optimization, overall benefit of cultivation increased from 42.07 billion Yuan to 42.47 billion Yuan, water consumption decreased from 15.90 billion m3 to 11.95 billion m3, the plantation benefit of unit water consumption increased from 2.65 Yuan/m3 to 3.55 Yuan/m3. Furthermore, the index of water consumption, benefit of cultivation and plantation benefit of unit water consumption showed an increasing trend with the increase of violation likelihood. However, through the quantification of λ from an economic perspective, the increasing of λ could not enhance plantation benefit of unit water consumption significantly.