Agricultural Multi-Water Source Allocation Model Based on Interval Two-Stage Stochastic Robust Programming under Uncertainty

Abstract

Numerous uncertainties and complexities exist in the agricultural irrigation water allocation system, that must be considered in the optimization of water resources allocation. In this paper, an agricultural multi-water source allocation model, consisting of stochastic robust programming and two-stage random programming and introducing interval numbers and random variables to represent the uncertainties, was proposed for the optimization of irrigation water allocation in Jiamusi City of Heilongjiang Province, China. The model could optimize the water allocaton to different crops of groundwater and surface water. Then, the optimal target value and the optimal water allocation of different water sources distributed to different crops could be obtained. The model optimized the economic benefits and stability of the agricultural irrigation water allocation system via the introduction of a the penalty cost variable measurement to the objective function. The results revealed that the total water shortage changed from [18.6, 32.3] × 108 m3 to [15.7, 26.2] × 108 m3 at a risk level ω from zero to five, indicating that the water shortage decreased and the reliability improved in the agricultural irrigation water allocation system. Additionally, the net economic benefits of irrigation changed from [287.21, 357.86] × 108 yuan to [253.23, 301.32] × 108 yuan, indicating that the economic benefit difference was reduced. Therefore, the model can be used by decision makers to develop appropriate water distribution schemes based on the rational consideration of the economic benefit, stability and risk of the agricultural irrigation water allocation system.