In this study, a nonlinear inexact two-stage management (NITM) model is proposed for optimal agricultural irrigation water management problems under uncertainty conditions. The model is derived from incorporating interval parameter programming (IPP), two-stage stochastic programming (TSP) and quadratic programming (QP) within the agricultural water management model. This model simultaneously handles uncertainties not only in discrete intervals, but also in probability distributions, as well as nonlinearity in the objective function. A concept of the law of diminishing marginal utility is introduced to reflect the relationship between unit benefits and allocated water, which can overcome the limitation of general TSP framework with a linear objective function. Moreover, these inexact linear functions of allocated water can be obtained by an interval regression analysis method. The model is applied to a real-world case study for optimal irrigation water allocation in midstream area of the Heihe River Basin in northwest China. Two Heihe River ecological water diversion plans, i.e., the original plan and an improved plan, will be used to determine the surface water availabilities under different inflow levels. Four scenarios associated with different irrigation target settings are examined. The results show that the entire study system can arrive at a minimum marginal utility and obtain maximum system benefits when optimal irrigation water allocations are the deterministic values. Under the same inflow level, the improved plan leads to a lower water shortage level than that of the original plan, and thus leads to less system-failure risk level. Moreover, the growth rate of the upper bound of economic benefits between each of two scenarios based on the improved plan are greater than that from the original plan. Therefore, these obtained solutions can provide the basis of decision-making for agricultural water allocation under uncertainty.
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