An inexact CVaR two-stage mixed-integer linear programming approach for agricultural water management under uncertainty considering ecological water requirement

In this study, an inexact CVaR (conditional value-at-risk) two-stage mixed-integer linear programming (ICTMLP) approach is developed for agricultural water management under uncertainty considering ecological water requirement. Techniques of interval parameter programming (IPP), two-stage stochastic programming (TSP), CVaR and integer programming (IP) are jointly incorporated into the general optimization framework. The developed model can deal with uncertainties presented as discrete intervals and probability distributions. It has advantages in: (1) considering economic benefits and risk in the objective function simultaneously, (2) reflecting the tradeoffs between conflicting economic benefits and penalties due to violated policies, (3) facilitating dynamic analysis of decision making and (4) generating more flexible solutions under different risk-aversion levels. The model is applied to a realistic case study of agricultural water resources allocation in the middle reaches of Heihe River Basin, northwest China, where three scenarios with different types of ecological water requirements are taken into account. Therefore, optimal water allocation solutions from the ICTMLP model can support in-depth analysis of interactions among economic benefits, violated policies and risk-aversion levels. Moreover, these results are useful for helping decision makers find better decision alternatives to support regional ecological protection and agricultural production.