非充分灌溉条件下多目标整数规划配水模型构建

农业用水面临可用水资源匮乏、面源污染严重的现状，通过综合考虑非充分灌溉对经济效益、作物品质和环境效应的影响从而实现农业水资源合理配置具有重要的现实意义。该研究基于非充分灌溉和灰水足迹理论，建立不确定性下经济-品质-环境多目标整数规划模型，对河套灌区作物生育期内的灌溉水量进行分配，得出了经济、品质和环境3种不同偏好水平下的决策方案。结果表明：偏好于环境目标的情景灌溉程度主要为33%，67%的灌溉程度次之，亏缺灌溉的程度更大；偏好于经济目标的灌溉程度大部分为100%，亏缺灌溉的程度较小；偏好于品质目标时则介于前述两种情况之间。通过与仅包括经济、品质和环境单目标的模型对比可见，多目标模型更兼顾品质指标、经济效益和灰水足迹，可以使得各项指标均处于总体较好的情况，其中番茄品质-经济-环境多目标模型品质指标为8.7，经济效益为21.3×108元，灰水足迹为1.62×104 m3，灌溉水量为3.51×107 m3，瓜类品质-经济-环境多目标模型品质指标为[25.3,32.7]，经济效益为[9.2×108,24.8×108]元，灰水足迹为[1.94×104,3.15×104] m3，灌溉水量为[6.32×107,7.62×107] m3，各指标表现更佳。模拟结果可为不同情景下灌溉水合理配置提供参考。

Construction of water allocation model with multi-objective integer programming under inadequate irrigation

The optimal allocation of water resources in irrigation areas is one of the important control methods to realize the sustainable utilization of agricultural water resources. However, two great challenges remain at present, including the water resources shortage and non-point source pollution. Therefore, it is highly urgent to optimize management practices and then reasonably allocate agricultural water resources during agricultural production. It is also of great practical significance to consider the multi-folded impacts of inadequate irrigation on economic benefits, crop quality, and environmental soundness. Among them, insufficient irrigation is an effective management measure to efficiently use irrigation water for the high quality and yield of crop production. Previous modeling of water resource allocation cannot fully reflect the economic and crop yield parameters in crop production and irrigation water resources system, the irrigation quantity on crop quality, the pollutant leaching, and the impacts of insufficient irrigation on the economy, quality and environment. In this study, an economic-quality-environment multi-objective mixed-integer programming model was established for the Hetao Irrigation District using insufficient irrigation and grey water footprint. An uncertainty quantity was also introduced into the water-quality model for the decision-making schemes under different preference levels using Analytic Hierarchy Process (AHP). The decision plans were then generated to allocate the irrigation water during the crop growth period under three scenarios, indicating different preferences over economy, quality, and environment. The results showed that the irrigation degree of preferred environmental goals was mainly 33%, followed by 66%, indicating a greater degree of deficit irrigation. The irrigation level of preferred economic goals was mostly 100%, indicating a smaller degree of deficit irrigation. A preference for the quality goals fell between the two levels. The developed model for the tomato and lemon was compared with those that only included the single target of economy, quality, and environment, showing more balanced plans with higher comprehensive benefits. Among them, the quality index of tomato quality-economy-environment multi-objective model was 8.7, the economic benefit was 21.3×108 yuan, the grey water footprint was 1.62×104 m3, and the amount of irrigation water was 3.51×107 m3. The quality index of melon quality-economy-environment multi-objective model was [25.3, 32.7], the economic benefit was [9.2×108, 24.8×108] yuan, the grey water footprints was [1.94×104, 3.15×104] m3, and the amount of irrigation water was [6.32×107, 7.62×107] m3. Consequently, the simulation increased the comprehensive benefits of crop production for the less grey water footprint, in order to promote the efficient and green utilization of irrigation water resources. An optimal solution was also proposed to adjust the crop planting structure and irrigation water allocation. The finding can also provide strong support to allocate the irrigation water under insufficient irrigation in the sustainable management of irrigation areas, without the loss of generality across the world.