Many economic, social and ecological problems can be attributed to the scarcity and mismanagement of water and land resources. In this study, a multi-objective fuzzy–robust programming (MOFRP) method was developed for supporting the optimal use of land and water resources in agriculture. MOFRP improved existing methods through taking ecological services of crop cultivation into account. It was also capable of reflecting fuzziness in preferences, priorities and parameters that were largely neglected in previous agricultural decision making. This method was applied to address a case in arid northwestern China. Optimal plans of crop cultivation reconfiguration were generated for sustaining local development under economic, ecological and social objectives as well as physical restraints in water and land resources. Compared to the status quo, the optimized plan would increase economic and ecological benefits by 12.2% and 18.8%, respectively. The efficiency of irrigation water could also be enhanced with the economic and ecological benefits per unit water being raised and the water consumption per unit land being reduced. The comparisons of the MOFRP model to four alternatives validated that it was capable of achieving satisfactory benefits and reducing system-violation risks without neglecting valuable uncertain information and ecological services of crops. The proposed method was also applicable to other multi-objective management problems under uncertainty without loss of generality.

Optimizing regional crop water consumption is considered to be a significant approach for increasing yields and reducing water consumption. This paper proposes a single-objective linear programming model which couples the distributed water consumption model with crop suitability. The impacts of meteorological, topographic, and soil factors were taken into account in both the distributed water consumption model and the crop suitability. The developed model was applied to a real case study in the middle reaches of Heihe River basin, in the northwest of China. In the optimization model, the net benefit which combined the water consumption with crop suitability was regarded as the objective function, while the limits on available water and planting area were set as the constraints. Optimal results regarding crop distribution and water consumption were generated for dry, normal, and wet hydrological years. Two optimization strategies were analyzed, including one with a fixed area of each crop and the other with a fixed total planting area. Economic analyses showed that net income under both optimization strategies increased by 31% and 33%, respectively. Although water consumption increased slightly in both optimization scenarios, the unit water income and unit area income were much higher than in the pre-optimization conditions. The obtained results are valuable for supporting the adjustment of planting patterns and the identification of desired plans for sustainable irrigation water allocation.

To optimize the water distribution of three industries based on the water demand prediction under multiple uncertainties, a fuzzy credibility-constrained interval two-stage stochastic programming (FCITSP) model base on the Cobb-Douglas production (CD) function was developed. The CD-FCITSP model integrated fuzzy credibility-constrained programming (FCP), an interval two-stage stochastic programming (ITSP) method and CD function. The developed model could deal with uncertainties with interval, random, and fuzzy features, reflect tradeoffs between different water use sectors, and provide water managers in arid regions with sustainable and reasonable water-allocation schemes under different credibility scenarios of local policies. Moreover, the relationships between economic benefits and water consumption were taken into consideration via the Cobb-Douglas production function. The developed model was applied to support the optimal allocation of limited water resources in Minqin County, northwest China. The obtained solution demonstrated that the developed method could help local water managers to effectively allocate limited water under multiple uncertainties and different credibility scenarios. In addition, water use efficiency could be promoted and the emissions of major pollutants could be reduced. The developed method could be extended to water management practices in other arid regions.

Agricultural water productivity (AWP), which is associated with multiple factors, is an important index for measuring the effectiveness of agricultural water management. The purpose of this study is to promote AWP through optimally allocating limited agricultural water resources with the coordination of related elements. Firstly, the coordination effects of multiple factors related to AWP are quantified as relative optimum membership degrees based on the fuzzy optimum selecting theory. Secondly, based on the relative optimum membership degrees for various crops, a linear fractional programming model is established to maximize AWP in agricultural water resources allocation. Thirdly, the impacts of the allocation schemes on the development of social-economy and ecological environment are discussed using the multi-dimensional regulation theory. The developed integrated system has advantages in increasing agricultural water productivity through the coordination of multiple factors with aspects of economy, society and resources. Moreover, the system is capable of screening schemes considering harmonious development of resources, economy, society and ecology based on optimization results, providing decision makers with more sustainable schemes for irrigation water allocation. The integrated system including the aforementioned three parts is applied to a real-world case study in China to demonstrate its feasibility and applicability. Different water allocation schemes for various crops under different scenarios were obtained. The average value of AWP is 1.85 kg/m³, which is 0.31 kg/m³ higher than the current value of AWP. An optimum scheme with 1.1405 × 10⁸ m³ of water being allocated was also selected due to its highest level of coordination for resources, economy, society and ecology. The developed system can provide an effective method for AWP promotion. The obtained results can help local decision makers adjust water resources allocation schemes.

The grey water footprint theory was introduced into a fractional programming model to alleviate non-point source pollution and increase water-use efficiency through the adjustment of crop planting structure. The interval programming method was also incorporated within the developed framework to handle parametric uncertainties. The objective function of the model was the ratio of economic benefits to grey water footprints from crop production, and the constraints contained water availability constraints, food security constraints, planting area constraints, grey water footprint constraints and non-negative constraints. The model was applied to the Hetao Irrigation District of China. It was found that, based on the data in the year of 2016, the optimal planting plans generated from the developed model would reduce 34,400 m³ of grey water footprints for every 100 million Yuan gained from crops. Under the optimal planting structure, the total grey water footprints would be reduced by 21.9 million m³, the total economic benefits from crops would be increased by 1.138 billion Yuan, and the irrigation water would be saved by 44 million m³. The optimal results could provide decision-makers with agricultural water use plans with reduced negative impacts on the environment and enhanced economic benefits from crops.

The water-energy-food (WEF) nexus, which is essential for supporting regional sustainable development, has become a popular research topic. This study proposed an optimization programming framework for improving water-use efficiency from a WEF nexus perspective. Through the incorporation of water rights transfer mechanism, water resources can be flexibly allocated between food and energy sectors. The proposed model could help decision makers to identify the optimal production scales of food and energy production, the potential of water conservation of food production, as well as the investment portfolio of water-saving engineering. The capability of proposed model was illustrated through a case study in Yellow River Basin, north China. Based on the proposed optimization model, the optimal allocation scheme of water resources between food and energy sectors were obtained. A total of 2.34 × 10⁷ m³ of water would be transferred from food production to energy sector. Compared with state quo, production scales of energy sector, as well as profits of both food and energy sectors would increase rapidly. Optimization results reveal that designed energy production scales proposed by local government and enterprises are attainable as long as there are sufficient water resources available for energy sector.