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Abstract
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.
Highlights
As populations expand, economies grow and dietary preferences change, the demand for agricultural production is expected to rise in the future [1,2]
The optimized planting structure, grey water footprint and economic benefit value could be obtained by solving the model
An agricultural water management model based on grey water footprint was established to deal with the optimization of ratio and uncertainty in pollutant migration and transformation
Summary
Economies grow and dietary preferences change, the demand for agricultural production is expected to rise in the future [1,2]. Earlier attempts were largely focused on single-objective optimization of agricultural systems, where economic performance was considered as the primary objective to maximize financial return of farmers [14] In these models, the complexity of ecological effects was largely ignored. Fractional programming is an effective tool to deal with optimization of ratios, where the objective is the quotient of two functions (e.g., cost/time, cost/volume, or output/input) [18]. It could directly compare objectives of different aspects through the original magnitudes and provide an unbiased measurement of system efficiency [17]. There were many studies which used fraction programming in agricultural systems [19,20]
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