Applying uncertain programming model to improve regional farming economic benefits and water productivity

The development of optimum crop area planning is valuable for agricultural water management in the arid and semiarid regions. However, the uncertain information existing in the crop area planning system is inevitable, and it cannot be tackled through the traditional multi-objective linear programming model (MOLP). In this study, an inexact multi-objective fuzzy programming model (IMOFP) was developed, considering the multi-objective characteristics, the vagueness associated with the objective functions and constraints, and the interval uncertainty in the parameters. Three objectives were considered including maximizing benefits, minimizing evapotranspiration (ET) and maximizing water productivity (WP). The IMOFP model was applied to solve the problem of crop area planning in Wuwei city of Gansu province in China, and the optimal results under different scenarios of water-saving levels and satisfactory degrees of the decision maker (DM) for available resources were obtained. Different scenarios were also considered to make in-depth analysis of interaction among weight coefficients, economic benefit and water conservation requirement. Moreover, violation variables were introduced to analyze the relationship among system satisfaction, risk level and benefit. Results indicate that using the IMOFP model made the economic benefit, water productivity and water production efficiency of planting in the region increased by 7.05-16.65%, 25.68-33.15% and 39.22-47.59% respectively, and the ET reduced by 20.96-23.10%. Compared to MOLP model, the proposed IMOFP model has advantages in effectively reflecting uncertainties expressed as discrete intervals and fuzzy sets, and can provide reasonable solutions and more stable decision alternatives.