Crop planting strategies under robust linear programming based on constrained approximation

Abstract

In the context of rural revitalization and agricultural modernization, the optimization of crop cultivation strategies is crucial to enhancing farmers' incomes and promoting sustainable economic development. Although the existing strategies are continuously optimized, the consideration of crop, land management and climate factors is still insufficient. Therefore, this paper proposes a crop planting strategy under robust linear programming based on constrained approximation, aiming at combining rural reality, scientifically allocating crop and plot resources, and formulating an optimal planting plan to maximize the planting income in the next seven years. Firstly, different crops and their planting plot types are summarized and processed, and the constraints are constraint-approximated and equated, and secondly, according to the distribution of crops, a variety of plot types are subdivided and the constraints are reduced accordingly.Finally, set the decision variable for the plant's planting area, for a certain quarter of a plant's planting per acre profit, for different chunks, consider and select the appropriate constraints, introduce a linear programming model, bring in the objective function, for more than part of the stagnant sales, resulting in a waste of the situation through the MATLAB to establish a linear programming model to maximize the total return, develop the optimal planting program and to find the maximum sales to get the first case the maximum total profit from 2024 to 2030 is $37008056. Due to multiple uncertainties in climate and market, multiple attributes of the crop will generate uncertainty, consider the fluctuation intervals of uncertain parameters, determine the boxed uncertainty set, and build a robust linear programming model to simulate the uncertainty scenario. The maximum total profit of $35,906,995 is obtained for the years 2024 to 2030 for this scenario.The results show that the robust linear programming model, after considering the uncertainty factors, the maximum total profit, although lower than the deterministic model, is still within the acceptable range, and can effectively improve the robustness and reliability of the planting program and reduce the impact of uncertainty factors on agricultural production, which has a high practical application value.