Multi-Scenario Crop Cultivation Optimization Strategies Based on Linear Programming and Dynamic Programming

This paper investigates optimization strategies under different scenarios to address the problems of limited resources, climate change and market volatility faced by crop farmers. The study aims to use agricultural resources efficiently through scientific planning and to improve farmers' profitability. Uncertainties in yield variability across plots and changes in market demand increase the difficulty of planning agricultural production. To solve these problems, this paper divides cropping scenarios into two categories: resource certainty and resource uncertainty, and assumes future changes in variables such as cropping costs and selling prices. A linear planning model and a dynamic planning model are then constructed. The specific steps include constructing the objective function, setting constraints, solving the deterministic problem using the simplex method, and solving the uncertainty problem using recursive dynamic programming. In addition, considering the substitutability and complementarity between crops, regression analysis and NSGA-II algorithm are combined to obtain the Pareto optimal solution. Numerical experiments show that the proposed model can significantly improve yields under all scenarios, which verifies the rationality and applicability of the model. This provides a scientific basis for the optimization of agricultural planting structure and a reference for agricultural modernization and rural revitalization.