Research on optimal planting scheme based on linear programming model

This study focuses on typical rural villages in North China to address crop planting optimization under multiple challenges including climate change, market fluctuations, and resource constraints. We propose an integrated decision-making model combining linear programming and Monte Carlo simulation to maximize economic benefits under limited arable land resources. By systematically incorporating multidimensional factors—such as planting area constraints, crop rotation systems (three-year soybean cycle), continuous cropping restrictions, and plot heterogeneity—a dual-scenario linear programming model was established based on the PuLP algorithm. Empirical results demonstrate that the model significantly enhances resource utilization efficiency and risk resilience, both under the risk of unsalable surplus yields and when allowing surplus products to be sold at a 50% discount. To overcome the limitations of traditional deterministic models, this study innovatively introduces a Monte Carlo algorithm to construct a stochastic optimization framework, quantifying the impacts of climate-induced per-mu yield fluctuations, market price variations, and planting cost uncertainties on system robustness. Through tens of thousands of iterative simulations, the optimized stochastic programming model achieves an 18% increase in revenue compared to the deterministic model while reducing income volatility, validating its adaptability in uncertain environments. Furthermore, by developing a crop substitution elasticity matrix and a price-cost cointegration model, this research reveals synergistic effects among crops and dynamic market correlation mechanisms. The integrated optimization model constructs a multi-objective decision function that considers factor interdependencies, achieving triple optimization of economic returns, risk aversion, and resource sustainability. Comparative experiments show that the model further improves land turnover efficiency, effectively reduces fertilizer application intensity, and maintains income fluctuations within acceptable thresholds. The findings provide a quantifiable decision-making tool for agricultural planting structure adjustment under rural revitalization strategies. The proposed multi-level optimization framework not only reconciles the conflict between economic benefits and risk mitigation but also offers methodological references for climate-smart agriculture practices, supporting scientific decision-making for sustainable rural development and rural revitalization.