Optimization of crop planting strategies in mountainous areas of North China based on mixed integer programming and Monte Carlo simulation

In this paper, a mixed integer programming model (MIP) and Monte Carlo simulation model were established to optimize the crop planting strategy of a village in the mountainous area of North China, considering the planting restrictions of different plots, crop growth laws and the uncertainty of external conditions. First, under stable market conditions, the MIP model can obtain the optimal planting plan for the next seven years by optimizing factors such as cultivated land area, land type restrictions, cropping constraints, legume crop planting requirements and field management. Secondly, the Monte Carlo simulation model considers the uncertainty of expected crop sales, per mu yield, planting cost and selling price, and obtains the optimal planting plan under uncertain conditions by simulating various market scenarios, effectively reducing risks and improving the robustness of returns. The results showed that the village should actively develop efficient cash crops, optimize planting structure, and adopt diversified planting strategies to cope with market risks and promote sustainable agricultural development.