Research on the Optimization Strategy of Crop Planting Combining Dynamic Programming and Monte Carlo Simulation

Abstract

 This paper explores the optimization of crop planting strategies by combining dynamic programming with Monte Carlo simulation. In the multi-stage decision-making for planting optimization, we decomposed the optimal planting plans for crops from 2024 to 2030 into annual best planting plans. We established an objective function aimed at maximizing total profit, taking into account factors such as planting area, crop yield, sales price, and planting cost. A series of constraints were also introduced, including that the planting area should not exceed the cultivated land area and that the total crop production should not surpass the expected sales volume. By employing dynamic programming and greedy algorithm models, we utilized the PuLP linear programming library to define problems, add constraints, and invoke solvers to find the optimal solution. The model considered not only the planting costs and sales prices but also treated excess sales volume as waste. In the result analysis phase, we analyzed the cyclical changes in data across different years and observed that the total profit exhibited a certain fluctuation trend. We also conducted error analysis on the potential errors introduced by the greedy algorithm, running the model multiple times to verify the stability of the results and ensure the reliability of the model. Finally, we discussed the complementarity and substitutability between crops, which significantly impact the total income in the actual planting process.