Research on Multi Constraint Problems based on Dynamic Optimization Models

Abstract

Under China’s Rural Revitalization Strategy, optimizing agricultural planting strategies is crucial for enhancing land-use efficiency and rural economic development. This study addresses multi-constraint crop planning for a village in North China from 2024 to 2030. We develop dynamic optimization models to maximize profits while incorporating constraints such as crop rotation, land suitability, and market uncertainties. For Problem 1, linear programming models are constructed for two oversupply scenarios: complete stagnation (unsold surplus) and half-price sales. The results show total profits of ¥7.77 million and ¥20.16 million, respectively. For Problem 2, Monte Carlo simulation is integrated with dynamic programming to handle annual fluctuations in sales volume (±5–10%), yield (±10%), cost (+5%), and price (variable by crop type), yielding a total profit of ¥24.83 million. In Problem 3, crop substitutability and complementarity are quantified using demand cross-elasticity, and correlations between sales, price, and cost are analyzed via Pearson coefficients. The optimized model achieves a total profit of ¥20.44 million, demonstrating improved stability for grain crops compared to Problem 2. This research provides a robust framework for multi-constraint agricultural decision-making under uncertainty, contributing to sustainable rural development.