Research on Strategy Optimization Based on Linear Programming and Conditional Value at Risk
DOI:
https://doi.org/10.62051/z5mfc990Keywords:
Arable Land Optimization; Linear Programming; Conditional Value at Risk; Genetic Algorithm; Correlation Analysis.Abstract
Arable land resources are limited in mountainous areas. How to develop scientific planting strategies that maximize economic benefits while coping with market uncertainties is a key issue for sustainable agricultural development. This paper constructs a comprehensive model framework that extends from deterministic optimization to risk-quantified decision-making. First, a linear programming model aimed at maximizing total profit is established to devise basic planting strategies under ideal market conditions. Second, to address the inherent uncertainties in expected sales volume, yield per mu, planting costs, and sales prices, the Conditional Value at Risk (CVaR) method is introduced to build an optimization model designed to balance expected returns and downside risks. Finally, Spearman correlation analysis is used to quantify the substitutive and complementary relationships between crops, as well as the interrelationships among key economic variables; these correlation constraints are then incorporated into the CVaR model to better reflect real market dynamics. The model is solved using a genetic algorithm. Results show that, within the deterministic model, a strategy considering discounted product sales yields a total profit of 58.44 million yuan, which is significantly higher than in an unsalable scenario. Although introducing the risk-averse CVaR model adjusts the total profit to 32.80 million yuan, it markedly enhances the robustness of the strategy.
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