Optimal Crop Planning for Small-Scale Farmers using Portfolio Theory Considering Income Stability

Small-scale farmers play an indispensable role in achieving food sovereignty in developing countries, as they supply a significant share of food along the agricultural value chain. One of the most critical decisions they face is crop planning. Because agricultural production follows seasonal cycles, farmers often experience periods with limited or no income, which can severely affect their financial stability. This research proposes a novel mathematical model to determine the optimal combination of crops for small-scale farmers using a portfolio theory approach. The model seeks to maximise income while ensuring income stability by explicitly accounting for risks and uncertainties related to price variability and production cycles. The methodology consists of three phases. First, agricultural products suitable for cultivation in rural areas of a Colombian city are characterised based on technical, economic, and contextual criteria. Second, the identified crops are prioritised using the TOPSIS multi-criteria decision-making method. Finally, a commitment-based mixed-integer linear programming model is developed using assumptions derived from the characterisation phase and monthly price scenarios. The results show that crop portfolios focused exclusively on risk minimisation led to highly conservative strategies with limited diversification, whereas income-maximising portfolios increase exposure to volatility. In contrast, the balanced scenario identifies diversified crop portfolios that stabilise monthly income while maintaining acceptable profitability. These findings demonstrate the practical value of the proposed model as a decision-support tool for small-scale farmers and agricultural advisors, enabling informed crop planning decisions that enhance income stability and reduce vulnerability to market fluctuations.