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

Abstract Small-scale farmers play an important role in food supply systems in developing countries. One of their main challenges is crop planning, since agricultural production follows seasonal cycles that often generate periods of low or unstable income. This research presents an integrated application of multi-criteria decision-making and portfolio-based optimisation methods to support crop planning decisions for small-scale farmers under conditions of price variability and production uncertainty. The methodology consists of three phases. First, crops suitable for cultivation in a rural area of a Colombian city are characterised using technical, economic, and contextual criteria. Second, crops are prioritised through the TOPSIS multi-criteria decision-making method to reduce the number of alternatives included in the optimisation model, considering the land, labour, and management limitations faced by small-scale farmer associations. Third, a commitment-based mixed-integer linear programming model is developed using information from the characterisation phase and monthly price scenarios. Results show important trade-offs between profitability and income stability. Portfolios focused exclusively on income maximisation achieved the highest total income (COP 36.3 billion) but also the highest income variability (MAD of COP 13.7 billion). In contrast, the risk-minimisation scenario reduced income variability by 87.7% but also reduced total income by 87.6%. The balanced scenario reduced income variability by 43.9% while maintaining 56.2% of the total income obtained in the income-maximisation scenario. These findings highlight the usefulness of the proposed approach for evaluating trade-offs between profitability and income variability in small-scale farming contexts.