Multi-objective optimization of the sustainable fruit crop planning problem with a focus on small colombian producers

This research proposes a compromise-based mixed-integer linear programming model to support sustainable crop planning for smallholder farmers. The framework integrates five sustainability metrics: carbon emissions, water consumption, production costs, unmet demand, and farmer preference satisfaction. Unlike single-objective approaches, the model adopts a max–min compromise formulation to ensure balanced performance across economic, environmental, and social dimensions. Uncertainty in demand and crop loss risk were incorporated through a stochastic simulation approach using 100 independent scenarios with uniformly distributed variations around baseline parameters. Results indicate that optimizing each objective independently generates significant trade-offs, confirming structural conflicts among sustainability dimensions. The compromise solution achieves intermediate but balanced outcomes, guaranteeing a minimum normalized performance level across all metrics. From an initial portfolio of 15 representative crops in Valle del Cauca (Colombia), the model consistently selected 10 crops that demonstrate robust performance under uncertainty. The findings highlight the environmental-economic coupling inherent in agricultural systems, particularly regarding water use and profitability. The proposed framework provides a practical decision-support tool for coordinated agricultural planning and represents a viable alternative to full Pareto frontier enumeration. It offers policymakers and producer associations a structured method to negotiate sustainability trade-offs under uncertain market and agronomic conditions.