A Constraint-Based Optimization Approach for Grain Blending in Multi-Level Silo Management with Quality Control

Grain blending within large-scale storage facilities is a critical operation in soybean export supply chains, directly affecting product quality, regulatory compliance, and profitability. Existing optimization frameworks typically assume homogeneous grain quality across storage bins, overlooking the vertical stratification inherent in industrial silos. In this context, we propose a Mixed-Integer Linear Programming (MILP) model for soybean blending under multi-level silo management, explicitly incorporating layer-specific quality attributes, sequential Last-In, First-Out (LIFO) discharge constraints, and minimum valve-consumption requirements. Additionally, a greedy heuristic that emulates manual operator decisions is developed as a baseline. Computational experiments on instances derived from a real agribusiness hub in Bahia, Brazil, demonstrate that the MILP model achieves zero constraint violations, fully complying with the Brazilian regulatory standard. In contrast, the heuristic approach incurred constraint violations of up to 508.26 units (aggregated quality-bound excess). Finally, the MILP solver averaged 4.24 seconds per instance, confirming practical tractability for industrial deployment.