Optimization of iron ore blending in daily planning through linear integer programming

Abstract

Iron ore blending requires a distinction between maximizing usable material and controlling the composition of daily plant feed. This paper develops a clarified two stage formulation and critically reexamines the historical two mine illustrations supplied with an earlier blending study. The model first selects material under linear mass and quality constraints, then schedules the selected material to fixed positive daily feed masses. Under divisible material flows, target deviations and successive day grade changes admit linear programming formulations using nonnegative deviation variables. Requiring whole blocks introduces binary assignments and yields a mixed integer linear program. Endogenous daily denominators generally retain a nonlinear fractional structure. Four reproducible synthetic checks demonstrate the practical consequences: divisible blending can remove a 10 percentage point mean daily deviation that remains under whole parcel scheduling; constant grade can coexist with changing contained metal mass; optional selection produces different continuous and integer optima; and target tracking and adjacent day stability can rank schedules differently. All original figures and equations are retained, with the latter identified as the historical formulation. The mine figures provide qualitative application context, but the absence of raw schedules, units for the monthly mass plots and solver logs prevents a new industrial performance claim. The contribution is a corrected, verifiable modelling framework with explicit conditions for linearity, feasibility and evaluation.