This work presents a hierarchical multi-refinery MILP framework for estimating daily refinery production, crude consumption, and processing margins while maintaining consistency with country-level monthly supply–demand balances. Traditional approaches solve each refinery independently on a daily basis, often leading to inconsistencies when aggregating production across multiple sites. The proposed method couples refinery models over an entire month using a sequence of MILPs that enforce feasible demand, minimize crude use, balance utilization and harmonize product allocation across refineries. A second stage refines daily crude runs and product profiles, followed by a daily operational MILP that maximizes margin under true daily constraints. Applied to South Korea's six refineries, the approach yields daily production estimates that align more closely with monthly national product balances than uncoupled daily LP models, while remaining computationally tractable despite its million-variable scale.