Adaptive-Robust Mean-CVaR Optimization for Crude Oil Blending and Scheduling under Property Uncertainty

Abstract

Abstract Refineries stabilize the crude distillation unit feed by blending grades delivered under long-term contracts with cargoes purchased on the spot market. The true boiling point (TBP) yields of a delivered batch deviate from the nominal assay, and an occasional spot cargo departs sharply; therefore, the blended yields carry a tail risk. A deterministic schedule secures the blend only at the nominal yields, and scenario-based methods certify feasibility only at the sampled records. This paper proposes a two-stage adaptive robust optimization model with a mean-conditional value-at-risk (CVaR) objective for crude oil blending and scheduling under this uncertainty. A budget uncertainty set is calibrated from historical assays, affine decision rules adjust the blending ratios to the assayed deviations, and the CVaR of the yield deviation is evaluated on scenarios resampled from the same records. Feasibility is enforced over the entire uncertainty set, and linear programming duality keeps the model as a mixed-integer linear program. On 1,000 evaluation scenarios resampled from held-out assays, the risk term lowers the loss in tail periods by 23.3% relative to the risk-neutral adaptive benchmark, at a 2.3% premium in typical periods, and halves the per-period CVaR99 from 2.20 to 1.11 m%. The proposed model incurs no constraint violations out-of-sample, whereas its scenario-based counterpart violates an operating constraint in 8.1% of the periods whose realized deviations fall inside the calibrated uncertainty set. The formulation offers refineries a mathematically rigorous and computationally tractable strategy for holding blended yields on target under volatile crude supply.