Two-stage robust optimization approach for flexible oxygen distribution under uncertainty in integrated iron and steel plants

Optimal oxygen distribution is one of the most important energy management problems in the modern iron and steel industry. Normally, the supply of the energy generation system is determined by the energy demand of manufacturing processes. However, the balance between supply and demand fluctuates frequently, owing to the uncertainty arising in manufacturing processes. In this study, we developed an optimal oxygen distribution strategy considering uncertain demands and proposed a two-stage robust optimization (TSRO) model with a budget-based uncertainty set that protects the initial distribution decisions with low conservativeness. The main goal of the TSRO model is to make “wait-and-see” decisions, maximizing energy profits, and make “here-and-now” decisions, minimizing operational stability and surplus/shortage penalty. To represent the uncertainty set of energy demands, we developed (1) a Gaussian process-based time-series model to forecast the demand intervals for continuous processes, and (2) a capacity-constrained scheduling model to generate multi-scenario demands for discrete processes. We performed extensive computational studies on TSRO and its components using well-synthesized instances from historical data. The results of model validation and analysis are promising and demonstrate that our approach is well adapted to solving industrial cases under uncertainty.