Gasoline Blend Planning under Demand Uncertainty: Aggregate Supply–Demand Pinch Algorithm with Rolling Horizon

While most products from oil refineries are produced to meet contracted known demand, there is an additional uncertain demand which refineries can satisfy to generate extra profit. Using a deterministic model leads to suboptimal solutions since such a model fails to account for future additional uncertain demand when making a production plan. In this paper, a rolling horizon optimization approach is utilized to develop a production planning model under time-varying uncertainty in demand and applied to the gasoline blending problem. The model utilizes loss function formulation to account for expected revenue generated from meeting future uncertain demand when making a production plan for the current period. Our model considers uncertainty to vary with time; demand uncertainty for periods further into the future is higher. In the gasoline production planning application under demand uncertainty, our stochastic model makes the current period decisions (i.e., blend recipes) based on the action of future uncertain demands, resulting in meeting higher product demands and higher profits compared to those of deterministic models. The model proposed is mixed integer nonlinear programming (MINLP), and its size depends on the number of periods in the production horizon which leads to computational difficulties for cases with a large number of periods. Difficulties are resolved by applying a supply–demand pinch algorithm to decompose the large MINLP model into two smaller models solved in sequence. The supply–demand pinch algorithm allows using a local solver which results in 2000- to 3000-fold reduction in computation times compared to the full-space algorithm, while still achieving solutions within 0.04% from the full space algorithm solutions.