Robust optimization for a steel production planning problem with uncertain demand and product substitution

This paper addresses a production planning problem in the steel industry, specifically focusing on determining production quantities and product -to -order assignment considering uncertain demand and product substitution. For the deterministic scenario, we formulate the problem as a mixed integer programming model to effectively represent its combinatorial nature. For uncertain scenarios, we develop a two -stage robust optimization model. This model represents demand values as a box uncertainty set and separates production quantities decision and product -to -order assignment decision into two stages to handle uncertainty effectively. To tackle the model, we propose an enhanced Benders decomposition algorithm that incorporates a problem -specific method for generating valid inequalities to strengthen the master problem, and a hybrid strategy that combines approximate and exact methods to solve the non -convex slave problem. We have performed a large number of computational experiments on synthetic examples to verify the performance of the proposed robust optimization method, and the results demonstrate its efficiency and effectiveness.