Two-Stage Adaptable Robust Optimization for Glass Production

In the glass industry, visual and thermal properties of the glass sheets are obtained via the deposit of thin layers of different materials. A standard way to perform this step is the use of a “magnetron,” in which the materials are transferred from cathodes to the sheets using a magnetic field. Since the cathodes are very expensive, activation and replacement decisions have to be carefully decided to keep the cost of the wasted materials low. The production is organized in campaigns and the activation and replacement decisions of the cathodes have to be taken before each campaign. Yet, the exact orders to process during a campaign are only revealed after the decisions have been taken. We focus here on the case of two campaigns, which we model as a two-stage robust optimization problem. We propose a method based on the finite adaptability approach of Bertsimas and Caramanis (2010) combined with the branch-and-bound of Subramanyam et al. (2020). Experiments on real instances show that our method leads to clear diminutions of the cost of wasted material in the worst cases, and—even more interesting—allow to find solutions for cases that are unfeasible with the heuristic used by the practitioners.