In this contribution, a computational approach for the manufacturing of multi-material lightweight parts is presented. For an efficient online optimization procedure, a proper orthogonal decomposition on offline obtained numerical results is carried out to construct a surrogate model. The functionality of the proposed framework is demonstrated on a use case study of a multi-material component consisting of a sheet metal basic structure and a plastic reinforcement structure. The manufacturing process chain consists of a deep drawing process followed by an injection molding process of short fiber reinforced plastics. The proposed methodology provides a fast and accurate computational model for structural properties with respect to the process settings.