Within product development processes, computational models are used with increasing frequency. However, the use of those methods is often restricted to the area of focus, where product design, manufacturing process, and process chain simulations are regarded independently. In the use case of multi-material lightweight structures, the desired products have to meet several requirements regarding structural performance, weight, costs, and environment. Hence, manufacturing-related effects on the product as well as on costs and environment have to be considered in very early phases of the product development process in order to provide a computational concept that supports concurrent engineering. In this contribution, we present an integrated computational concept that includes product engineering and production engineering. In a multi-scale framework, it combines detailed finite element analyses of products and their related production process with process chain and factory simulations. Including surrogate models based on machine learning, a fast evaluation of production impacts and requirements can be realized. The proposed integrated computational product and production engineering concept is demonstrated in a use case study on the manufacturing of a multi-material structure. Within this study, a sheet metal forming process in combination with an injection molding process of short fiber reinforced plastics is investigated. Different sets of process parameters are evaluated virtually in terms of resulting structural properties, cycle times, and environmental impacts.