Large logistics service providers often need to containerize and route thousands or millions of items per year. In practice, companies specify business rules of how to pack and transport items from their origin to destination. Handling and respecting those business rules manually is a complex and time-consuming task. We propose a variant of the variable sized bin packing problem applicable to the containerization process occurring at logistics service providers. This novel model variant extends the bin packing problem with color constraints by adding multiple item mixing constraints. We present a binary integer program along with a first-fit decreasing heuristic and compare the performance on in- stances from a global logistics service provider. The numerical results indicate promising results to solve this computationally hard combinatorial optimization problem.