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In logistic problems, an Integral Multi-Commodity Network Design Problem on a time-space network is often used to model the problem of routing transportation means and assigning freight units to those means. In Physical Internet and Synchromodal networks an interactive planning approach is preferable, meaning that calculation times of a single planning step should be short. In this paper we provide finding ways to reduce the number of variables in the problem formulation, that are effective at reducing the computation time for ILP-based solution methods.