The Scheduled Service Network Design Problem (SSNDP) models a wide range of tactical planning issues in the operation of freight transportation networks. Most variants of the problem model transportation costs that follow a step function that represents constant per-vehicle costs. However, piecewise linear functions have also been used to model cases where transportation costs are quoted on a per-unit-of-flow basis, with the rate decreasing in the amount of flow. We present a formulation strategy for the SSNDP that can be used for cost functions of any structure as it is based on encoding cost functions in data. With an extensive computational study we study the performance of solving instances of these formulations with an off-the-shelf solver.