From single commodity to multiattribute models for locomotive optimization: A comparison of optimal integer programming and approximate dynamic programming

We present a general optimization framework for locomotive models that captures different levels of detail, ranging from single and multicommodity flow models that can be solved using commercial integer programming solvers, to a much more detailed multiattribute model that we solve using approximate dynamic programming (ADP). Both models have been successfully implemented at Norfolk Southern for different planning applications. We use these models, presented using a common notational framework, to demonstrate the scope of different modeling and algorithmic strategies, all of which add value to the locomotive planning problem. We demonstrate how ADP can be used for both deterministic and stochastic models that capture locomotives and trains at a very high level of detail.