Multi-Column Generation Model for the Locomotive Assignment Problem

We propose a new decomposition model and a multi-column generation algorithm for solving the Locomotive Assignment Problem (LAP). The decomposition scheme relies on consist configurations, where each configuration is made of a set of trains pulled by the same set of locomotives. We use the concept of conflict graphs in order to reduce the number of trains to be considered in each consist configuration generator problem: this contributes to significantly reduce the fraction of the computational times spent in generating new potential consists. In addition, we define a column generation problem for each set of variables, leading to a multi-column generation process, with different types of columns. Numerical results, with different numbers of locomotives, are presented on adapted data sets coming from Canada Pacific Railway (CPR). They show that the newly proposed algorithm is able to solve exactly realistic data instances for a timeline spanning up to 6 weeks, in very reasonable computational times