Simultaneous locomotive and car assignment at VIA Rail Canada

In this paper, we present a sophisticated model and a heuristic solution approach based on mathematical optimization for the assignment of locomotives and cars to passenger trains. Given a periodic schedule and a fleet composed of several types of locomotives and cars, our approach determines a set of equipment cycles that cover all scheduled trains while satisfying a number of operational constraints. We first present a basic formulation that translates maintenance requirements and other fundamental difficulties of the problem. We then discuss several extensions, such as substitution possibilities and the minimization of switching operations, which are required in a real-life application. The resulting model is optimized through a branch-and-bound method in which the linear relaxations are solved by column generation. The model and solution strategy were tested on data from VIA Rail in Canada and a complete system based on this approach is now implemented at the company.