The Locomotive Assignment Problem with Distributed Power at the Canadian National Railway Company

Some of the most important optimization problems faced by railway operators arise from the management of their locomotive fleet. In this paper, we study a general version of the locomotive assignment problem encountered at the tactical level by one of the largest railroads in North America: the Canadian National Railway Company (CN). We present a modeling framework with two integer linear programming formulations and contribute to the state of the art by allowing to decide each train's operating mode (distributed power or not) over the whole (weekly) planning horizon without partitioning it into smaller time windows. Given the difficulty to solve the problem, one of the formulations is enhanced through various refinements such as constraint relaxations, preprocessing and fixed cost approximations. We thus achieve a significant reduction in the required computational time to solve instances of realistic size. We also present two versions of a Benders decomposition-based algorithm to obtain feasible solutions. On average, it allows to reduce the associated computational time by two hours. Results from an extensive computational study and a case study with data provided by CN confirm the potential benefits of the model and solution approach.