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 (CN) Railway Company. We present a modeling framework with two integer linear programming formulations and contribute to the state of the art by allowing decisions on each train’s operating mode (distributed power or not) over the whole (weekly) planning horizon without partitioning it winto smaller time windows. Given the difficulty in solving 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 a reduction of 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.

Application of the optimal network flow method to the problem of locomotive selection for freight trains on the Eastern Polygon

Моделируется подбор тяговых ресурсов (локомотивов - в данном случае) для провоза грузовых поездов. В качестве входных данных рассматриваются маршрут поезда, время готовности поезда к отправлению, средняя скорость и вес поезда. Имеется множество локомотивов, обладающих грузоподъемностью и областью разрешенного действия. Цель - оптимально подобрать ресурс для каждого участка маршрута поезда. Решение ищется методом потока ресурсов минимальной суммарной стоимости через специально сконструированную сеть. Сеть построена на основе взвешенного орграфа из ребер графика поездов на линейных участках и ребер альтернативы, в процессе прохода по которым осуществляется “смена деятельности” локомотива (например, отцепление от одного поезда и подцепка к другому). Полученное решение обладает свойством глобальной оптимальности по времени. The selection of traction resources (locomotives) for the transport of freight trains is modelled. The input data are the train route, the readiness time of the train for departure, the average speed and weight of the train. In addition, there are many locomotives with a carrying capacity and an area of permitted action. The research objective is to optimally select a resource for each segment of the train route. The solution is sought by the resource flow method of the minimum total cost through a specially designed network. The network includes edges created from train schedule segments whose filling means locomotive assignment to train at the segment, and special alternative edges, passing through which a locomotive alternates its assignment. The algorithm for finding the optimal solution is the method of pushing through the pre-flow proposed by A. Goldberg and R. Tarjan. This is one of the fastest algorithms converging to a global optimum. Two test cases were investigated: a trivial one, out of six trains and three locomotives, and a more complicated one, which is a model example the size of 10% of the full scale model and consists of 150 trains. Full scale calculations provide planning of the freight transportation on the Eastern Operational domain of the Russian Railways. The model includes 1800 locomotives and about 3000 trains on the time horizon of 48 hours. Solution is found in less than 5 minutes of processor time for a PC powered by Intel(R) Pentium(R) G2010 2.80 GHz processor.

Literature Review of Locomotive Assignment Problem from Service Operations Perspective: The Case of Indian Railways

Since the appearance of mechanized rail transport systems in England in the 1820s, the railway has evolved as an essential service and has become the primary mode of long-distance land transportation for people as well as for bulk material across the world. It is essential for every railway organization to maintain high quality of service to not only differentiate itself and create a competitive edge over other modes of transport but also to survive. Factors such as speed, reliability, passenger comfort, convenience, system safety, special services, innovations, efficiency, itinerary accuracy and so on are important to ensure satisfactory services. The locomotive assignment problem (LAP) is one problem which, if addressed properly, would go a long way to improve the quality of services provided by the railway organization. In this work, we thoroughly study the literature pertaining to LAP to identify the constraints that have been considered hitherto by various authors. We also try to single out constraints that are relevant but ignored by most of the studies. Finally, we review studies that are specific to the Indian context and highlight the scope for further work.