A Mixed Integer Linear Program for Optimizing the Utilization of Locomotives with Maintenance Constraints

Abstract

In this paper we investigate the Locomotive Scheduling Problem, i.e., the optimization of locomotive utilization with prior known transports that must be performed. Railway timetables are typically planned a year in advance and then revised, updated and fixed for shorter time periods, e.g., for a week, during the year. Our aim is to assign locomotives to the trains such that the locomotive utilization is maximized considering maintenances. We model this optimization problem on a sparse weighted directed multigraph that defines the input variables for our proposed Mixed Integer Linear Program (MILP). We consider two different objective functions: We minimize over the number of deadhead kilometers, i.e., kilometers from a locomotive driven without pulling a train, and over the number of locomotives used. Finally, we conduct a computational study to compare the performance of our MILP with the different proposed objective functions and show how the MILP can be used within a rolling horizon approach.