Solving a real-world Locomotive Scheduling Problem with Maintenance Constraints

Abstract This work addresses the Locomotive Scheduling Problem with Maintenance Constraints ( LSPM ). The basic Locomotive Scheduling Problem ( LSP ), which depicts one of the most crucial optimization problems occurring in the railway industry, aims at assigning a fleet of locomotives to a set of scheduled trains such that the overall costs are minimized. As the rolling stock represents one of the main costs of a rail company, the focus lies on maximizing the utilization of the locomotives. This requires the incorporation of special maintenance constraints that increase the computational difficulty of the problem significantly. In our previous work, we proposed a Mixed-Integer Linear Programming formulation for solving the LSPM and continue in this paper by investigating different heuristic solution approaches, i.e., an Overlapping Rolling Horizon Approach and a Two-Stage Matheuristic ( 2SMH ). In the objective function, realistic costs for deadheading, the number of used locomotives and maintenance jobs are taken into account. An extensive computational study is conducted on instances with up to 2,290 trains derived from real-world data provided by RCA , the largest Austrian rail company for freight transportation. All solution approaches are analyzed in detail and compared against each other in order to show their benefits and disadvantages. We show that our approaches are capable of delivering high-quality solutions within short computation times. In fact, the performance of the 2SMH qualifies it to form the basis of a large scale real-time application to support railroad managers in their daily operations.