On a Railway Maintenance Scheduling Problem with Customer Costs and Multi-Depots

An important aspect of infrastructure management is the scheduling of maintenance tasks. That implies the allocation of tasks to different crews or machines and the determination of an execution order. To this end, different aspects have to be considered. On the one hand, the maintenance operator is interested in reducing the direct maintenance costs. On the other hand, priorities must be considered by scheduling maintenance tasks. Often, this is done by urgency rules, an inflexible method that resolves prioritised tasks first. In this paper, another approach is discussed. Instead of urgency rules, the maintenance tasks are afflicted with penalty costs that have to be paid for every day until the task is resolved. Then, the later the resolving time of such a job, the higher are the penalty costs. By minimising penalty costs and travel costs in one objective function, a solution with small travel costs and also small penalty costs can be found. For the resulting scheduling problem, a multi-depot vehicle routing problem with customer costs, different mixed-integer linear programming models are developed and compared in respect of their runtime in a solving method using CPLEX. Keyword: Integer Programming, Railway Infrastructure Maintenance Scheduling, VRP, Mathematical Modelling