Conference Agenda

The management of locomotives and crew is a crucial tactical planning problem for railways. Due to the complexity of the individual problems, railway companies solve these problems in a sequential manner, i.e. they first generate circulation plans and then shift plans. As a result, the quality of the shift plans depends on the constraints induced by the circulation plan, and information dependencies between both planning steps cannot be exploited. Hence, in this paper, we aim to determine locomotive and driver schedules in an integrated manner. To this end, we minimize the number of locomotives and the number of driver shifts using a time-space network formulation. We investigate the effect of contractual aspects for drivers for both objectives and a cost-based bi-objective formulation. We also consider variants including buffers to determine reliable locomotive and driver schedules. Finally, We present results on the integrated schedules for real-world Austrian railway use cases.

In the project “Network Capacity” we develop an approach allowing to compute the residual freight capacity for a given passenger timetable, considering freight traffic demand while maintaining punctuality and reliability in operations. This approach combines train scheduling with robustness evaluation based on a (max,+) model for delay propagation. Since timetable-based capacity assessment suffers from fluctuating freight traffic demand, we use pre-constructed slots on net segments which will be combined to train paths as the basis of our model. Precisely, slots are selected and connected to build up conflict-free trains paths for actual freight traffic demand in short-time.

Initially, we construct (possible overlapping) slots for freight traffic fitting into the passenger timetable and considering node capacities. These slots are the basis for routing freight traffic demand. The demand is given as a set of requests, each defined by a source, a destination, a train category and a preferred start time, amongst others. For each, we have to select slots such that they construct a route from source to destination, fits to the train category and preferred start time, and are not in conflict with any other selected slot. Furthermore, several additional constraints have to be hold, e.g. the driving and rest periods for drivers must be considered. The objective is to maximize the freight traffic quality which is compounded by cost-effectiveness and robustness against delays. The resulting optimization problem is close to the Multi-Commodity-Flow-Problem. To solve it, we develop MIP formulations to apply suitable optimization techniques, e.g. Column Generation or Branch-and-Price.

Many railway companies operate with periodic schedules. The periodic event scheduling problem (PESP) was investigated by many different authors and was applied to real-world instances. It has proven its practicability in different case studies.

PESP models normally assume a macroscopic infrastructure, thereby overlooking microscopic details (such as signal positions and switches) that are crucial for precise timetabling. These models often rely on predefined standards for timetabling constraints, like default time values for train separation at stations, which means they cannot ensure the practical feasibility of the timetable. Therefore, macroscopic models need to be enhanced or combined with more microscopic models to guarantee the operational feasibility of the timetable. This leads to complex, time-consuming iterations between the macroscopic and microscopic models.

In the context of an applied research project together with the Swiss Railway Company, we address this problem by combining two well-known approaches.

On one hand, we make use of a known, flexible PESP formulation (FPESP), i.e., we calculate time intervals instead of time points for the arrival resp. departures times at operating points. On the other hand, we will use a micro-macro approach to transform the microscopic data on infrastructure and operation to an aggregated level, i.e. macroscopic. By skilfully integrating the micro-macro approach information into the FPESP model the feasibility of the timetables on the microscopic infrastructure will be enhanced. First numerical results of a small case study will be shown.