Integrated Periodic Timetabling and Vehicle Circulation Scheduling

Periodic timetabling is one of the most well-researched problems in the public transport optimization literature. However, the impact that timetabling has on the number of required vehicles, which directly translates to operator costs, is rarely considered. Therefore, in this paper, we consider the problem of jointly optimizing the timetable and the vehicle circulation schedule, which specifies the cyclic sequences of trips that vehicles perform. In order to obtain high-quality solutions to realistic instances, we improve an earlier proposed formulation by contraction techniques, three new valid inequalities, and symmetry-breaking constraints. Ultimately, this allows us to explore the trade-off between the number of vehicles and the attractiveness of the timetable from the passengers’ perspective. An extensive computational study demonstrates the effectiveness of the improved formulation. Moreover, using this approach, we are able to find timetables requiring substantially fewer vehicles at the cost of minimal increases of the average travel time of passengers.

Periodic Timetabling with Integrated Routing: Toward Applicable Approaches

Periodic timetabling is an important, yet computationally challenging, problem in public transportation planning. The usual objective when designing a timetable is to minimize passenger travel time. However, in most approaches, it is ignored that the routes of the passengers depend on the timetable, so handling their routing separately leads to timetables that are suboptimal for the passengers. This has recently been recognized, but integrating the passenger routing in the optimization is computationally even harder than solving the classic periodic timetabling problem. In our paper, we develop an exact preprocessing method for reducing the problem size and a heuristic reduction approach in which only a subset of the passengers is considered. It provides upper and lower bounds on the objective value, such that it can be adjusted with respect to quality and computation time. Together, we receive an approach that is applicable for real-world problems. We experimentally evaluate the performance of the approach on a benchmark example and on three close-to-real-world instances. Furthermore, we prove that the ratio between the classic problem without routing and the problem with integrated routing is bounded under weak and realistic assumptions.

NETGRAPH – AN EFFICIENT TOOL FOR PERIODIC TIMETABLING AND CAPACITY PLANNING

A netgraph is a graphical representation of a periodic timetable concept for given spatial or modal scope. It adds a third dimension to the network plan – time. Despite no strictly prescribed rules, a common practice notation has been settled over time. The authors propose an extension of a netgraph for planning of periodic railway capacity and operation, including related notation rules.