The Maraca: a tool for minimizing resource conflicts in a non-periodic railway timetable

While mathematical optimization and operations research receive growing attention in the railway sector, computerized timetabling tools that actually make significant use of optimization remain relatively rare. SICS has developed a prototype tool for non-periodic timetabling that minimizes resource conflicts, enabling the user to focus on the strategic decisions. The prototype is called the Maraca and has been used and evaluated during the railway timetabling construction phase at the Swedish Transport Administration between April and September 2010

Separation of Cycle Inequalities for the Periodic Timetabling Problem

Cycle inequalities play an important role in the polyhedral study of the periodic timetabling problem. We give the first pseudo-polynomial time separation algorithm for cycle inequalities, and we give a rigorous proof for the pseudo-polynomial time separability of the change-cycle inequalities. The efficiency of these cutting planes is demonstrated on real-world instances of the periodic timetabling problem

A multi-stage IP-based heuristic for class timetabling and trainer rostering

© 2015, Springer Science+Business Media New York. We consider a timetabling and rostering problem involving periodic retraining of large numbers of employees at an Australian electricity distributor. This problem is different from traditional high school and university timetabling problems studied in the literature in several aspects. We propose a three-stage heuristic consisting of timetable generation, timetable improvement, and trainer rostering. Large-scale integer linear programming models for both the timetabling and the rostering components are proposed, and several unique operational constraints are discussed. We show that this solution approach is able to produce good solutions in practically acceptable time

A Matching Approach for Periodic Timetabling

The periodic event scheduling problem (PESP) is a well studied problem known as intrinsically hard, but with important applications mainly for finding good timetables in public transportation. In this paper we consider PESP in public transportation, but in a reduced version (r-PESP) in which the driving and waiting times of the vehicles are fixed to their lower bounds. This results in a still NP-hard problem which has less variables, since only one variable determines the schedule for a whole line. We propose a formulation for r-PESP which is based on scheduling the lines. This enables us on the one hand to identify a finite candidate set and an exact solution approach. On the other hand, we use this formulation to derive a matching-based heuristic for solving PESP. Our experiments on close to real-world instances from LinTim show that our heuristic is able to compute competitive timetables in a very short runtime

Opportunities and challenges with new railway planning approach in Sweden

Long lead times in railway planning can give rise to a significant discrepancy between the original plan and the traffic eventually operated, resulting in inefficient utilization of capacity. Research shows that the railway sector in Sweden would benefit from a different planning approach in which capacity consuming decisions are pushed forward in time whenever possible. This approach is currently being implemented at Trafikverket, the Swedish Transport Administration. With it follows a number of mathematical opportunities and challenges, some of which will be presented in this paper

Generation of the transport service offer with application to timetable planning considering constraints due to maintenance work

Line planning is an important step in strategic timetable planning in public transport. In this step the transport offer for the customer is generated by the public transport operator, whereby the resulting costs for the operator should be as deep as possible. Mathematical models for line planning allow to create optimized line plans quickly. Planners can use these models to rate and select different alternatives. This is particularly valuable under the aspect of increasing maintenance and construction tasks of the railway infrastructure. We show, that in this case, it is possible to create functional requirements for automated timetable creation from the result of line planning step. The practical use of the involved models is illustrated by a real application example

Design and analysis of demand-adapted railway timetables

Railway scheduling and timetabling are common stages in the classical hierarchical railway planning process and they perhaps represent the step with major influence on user's perception about quality of service. This aspect, in conjunction with their contribution to service profitability, makes them a widely studied topic in the literature, where nowadays many efforts are focused on improving the solving methods of the corresponding optimization problems. However, literature about models considering detailed descriptions of passenger demand is sparse. This paper tackles the problem of timetable determination by means of building and solving a non-linear integer programming model which fits the arrival and departure train times to a dynamic behavior of demand. The optimization model results are then used for computing several measures to characterize the quality of the obtained timetables considering jointly both user and company points of view. Some aspects are discussed, including the influence of train capacity and the validity of Random Incidence Theorem. An application to the C5 line of Madrid rapid transit system is presented. Different measures are analyzed in order to improve the insight into the proposed model and analyze in advance the influence of different objectives on the resulting timetable

On the delivery robustness of train timetables with respect to production replanning possibilities

Measuring timetable robustness is a complex task. Previous efforts have mainly been focused on simulation studies or measurements of time supplements. However, these measurements don't capture the production flexibility of a timetable, which is essential for measuring the robustness with regard to the trains' commercial activity commitments, and also for merging the goals of robustness and efficiency. In this article we differentiate between production timetables and delivery timetables. A production timetable contains all stops, meetings and switch crossings, while a delivery timetable only contains stops for commercial activities. If a production timetable is constructed such that it can easily be replanned to cope with delays without breaking any commercial activity commitments it provides delivery robustness without compromising travel efficiency. Changing meeting locations is one of the replanning tools available during operation, and this paper presents a new framework for heuristically optimising a given production timetable with regard to the number of alternative meeting locations. Mixed integer programming is used to find two delivery feasible production solutions, one early and one late. The area between the two solutions represents alternative meeting locations and therefore also the replanning enabled robustness. A case study from Sweden demonstrates how the method can be used to develop better production timetables