New Models and Applications for Railway Timetabling

A timetable is a crucial element for the daily operations of a railway operator. At the same time, designing such a timetable is an extremely complex puzzle, and years of investigations are necessary to design a timetable from scratch. Amongst several other aspects, planners should take the travel demand, connections between trains, capacity on the tracks and in the train, and daily disturbances into account when designing a timetable. Next to this, there are often too many restrictions that a timetable has to satisfy, such that no longer a timetable can exist satisfying all these restrictions. In this thesis, methods are developed that can support the design of a timetable such that the timetable is as good as possible. For example, we can compute an ideal timetable, matching with travel demand as good as possible. Using this ideal timetable, one can make clear whether regular departure patterns are useful or not, and how this is related with the expected travel time of passengers. This can also be used to determine infrastructure-bottlenecks. Other methods in this thesis aim at relaxing a set of restrictions, if there are too many restrictions, or to make a timetable that is robust against minor disturbances

An iterative heuristic for passenger-centric train timetabling with integrated adaption times

In this paper we present a method to construct a periodic timetable from a tactical planning perspective. We aim at constructing a timetable that is feasible with respect to infrastructure constraints and minimizes average perceived passenger travel time. In addition to in-train and transfer times, our notion of perceived passenger time includes the adaption time (waiting time at the origin station). Adaption time minimization allows us to avoid strict frequency regularity constraints and, at the same time, to ensure regular connections between passengers’ origins and destinations. The combination of adaption time minimization and infrastructure constraints satisfaction makes the problem very challenging. The described periodic timetabling problem can be modelled as an extension of a Peri- odic Event Scheduling Problem (PESP) formulation, but requires huge computing times if it is directly solved by a general-purpose solver for instances of realistic size. In this paper, we propose a heuristic approach consisting of two phases that are executed iteratively. First, we solve a mixed-integer linear program to determine an ideal timetable that mini- mizes the average perceived passenger travel time but neglects infrastructure constraints. Then, a Lagrangian-based heuristic makes the timetable feasible with respect to infras- tructure constraints by modifying train departure and arrival times as little as possible. The obtained feasible timetable is then evaluated to compute the resulting average per- ceived passenger travel time, and a feedback is sent to the Lagrangian-based heuristic so as to possibly improve the obtained timetable from the passenger perspective, while still respecting infrastructure constraints. We illustrate the proposed iterative heuristic approach on real-life instances of Netherlands Railways and compare it to a benchmark approach, showing that it finds a feasible timetable very close to the ideal one

Timetabling for strategic passenger railway planning

In research and practice, public transportation planning is executed in a series of steps, which are often divided into the strategic, the tactical, and the operational planning phase. Timetables are normally designed in the tactical phase, taking into account a given line plan, safety restrictions arising from infrastructural constraints, as well as regularity requirements and bounds on transfer times. In this paper, however, we propose a timetabling approach that is aimed at decision making in the strategic phase of public transportation planning and to determine an outline of a timetable that is good from the passengers’ perspective. Instead of including explicit synchronization constraints between train runs (as most timetabling models do), we include the adaption time (waiting time at the origin station) in the objective function to ensure regular connections between passengers’ origins and destinations. We model the problem as a mixed integer quadratic program and linearize it. Furthermore we propose a heuristic to generate starting solutions. We illustrate the trade-offs between dwell times and regularity of trains in two case studies based on the Dutch railway network

Resolving infeasibilities in railway timetabling instances

One of the key assumptions of timetabling algorithms is that a solution exists that meets the pre-specified constraints, like driving times, transfer constraints and headway constraints. If this assumption is satisfied, in most cases a timetable can be found rapidly. Nowadays, railways are being used more intensively, which leads to a higher utilization of the network. Due to this increased utilisation, capacity conflicts occur, so that no feasible solution to the timetabling models can be found, without making subtle but non-trivial changes to the initial input. Resolving these conflicts is essential for railway companies with high utilization of infrastructure. In this paper, we consider infeasible timetabling instances together with a list of allowed modifications of the constraints. We iteratively identify local conflicts in these instances and resolve them by adapting some of the constraints, until there are no more conflicts. The adaptations of the constraints are changes in the right-hand sides that we try to make as small as possible but that resolve the infeasibility. We empirically show that our method can be improved by enriching the initial minimal conflicts found with more constraints. In order to keep the problems tractable, an iterative procedure is used to find solutions to subproblems corresponding to conflicts in the complete timetabling instance. In a case study on instances from the Dutch railway network, we show that these instances can be made feasible within a few minutes

An Adjustable Robust Optimization Approach for Periodic Timetabling

In this paper, we consider the Robust Periodic Timetabling Problem (RPTP), the problem of designing an adjustable robust periodic timetable. We develop a solution method for a parametrized class of uncertainty regions. This class relates closely to uncertainty regions known in the robust optimization literature, and naturally denes a metric for the robustness of the timetable. The proposed solution method combines a linear decision rule with well-known reformulation techniques and cutting-plane methods. We show that the RPTP can be solved for practical-sized instances by applying the solution method to practical cases of Netherlands Railways (NS). In particular, we show that the trade-o between the e- ciency and robustness of a timetable can be analyzed using our solution method

Functional treatment versus plaster for simple elbow dislocations (FuncSiE): a randomized trial

Background. Elbow dislocations can be classified as simple or complex. Simple dislocations are characterized by the absence of fractures, while complex dislocations are associated with fractures. After reduction of a simple dislocation, treatment options include immobilization in a static plaster for different periods of time or so-called functional treatment. Functional treatment is characterized by early active motion within the limits of pain with or without the use of a sling or hinged brace. Theoretically, functional treatment should prevent stiffness without introducing increased joint instability. The primary aim of this randomized controlled trial is to compare early functional treatment versus plaster immobilization following simple dislocations of the elbow. Methods/Design. The design of the study will be a multicenter randomized controlled trial of 100 patients who have sustained a simple elbow dislocation. After reduction of the dislocation, patients are randomized between a pressure bandage for 5-7 days and early functional treatment or a plaster in 90 degrees flexion, neutral position for pro-supination for a period of three weeks. In the functional group, treatment is started with early active motion within the limits of pain. Function, pain, and radiographic recovery will be evaluated at regular intervals over the subsequent 12 months. The primary outcome measure is the Quick Disabilities of the Arm, Shoulder, and Hand score. The secondary outcome measures are the Mayo Elbow Performance Index, Oxford elbow score, pain level at both sides, range of motion of the elbow joint at both sides, rate of secondary interventions and complication rates in both groups (secondary dislocation, instability, relaxation), health-related quality of life (Short-Form 36 and EuroQol-5D), radiographic appearance of the elbow joint (degenerative changes and heterotopic ossifications), costs, and cost-effectiveness. Discussion. The successful completion of this trial will provide evidence on the effectiveness of a functional treatment for the management of simple elbow dislocations. Trial Registration. The trial is registered at the Netherlands Trial Register (NTR2025)

Early mobilization versus plaster immobilization of simple elbow dislocations: a cost analysis of the FuncSiE multicenter randomized clinical trial

Introduction: The primary aim was to assess and compare the total costs (direct health care costs and indirect costs due to loss of production) after early mobilization versus plaster immobilization in patients with a simple elbow dislocation. It was hypothesized that early mobilization would not lead to higher direct and indirect costs. Materials and methods: This study used data of a multicenter randomized clinical trial (FuncSiE trial). From August 25, 2009 until September 18, 2012, 100 adult patients with a simple elbow dislocation were recruited and randomized to early mobilization (immediate motion exercises; n = 48) or 3 weeks plaster immobilization (n = 52). Patients completed questionnaires on health-related quality of life [EuroQoL-5D (EQ-5D) and Short Form-36 (SF-36 PCS and SF-36 MCS)], health care use, and work absence. Follow-up was 1 year. Primary outcome were the total costs at 1 year. Analysis was by intention to treat. Results: There were no significant differences in EQ-5D, SF-36 PCS, and SF-36 MCS between the two groups. Mean total costs per patient were €3624 in the early mobilization group versus €7072 in the plaster group (p = 0.094). Shorter work absenteeism in the early mobilization group (10 versus 18 days; p = 0.027) did not lead to significantly lower costs for loss of productivity (€1719 in the early mobilization group versus €4589; p = 0.120). Conclusion: From a clinical and a socio-economic point of view, early mobilization should be the treatment of choice for a simple elbow dislocation. Plaster immobilization has inferior results at almost double the cost

Publisher Correction: Economic evaluation of operative versus nonoperative treatment of a humeral shaft fracture: economic analyses alongside a multicenter prospective cohort study (HUMMER) (European Journal of Trauma and Emergency Surgery, (2022), 10.1007/s00068-022-02160-1)

In this article, the order that the authors appeared in the author list was incorrect. The correct order is: Saskia H. Van Bergen1 · Esther M. M. Van Lieshout1 · Kiran C. Mahabier1 · Alexandra J. L. M. Geraerds2 · Suzanne Polinder2 · Dennis Den Hartog1 · Michael H. J. Verhofstad1 · on behalf of the HUMMER Investigators