The New Dutch Timetable: The OR Revolution

On April 14, 2008, INFORMS (The Institute for Operations Research and Management Sciences) announced Netherlands Railways to be the winner of the 2008 Franz Edelman Award. In this extended abstract, we give a short summary of both the paper and the presentation of the winning team

A column generation approach to solve the crew re-scheduling problem

When tracks are out of service for maintenance during a certain period, trains cannot be operated on those tracks. This leads to a modified timetable, and results in infeasible rolling stock and crew schedules. Therefore, these schedules need to be repaired. The topic of this paper is the rescheduling of crew. In this paper, we define the Crew Re-Scheduling Problem (CRSP). Furthermore, we show that it can be formulated as a large-scale set covering problem. The problem is solved with a column generation based algorithm. The performance of the algorithm is tested on real-world instances of NS, the largest passenger railway operator in the Netherlands. Finally, we discuss some benefits of the proposed methodology for the company

Algorithmic Support for Railway Disruption Management

Disruptions of a railway system are responsible for longer travel times and much discomfort for the passengers. Since disruptions are inevitable, the railway system should be prepared to deal with them effectively. This paper explains that, in case of a disruption, rescheduling the timetable, the rolling stock circulation, and the crew duties is so complex that solving them manually is too time consuming in a time critical situation where every minute counts. Therefore, algorithmic support is badly needed. To that end, we describe models and algorithms for real-time rolling stock rescheduling and real-time crew rescheduling that are currently being developed and that are to be used as the kernel of decision support tools for disruption management. Furthermore, this paper argues that a stronger passenger orientation, facilitated by powerful algorithmic support, will allow to mitigate the adverse effects of the disruptions for the passengers. The latter will contribute to an increased service quality provided by the railway system. This will be instrumental in increasing the market share of the public transport system in the mobility market

Fast Heuristics for Delay Management with Passenger Rerouting

Delay management models determine which connections should be maintained in case of a delayed feeder train. Recently, delay management models are developed that take into account that passengers will adjust their routes when they miss a connection. However, for large-scale real-world instances, these extended models become too large to be solved with standard integer programming techniques. We therefore develop several heuristics to tackle these larger instances. The dispatching rules that are used in practice are our first heuristic. Our second heuristic applies the classical delay management model without passenger rerouting. Finally, the third heuristic updates the parameters of the classical model iteratively. We compare the quality of these heuristic solution methods on real-life instances from Netherlands Railways. In this experimental study, we show that our iterative heuristic can solve large real-world instances within a short computation time. Furthermore, the solutions obtained by this iterative heuristic are of good quality

A solution approach for dynamic vehicle and crew scheduling

In this paper, we discuss the dynamic vehicle and crew scheduling problem and we propose a solution approach consisting of solving a sequence of optimization problems. Furthermore, we explain why it is useful to consider such a dynamic approach and compare it with a static one. Moreover, we perform a sensitivity analysis on our main assumption that the travel times of the trips are known exactly a certain amount of time before actual operation. We provide extensive computational results on some real-world data instances of a large public transport company in the Netherlands. Due to the complexity of the vehicle and crew scheduling problem, we solve only small and medium-sized instances with such a dynamic approach. We show that the results are good in the case of a single depot. However, in the multiple-depot case, the dynamic approach does not perform so well. We investigate why this is the case and conclude that the fact that the instance has to be split in several smaller ones, has a negative effect on the performance

Algorithmic Support for Disruption Management at Netherlands Railways

In the Netherlands, relatively large disruptions occur on average about three times per day, each time leading to a temporary and local unavailability of the railway system. Faster response times and better solutions can be expected by the application of algorithmic support in the disruption management process. That is, the modified timetable, rolling stock circulation, and crew duties are generated automatically based on appropriate mathematical models and algorithms for solving these models. In this paper, we present such models and algorithms that were developed at Erasmus University Rotterdam and are being implemented at Netherlands Railways. Finally, we discuss challenges for research and implementation in practice

Adjusting a Railway Timetable in case of Partial or Complete Blockades

Unexpected events, such as accidents or track damages, can have a significant impact on the railway system so that trains need to be canceled and delayed. In case of a disruption it is important that dispatchers quickly present a good solution in order to minimize the nuisance for the passengers. In this paper, we focus on adjusting the timetable of a passenger railway operator in case of major disruptions. Both a partial and a complete blockade of a railway line are considered. Given a disrupted infrastructure situation and a forecast of the characteristics of the disruption, our goal is to determine a disposition timetable, specifying which trains will still be operated during the disruption and determining the timetable of these trains. Without explicitly taking the rolling stock rescheduling problem into account, we develop our models such that the probability that feasible solutions to this problem exists, is high. The main objective is to maximize the service level offered to the passengers. We present integer programming formulations and test our models using instances from Netherlands Railways

Analyzing a Family of Formulations for Cyclic Crew Rostering

In this paper, we analyze a family of formulations for the Cyclic Crew Rostering Problem (CCRP), in which a cyclic roster has to be constructed for a group of employees. Each formulation in the family is based on a partition of the roster. Intuitively, finer partitions give rise to a formulation with fewer variables, but possibly more constraints. Coarser partitions lead to more variables, but might allow to incorporate many of the constraints implicitly. We derive analytical results regarding the relative strength of the different formulations, which can serve as a guideline for formulating a given problem instance. Furthermore, we propose a column generation approach, and use it to compare the strength of the formulations empirically. Both the theoretical and computational results demonstrate the importance of choosing a suitable formulation. In particular, for practical instances of Netherlands Railways, stronger lower bounds are obtained, and more than 90% of the roster constraints can be modeled implicitly

Vehicle and crew scheduling: solving large real-world instances with an integrated approach

In this paper we discuss several methods to solve large real-world instances of the vehicle and crew scheduling problem. Although, there has been an increased attention to integrated approaches for solving such problems in the literature, currently only small or medium-sized instances can be solved by such approaches. Therefore, large instances should be split into several smaller ones, which can be solved by an integrated approach, or the sequential approach, i.e. first vehicle scheduling and afterwards crew scheduling, is applied. In this paper we compare both approaches, where we consider different ways of splitting an instance varying from very simple rules to more sophisticated ones. Those ways are extensively tested by computational experiments on real-world data provided by the largest Dutch bus company