A solution approach for dynamic vehicle and crew scheduling

In this paper, we discuss the dynamic vehicle and crew schedulingproblem and we propose a solution approach consisting of solving asequence of optimization problems. Furthermore, we explain why itis useful to consider such a dynamic approach and compare it witha static one. Moreover, we perform a sensitivity analysis on ourmain assumption that the travel times of the trips are knownexactly a certain amount of time before actual operation.We provide extensive computational results on some real-world datainstances 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 dynamicapproach. We show that the results are good in the case of asingle depot. However, in the multiple-depot case, the dynamicapproach does not perform so well. We investigate why this is thecase and conclude that the fact that the instance has to be splitin several smaller ones, has a negative effect on the performance.transportation;vehicle and crew scheduling;large-scale optimization;dynamic planning

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.public transportation;daily management;passenger rerouting;railway operations

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

When tracks are out of service for maintenance during a certainperiod, trains cannot be operated on those tracks. This leads to amodified timetable, and results in infeasible rolling stock andcrew 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-scaleset covering problem. The problem is solved with a columngeneration based algorithm. The performance of the algorithm istested on real-world instances of NS, the largest passengerrailway operator in the Netherlands. Finally, we discuss somebenefits of the proposed methodology for the company.column generation;transportation;railways;crew re-scheduling;large-scale optimization

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

In this paper we discuss several methods to solve large real-worldinstances of the vehicle and crew scheduling problem. Although,there has been an increased attention to integrated approaches forsolving such problems in the literature, currently only small ormedium-sized instances can be solved by such approaches.Therefore, large instances should be split into several smallerones, which can be solved by an integrated approach, or thesequential approach, i.e. first vehicle scheduling and afterwardscrew scheduling, is applied.In this paper we compare both approaches, where we considerdifferent ways of splitting an instance varying from very simplerules to more sophisticated ones. Those ways are extensivelytested by computational experiments on real-world data provided bythe largest Dutch bus company.

Models and algorithms for Integration of Vehicle and Crew Scheduling

This paper deals with models, relaxations and algorithms for an integrated approach to vehicle and crew scheduling. We discuss potential benefits of integration and provide an overview of the literature, which considers mainly partial integration. Our approach is new in the sense that we can tackle integrated vehicle and crew scheduling problems of practical size.We propose new mathematical formulations for integrated vehicle and crew scheduling problems and we discuss corresponding Langrangian relaxations and Lagrangian heuristics. To solve the Lagrangian relaxations, we use column generation applied to set partitioning type of models. The paper is concluded with a computational study using real life data, which shows the applicability of the proposed techniques to practical problems. Furthermore, we also address the effectiveness of integration in different situations.Lagrangian relaxation;column generation;crew scheduling;integrated planning;vehicle scheduling

A dynamic approach to vehicle scheduling

This paper presents a dynamic approach to the vehicle scheduling problem. We discuss the potential benefit of our approach compared to the traditional one, where the vehicle scheduling problem is solved only once for a whole period and the travel times are assumed to be fixed. In our dynamic approach, we solve a sequence of optimization problems, where we take into account different scenarios for future travel times. Because in the multiple-depot case we cannot solve the problem exactly within reasonable computation time, we use a "cluster-reschedule" heuristic where we first assign trips to depots by solving the static problem and then solve dynamic single-depot problems. We use new mathematical formulations of these problems that allow a fast solution by standard optimization software. We report on the results of a computational study with real life data, in which we compare different variants of our approach and perform a sensitivity analysis with respect to deviations of the actual travel times from the estimated ones.vehicle scheduling;dynamic scheduling;public transport;stochastic programming;stochastic traveltimes

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.

Operations research in passenger railway transportation

In this paper, we give an overview of state-of-the-art OperationsResearch models and techniques used in passenger railwaytransportation. For each planning phase (strategic, tactical andoperational), we describe the planning problems arising there anddiscuss some models and algorithms to solve them. We do not onlyconsider classical, well-known topics such as timetabling, rollingstock scheduling and crew scheduling, but we also discuss somerecently developed topics as shunting and reliability oftimetables.Finally, we focus on several practical aspects for each of theseproblems at the largest Dutch railway operator, NS Reizigers.passenger railway transportation;operation research;planning problems

Combining Column Generation and Lagrangian Relaxation

Although the possibility to combine column generation and Lagrangian relaxation has been known for quite some time, it has only recently been exploited in algorithms. In this paper, we discuss ways of combining these techniques. We focus on solving the LP relaxation of the Dantzig-Wolfe master problem. In a first approach we apply Lagrangian relaxation directly to this extended formulation, i.e. no simplex method is used. In a second one, we use Lagrangian relaxation to generate new columns, that is Lagrangian relaxation is applied to the compact for-mulation. We will illustrate the ideas behind these algorithms with an application in Lot-sizing. To show the wide applicability of these techniques, we also discuss applications in integrated vehicle and crew scheduling, plant location and cutting stock problems.column generation;Lagrangean relaxation;cutting stock problem;lotsizing;vehicle and crew scheduling

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