http://repub.eur.nl/res/aut/378/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/37239/ 2012-09-11T00:00:00Z The question of delay management is whether trains should wait for delayed feeder trains or should depart on time. Solutions to this problem strongly depend on the available capacity of the railway infrastructure. While the limited capacity of the tracks has been considered in delay management models, the limited capacity of the stations has been neglected so far. In this paper, we develop a model for the delay management problem that includes the stations’ capacities. This model allows to reschedule the platform assignment dynamically. Furthermore, we propose an iterative algorithm in which we first solve the delay management model with a fixed platform assignment and then improve this platform assignment in each step. We show that the latter problem can be solved in polynomial time by presenting a totally unimodular IP formulation. Finally, we present an extension of the model that balances the delay of the passengers on the one hand and the number of changes in the platform assignment on the other. All models are evaluated on real-world instances from Netherlands Railways. http://repub.eur.nl/res/pub/37246/ 2012-09-01T00:00:00Z 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. http://repub.eur.nl/res/pub/32416/ 2012-05-23T00:00:00Z Delay management determines which connections should be maintained in case of a delayed feeder train. Recent delay management models incorporate the limited capacity of the railway infrastructure. These models introduce headway constraints to make sure that safety regulations are satisfied. Unfortunately, these headway constraints cannot capture the full details of the railway infrastructure, especially within the stations. We therefore propose an iterative optimization approach that iteratively solves a macroscopic delay management model on the one hand, and a microscopic train scheduling model on the other hand. The macroscopic model determines which connections to maintain and proposes a disposition timetable. This disposition timetable is then validated microscopically for a bottleneck station of the network, proposing a feasible schedule of railway operations. This schedule reduces delay propagation and thereby minimizes passenger delays. We evaluate our iterative optimization framework using real-world instances around Utrecht in the Netherlands. http://repub.eur.nl/res/pub/32409/ 2012-05-11T00:00:00Z Express service providers manage shipments from senders to receivers under strict service level agreements. Such shipments are usually not sufficient to justify a single transportation, so it is preferred to maximize consolidation of these shipments to reduce cost. The consolidation is organized via depots and hubs: depots are local sorting centers that take care of the collection and delivery of the parcels at the customers, and hubs are used to consolidate the transportation between the depots. A single transportation between two locations, carried out by a certain vehicle at a specific time, is defined as a movement. In this paper, we address the problem of scheduling all movements in an express network at minimum cost. Our approach allows to impose restrictions on the number of arriving/departing movements at the hubs so that sufficient handling capacity is ensured. As the movement scheduling problem is complex, it is divided into two parts: one part concerns the movements between depots and hubs; the other part considers the movements between the hubs. We use a column generation approach and a local search algorithm to solve these two subproblems, respectively. Computational experiments show that by using this approach the total transportation costs are decreased. http://repub.eur.nl/res/pub/22106/ 2012-02-01T00:00:00Z Railway operations are disrupted frequently. For example, the Dutch railway network experiences about three large disruptions per day on average. In a disrupted situation, a railway operator needs to quickly adjust the timetable and the resource schedules. Usually the timetable, the rolling stock and the crew schedule are recovered in a sequential way. In this paper, we model and solve the crew rescheduling problem with retiming. This problem extends the crew rescheduling problem by the possibility to slightly delay the departure of some trains, so that some more flexibility in the crew scheduling process is obtained. Our algorithm focuses on rescheduling the duties of the train drivers. It is based on column generation techniques combined with Lagrangian heuristics. In order to prevent a large increase in computation time, retiming is allowed only for a limited number of trains for which it seems promising. Computational experiments with train driver duties and real-life disruption data show that, compared to the classical approach, it is possible to find better solutions by using crew rescheduling with retiming. Research highlights ► We propose a new column generation based algorithm for railway crew rescheduling. ► The approach is able to solve the problem within minutes. ► We compare our new approach with retiming with an approach without retiming. ► Allowing retiming leads to better crew schedules with less canceled tasks. http://repub.eur.nl/res/pub/37693/ 2012-02-01T00:00:00Z The question of delay management (DM) is whether trains should wait for a delayed feeder train or should depart on time. In classical DM models, passengers are assumed to take their originally planned routes. After the wait-depart decisions are made, passengers will certainly change to the best-possible route according to these decisions. In this paper, we propose a model where such a rerouting of passengers is incorporated in the DM process. To describe the problem, we represent it as an event-activity network similar to the one used in classical DM, with some additional events to incorporate origin and destination of the passengers. We present an integer programming formulation of this problem. Furthermore, we discuss the variant in which we assume fixed costs for maintaining connections, and we present a polynomial algorithm for the special case of only one origindestination pair that we later use to derive a strong lower bound for the integer program. Finally, computational experiments based on real-world data from Netherlands Railways show that significant improvements with respect to the passengers' traveling times can be obtained by taking the rerouting of passengers into account in the model. http://repub.eur.nl/res/pub/26866/ 2011-10-01T00:00:00Z 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. http://repub.eur.nl/res/pub/32050/ 2011-06-01T00:00:00Z This paper deals with large-scale crew scheduling problems arising at the main Dutch railway operator, Netherlands Railways (NS). NS operates about 30000 trains a week. All these trains need a driver and a certain number of guards. Some labor rules restrict the duties of a certain crew base over the complete week. Therefore, splitting the problem in several subproblems per day leads to suboptimal solutions. In this paper, we present an algorithm, called LUCIA, which can solve such huge instances without splitting. This algorithm combines Lagrangian heuristics, column generation and fixing techniques. We compare the results with existing practice. The results show that the new method significantly improves the solution. http://repub.eur.nl/res/pub/22456/ 2011-02-10T00:00:00Z 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. http://repub.eur.nl/res/pub/21711/ 2010-12-07T00:00:00Z This paper deals with large-scale crew scheduling problems arising at the Dutch railway operator, Netherlands Railways (NS). NS operates about 30,000 trains a week. All these trains need a driver and a certain number of guards. Some labor rules restrict the duties of a certain crew base over the complete week. Therefore splitting the problem in several subproblems per day leads to suboptimal solutions. In this paper, we present an algorithm, called LUCIA, which can solve such huge instances without splitting. This algorithm combines Lagrangian heuristics, column generation and fixing techniques. We compare the results with existing practice. The results show that the new method significantly improves the solution. http://repub.eur.nl/res/pub/21591/ 2010-11-01T00:00:00Z The Dutch railway network experiences about three large disruptions per day on average. In this paper, we present an algorithm to reschedule the crews when such a disruption occurs. The algorithm is based on column generation techniques combined with Lagrangian heuristics. Since the number of duties is very large in practical instances, we first define a core problem of tractable size. If some tasks remain uncovered in the solution of the core problem, we perform a neighborhood exploration to improve the solution. Computational experiments with real-life instances show that our method is capable of producing good solutions within a couple of minutes of computation time. http://repub.eur.nl/res/pub/17385/ 2010-06-01T00:00:00Z This paper addresses the Rolling Stock Rebalancing Problem (RSRP) which arises within a passenger railway operator when the rolling stock has to be rescheduled due to changing circumstances. RSRP is relevant both in the short-term planning stage and in the real-time operations. RSRP has as input a timetable and a rolling stock circulation where the allocation of the rolling stock among the stations at the start or at the end of a certain planning period does not match with the allocation before or after that planning period. The problem is then to modify the input rolling stock circulation in such a way that the number of remaining off-balances is minimal. If all off-balances have been solved, then the obtained rolling stock circulation can be implemented in practice. For practical usage of solution approaches for RSRP, it is important to solve the problem quickly. Since we prove that RSRP is NP-hard, we focus on heuristic solution approaches: we describe two heuristics and compare them with each other on (variants of) real-life instances of NS, the main Dutch passenger railway operator. Finally, to get further insight in the quality of the proposed heuristics, we also compare their outcomes with optimal solutions obtained by solving an existing rolling stock circulation model. http://repub.eur.nl/res/pub/19445/ 2010-05-11T00:00:00Z The question of delay management is whether trains should wait for a delayed feeder train or should depart on time. In classical delay management models passengers always take their originally planned route. In this paper, we propose a model where re-routing of passengers is incorporated. To describe the problem we represent it as an event-activity network similar to the one used in classical delay management, with some additional events to incorporate origin and destination of the passengers. We present an integer programming formulation of this problem. Furthermore, we discuss the variant in which we assume fixed costs for maintaining connections and we present a polynomial algorithm for the special case of only one origin-destination pair. Finally, computational experiments based on real-world data from Netherlands Railways show that significant improvements can be obtained by taking the re-routing of passengers into account in the model. http://repub.eur.nl/res/pub/18255/ 2010-02-23T00:00:00Z In the oil industry, different oil components are blended in a refinery to fuel products. These products are transported to different harbors by ship. Due to the limited storage capacity at the harbors and the undesirability of a stock-out, inventory levels at the harbors have to be taken into account during the construction of the ship routes. In this paper, we give a detailed description of this problem, which we call the ship routing problem with multiple products and inventory constraints. Furthermore, we formulate this problem as a generalized set-covering problem, and we present a Branch-and-Price algorithm to solve it. The pricing problems have a very complex nature. We discuss a dynamic programming algorithm to solve them to optimality. http://repub.eur.nl/res/pub/17524/ 2009-12-17T00:00:00Z 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. http://repub.eur.nl/res/pub/16746/ 2009-09-15T00:00:00Z Railway operations are disrupted frequently, e.g. the Dutch railway network experiences about three large disruptions per day on average. In such a disrupted situation railway operators need to quickly adjust their resource schedules. Nowadays, the timetable, the rolling stock and the crew schedule are recovered in a sequential way. In this paper, we model and solve the crew rescheduling problem with retiming. This problem extends the crew rescheduling problem by the possibility to delay the departure of some trains. In this way we partly integrate timetable adjustment and crew rescheduling. The algorithm is based on column generation techniques combined with Lagrangian heuristics. In order to prevent a large increase in computational time, retiming is allowed only for a limited number of trains where it seems very promising. Computational experiments with real-life disruption data show that, compared to the classical approach, it is possible to find better solutions by using crew rescheduling with retiming. http://repub.eur.nl/res/pub/16070/ 2009-06-01T00:00:00Z This paper is about a marketing decision support system in the movie industry. The decision support system of interest is a model that generates weekly movie schedules in a multiplex movie theater. A movie schedule specifies, for each day of the week, on which screen(s) different movies will be played, and at which time(s). The model integrates elements from marketing (the generation of demand figures) with approaches from operations research (the optimization procedure). Therefore, it consists of two parts: (i) conditional forecasts of the number of visitors per show for any possible starting time, and (ii) a scheduling procedure that quickly finds a near optimal schedule (which can be demonstrated to be close to the optimal schedule). To generate this schedule, we formulate the "movie scheduling problem" as a generalized set partitioning problem. The latter is solved with an algorithm based on column generation techniques. We tested the combined demand forecasting/schedule optimization procedure in a multiplex in Amsterdam, generating movie schedules for fourteen weeks. The proposed model not only makes movie scheduling easier and less time consuming, but also generates schedules that attract more visitors than current "intuition-based" schedules. http://repub.eur.nl/res/pub/18654/ 2009-06-01T00:00:00Z This paper describes a method for solving the cyclic crew rostering problem (CCRP). This is the problem of cyclically ordering a set of duties for a number of crew members, such that several complex constraints are satisfied and such that the quality of the obtained roster is as high as possible. The described method was tested on a number of instances of NS, the largest operator of passenger trains in the Netherlands. These instances involve the generation of rosters for groups of train drivers or conductors of NS. The tests show that high quality solutions for practical instances of the CCRP can be generated in an acceptable amount of computing time. Finally, we describe an experiment where we constructed rosters in an automatic way for a group of conductors. They preferred our—generated—rosters over their own manually constructed rosters. http://repub.eur.nl/res/pub/18487/ 2009-02-01T00:00:00Z Given a set of timetabled tasks, the multi-depot vehicle scheduling problem consists of determining least-cost schedules for vehicles assigned to several depots such that each task is accomplished exactly once by a vehicle. In this paper, we propose to compare the performance of five different heuristics for this well-known problem, namely, a truncated branch-and-cut method, a Lagrangian heuristic, a truncated column generation method, a large neighborhood search heuristic using truncated column generation for neighborhood evaluation, and a tabu search heuristic. The first three methods are adaptations of existing methods, while the last two are new in the context of this problem. Computational results on randomly generated instances show that the column generation heuristic performs the best when enough computational time is available and stability is required, while the large neighborhood search method is the best alternative when looking for good quality solutions in relatively fast computational times. http://repub.eur.nl/res/pub/18643/ 2009-02-01T00:00:00Z In December 2006, Netherlands Railways introduced a completely new timetable. Its objective was to facilitate the growth of passenger and freight transport on a highly utilized railway network and improve the robustness of the timetable, thus resulting in fewer operational train delays. Modifications to the existing timetable, which was constructed in 1970, were not an option; additional growth would require significant investments in the rail infrastructure. Constructing a railway timetable from scratch for about 5,500 daily trains was a complex problem. To support this process, we generated several timetables using sophisticated operations research techniques. Furthermore, because rolling-stock and crew costs are principal components of the costs of a passenger railway operator, we used innovative operations research tools to devise efficient schedules for these two resources. The new resource schedules and the increased number of passengers resulted in an additional annual profit of 40 million ($60 million); the additional revenues generated approximately 10 million of this profit. We expect this profit to increase to 70 million ($105 million) annually in the coming years. However, the benefits of the new timetable for the Dutch society as a whole are much greater: more trains are transporting more passengers on the same railway infrastructure, and these trains are arriving and departing on schedule more than they ever have in the past. In addition, the rail transport system will be able to handle future transportation demand growth and thus allow cities to remain accessible to more people. Therefore, we expect that many will switch from car transport to rail transport, thus reducing the emission of greenhouse gases. http://repub.eur.nl/res/pub/14423/ 2008-12-19T00:00:00Z The Dutch railway network experiences about three large disruptions per day on average. In this paper, we present an algorithm to reschedule the crews when such a disruption occurs. The algorithm is based on column generation techniques combined with Lagrangian heuristics. Since the number of duties is very large in practical instances, we first define a core problem of tractable size. If some tasks remain uncovered in the solution of the core problem, we perform a neighborhood exploration to improve the solution. Computational experiments with real-life instances show that our method is capable of producing good solutions within a couple of minutes of Computation time. http://repub.eur.nl/res/pub/13767/ 2008-11-10T00:00:00Z In December 2006, Netherlands Railways introduced a completely new timetable. Its objective was to facilitate the growth of passenger and freight transport on a highly utilized railway network, and improve the robustness of the timetable resulting in less train delays in the operation. Further adjusting the existing timetable constructed in 1970 was not option anymore, because further growth would then require significant investments in the rail infrastructure. Constructing a railway timetable from scratch for about 5,500 daily trains was a complex problem. To support this process, we generated several timetables using sophisticated operations research techniques, and finally selected and implemented one of these timetables. Furthermore, because rolling-stock and crew costs are principal components of the cost of a passenger railway operator, we used innovative operations research tools to devise efficient schedules for these two resources. The new resource schedules and the increased number of passengers resulted in an additional annual profit of 40 million euros ($60 million) of which about 10 million euros were created by additional revenues. We expect this to increase to 70 million euros ($105 million) annually in the coming years. However, the benefits of the new timetable for the Dutch society as a whole are much greater: more trains are transporting more passengers on the same railway infrastructure, and these trains are arriving and departing on schedule more than they ever have in the past. In addition, the rail transport system will be able to handle future transportation demand growth and thus allow cities to remain accessible. Therefore, people can switch from car transport to rail transport, which will reduce the emission of greenhouse gases. http://repub.eur.nl/res/pub/14596/ 2008-10-17T00:00:00Z 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. http://repub.eur.nl/res/pub/19251/ 2007-07-01T00:00:00Z 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 re-scheduling 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 http://repub.eur.nl/res/pub/10345/ 2007-06-21T00:00:00Z This paper addresses the Rolling Stock Balancing Problem (RSBP). This problem arises at a passenger railway operator when the rolling stock has to be re-scheduled due to changing circumstances. These problems arise both in the planning process and during operations. The RSBP has as input a timetable and a rolling stock schedule where the allocation of the rolling stock among the stations does not fit to the allocation before and after the planning period. The problem is then to correct these off-balances, leading to a modified schedule that can be implemented in practice. For practical usage of solution approaches for the RSBP, it is important to solve the problem quickly. Therefore, the focus is on heuristic approaches. In this paper, we describe two heuristics and compare them with each other on some (variants of) real-life instances of NS, the main Dutch passenger railway operator. Finally, to get some insight in the quality of the proposed heuristics, we also compare their outcomes with optimal solutions obtained by solving existing rolling stock circulation models. http://repub.eur.nl/res/pub/10346/ 2007-06-21T00:00:00Z In this paper we describe Operations Research (OR) models and techniques that can be used for determining (cyclic) railway timetables. We discuss the two aspects of railway timetabling: ($i$) the determination of arrival and departure times of the trains at the stations and other relevant locations such as junctions and bridges, and ($ii$) the assignment of each train to an appropriate platform and corresponding inbound and outbound routes in every station. Moreover, we discuss robustness aspects of both subproblems. http://repub.eur.nl/res/pub/10093/ 2007-05-11T00:00:00Z This paper describes a model that generates weekly movie schedules in a multiplex movie theater. A movie schedule specifies within each day of the week, on which screen(s) different movies will be played, and at which time(s). The model consists of two parts: (i) conditional forecasts of the number of visitors per show for any possible starting time; and (ii) an optimization procedure that quickly finds an almost optimal schedule (which can be demonstrated to be close to the optimal schedule). To generate this schedule we formulate the so-called movie scheduling problem as a generalized set partitioning problem. The latter is solved with an algorithm based on column generation techniques. We have applied this combined demand forecasting /schedule optimization procedure to a multiplex in Amsterdam where we supported the scheduling of fourteen movie weeks. The proposed model not only makes movie scheduling easier and less time consuming, but also generates schedules that would attract more visitors than the current ‘intuition-based’ schedules. http://repub.eur.nl/res/pub/10069/ 2007-05-10T00:00:00Z This paper describes a model that generates weekly movie schedules in a multiplex movie theater. A movie schedule specifies within each day of the week, on which screen(s) different movies will be played, and at which time(s). The model consists of two parts: (i) conditional forecasts of the number of visitors per show for any possible starting time; and (ii) an optimization procedure that quickly finds an almost optimal schedule (which can be demonstrated to be close to the optimal schedule). To generate this schedule we formulate the so-called movie scheduling problem as a generalized set partitioning problem. The latter is solved with an algorithm based on column generation techniques. We have applied this combined demand forecasting /schedule optimization procedure to a multiplex in Amsterdam where we supported the scheduling of fourteen movie weeks. The proposed model not 2 only makes movie scheduling easier and less time consuming, but also generates schedules that would attract more visitors than the current ‘intuition-based’ schedules. http://repub.eur.nl/res/pub/8527/ 2007-01-31T00:00:00Z This paper deals with disruption management in passenger railway transportation. In the disruption management process, many actors belonging to different organizations play a role. In this paper we therefore describe the process itself and the roles of the different actors. Furthermore, we discuss the three main subproblems in railway disruption management: timetable adjustment, and rolling stock and crew re-scheduling. Next to a general description of these problems, we give an overview of the existing literature and we present some details of the specific situations at DSB S-tog and NS. These are the railway operators in the suburban area of Copenhagen, Denmark, and on the main railway lines in the Netherlands, respectively. Since not much research has been carried out yet on Operations Research models for disruption management in the railway context, models and techniques that have been developed for related problems in the airline world are discussed as well. Finally, we address the integration of the re-scheduling processes of the timetable, and the resources rolling stock and crew. http://repub.eur.nl/res/pub/8069/ 2006-11-07T00:00:00Z Given a set of timetabled tasks, the multi-depot vehicle scheduling problem is a well-known problem that consists of determining least-cost schedules for vehicles assigned to several depots such that each task is accomplished exactly once by a vehicle. In this paper, we propose to compare the performance of five different heuristic approaches for this problem, namely, a heuristic \\mip solver, a Lagrangian heuristic, a column generation heuristic, a large neighborhood search heuristic using column generation for neighborhood evaluation, and a tabu search heuristic. The first three methods are adaptations of existing methods, while the last two are novel approaches for this problem. Computational results on randomly generated instances show that the column generation heuristic performs the best when enough computational time is available and stability is required, while the large neighborhood search method is the best alternative when looking for a compromise between computational time and solution quality. http://repub.eur.nl/res/pub/15284/ 2006-09-01T00:00:00Z A railway system needs a substantial amount of maintenance. To prevent unexpected breakdowns as much as possible, preventive maintenance is required. In this paper we discuss the preventive maintenance scheduling problem (PMSP), where (short) routine activities and (long) unique projects have to be scheduled in a certain period. To reduce costs and inconvenience for the travellers and operators, these activities should be scheduled together as much as possible. We present two versions of the PMSP, one with fixed intervals between two consecutive executions of the same routine work, and one with only a maximum interval. Apart from giving a math programming formulation for the PMSP and for its extension we also present some heuristics. In addition, we compare the performance of these heuristics with the optimal solution using some randomly generated instances http://repub.eur.nl/res/pub/14389/ 2006-06-16T00:00:00Z 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. http://repub.eur.nl/res/pub/7248/ 2006-01-24T00:00:00Z This paper describes a method for solving the cyclic crew rostering problem (CCRP). This is the problem of cyclically ordering a set of duties for a number of crew members, such that several complex constraints are satisfied and such that the quality of the obtained roster is as high as possible. The described method was tested on a number of instances of NS, the largest operator of passenger trains in the Netherlands. These instances involve the generation of rosters for groups of train drivers or conductors of NS. The tests show that high quality solutions for practical instances of the CCRP can be generated in an acceptable amount of computing time. Finally, we describe an experiment where we constructed rosters in an automatic way for a group of conductors. They preferred our - generated - rosters over their own manually constructed rosters. http://repub.eur.nl/res/pub/7149/ 2005-12-07T00:00:00Z 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. http://repub.eur.nl/res/pub/14173/ 2005-11-01T00:00:00Z In this paper we give an overview of state-of-the-art Operations Research models and techniques used in passenger railway transportation. For each planning phase (strategic, tactical and operational), we describe the planning problems arising there and discuss some models and algorithms to solve them. We do not only consider classical, well-known topics such as timetabling, rolling stock scheduling and crew scheduling, but we also discuss some recently developed topics such as shunting and reliability of timetables. Finally, we focus on several practical aspects for each of these problems at the largest Dutch railway operator, NS Reizigers. http://repub.eur.nl/res/pub/14399/ 2005-11-01T00:00:00Z This paper presents two different models and algorithms for integrated vehicle and crew scheduling in the multiple-depot case. The algorithms are both based on a combination of column generation and Lagrangian relaxation. Furthermore, we compare those integrated approaches with each other and with the traditional sequential one on randomly generated, as well as real-world, data instances for a suburban/extraurban mass transit system. To simulate such a transit system, we propose a new way of randomly generating data instances such that their properties are the same as for our real-world instances. http://repub.eur.nl/res/pub/14171/ 2005-05-01T00:00:00Z In this paper we introduce the problem of shunting passenger train units in a railway station. Shunting occurs whenever train units are temporarily not needed to operate a given timetable. We discuss several aspects of this problem and focus on two subproblems. We propose mathematical models for the problem and both subproblems, one of which is solved with a solution method based on column generation. Furthermore, we introduce a new efficient and speedy solution technique for pricing problems in column generation algorithms. Finally, we present computational results based on real-life instances from Netherlands Railways. http://repub.eur.nl/res/pub/2012/ 2005-04-28T00:00:00Z In this paper, we give an overview of state-of-the-art Operations Research models and techniques used in passenger railway transportation. For each planning phase (strategic, tactical and operational), we describe the planning problems arising there and discuss some models and algorithms to solve them. We do not only consider classical, well-known topics such as timetabling, rolling stock scheduling and crew scheduling, but we also discuss some recently developed topics as shunting and reliability of timetables. Finally, we focus on several practical aspects for each of these problems at the largest Dutch railway operator, NS Reizigers. http://repub.eur.nl/res/pub/1941/ 2005-04-07T00:00:00Z In this paper, we give an overview of state-of-the-art Operations Research models and techniques used in passenger railway transportation. For each planning phase (strategic, tactical and operational), we describe the planning problems arising there and discuss some models and algorithms to solve them. We do not only consider classical, well-known topics such as timetabling, rolling stock scheduling and crew scheduling, but we also discuss some recently developed topics as shunting and reliability of timetables. Finally, we focus on several practical aspects for each of these problems at the largest Dutch railway operator, NS Reizigers. http://repub.eur.nl/res/pub/14404/ 2004-11-01T00:00:00Z This paper presents a solution approach to the dynamic vehicle scheduling problem. This approach consists of solving a sequence of optimization problems, where we take into account different scenarios for future travel times. 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. 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 fast solution by standard optimization software. Results of a computational study with real-life data are presented, in which we compare different variants of our approach and perform a sensitivity analysis with respect to deviations of the actual travel times from estimated ones. http://repub.eur.nl/res/pub/1632/ 2004-09-22T00:00:00Z A railway system needs a substantial amount of maintenance. To prevent unexpected breakdowns as much as possible, preventive maintenance is required. In this paper we discuss the Preventive Maintenance Scheduling Problem (PMSP), where (short) routine activities and (long) unique projects have to be scheduled in a certain period. To reduce costs and inconvenience for the travellers and operators, these activities have to be scheduled as much as possible together. We present a mathematical formulation for this problem and some greedy heuristics to solve it fast. Moreover, we compare the performance of these heuristics with the optimal solution using some randomly generated instances. http://repub.eur.nl/res/pub/1204/ 2004-04-01T00:00:00Z 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. http://repub.eur.nl/res/pub/1182/ 2004-03-08T00:00:00Z 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. http://repub.eur.nl/res/pub/6779/ 2004-02-20T00:00:00Z Due to increased competition in the public transport market and the pressure on governments to cut expenses, increasing attention has been paid to cost reductions in public transportation. Since the main resources used in public transportation are vehicles and crews, producing efficient vehicle and crew schedules is an important issue. A sequential approach, i.e. vehicle scheduling followed by crew scheduling, does not guarantee an overall optimal solution. Therefore, integrated approaches are considered in this thesis. For different cases, mathematical models are presented and several algorithms are developed to solve these models. Computational tests demonstrate the quality of these algorithms. In addition to cost reductions, the reliability of the public transport services for the passengers is an important issue. The disadvantage of the traditional, static approach is that, when a delay occurs, the next trip performed by that vehicle and/or driver will often start late. Therefore, new delays can occur which may have a similar `snowball’ effect. A dynamic approach has been developed to prevent such an effect. http://repub.eur.nl/res/pub/1684/ 2003-02-17T00:00:00Z This paper presents two different models and algorithms for integrated vehicle and crew scheduling in the multiple-depot case. The algorithms are both based on a combination of column generation and Lagrangian relaxation. Furthermore, we compare those integrated approaches with each other and with the traditional sequential one on random generated as well as real-world data instances for a suburban/extra-urban mass transit system. To simulate such a transit system, we propose a new way of generating randomly data instances such that their properties are the same as for our real-world instances. http://repub.eur.nl/res/pub/1098/ 2003-01-01T00:00:00Z 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. http://repub.eur.nl/res/pub/221/ 2002-09-09T00:00:00Z In this paper we introduce the problem of shunting passenger train units in a railway station. Shunting occurs whenever train units are temporarily not necessary to operate a given timetable. We discuss several aspects of this problem and focus on two subproblems. We propose mathematical models for these subproblems together with a solution method based on column generation. Furthermore, a new efficient and speedy solution technique for pricing problems in column generation algorithms is introduced. Finally, we present computational results based on real life instances from Netherlands Railways. http://repub.eur.nl/res/pub/101/ 2001-07-03T00:00:00Z 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. http://repub.eur.nl/res/pub/40/ 2000-07-12T00:00:00Z This paper deals with a practical application of an integrated approach to vehicle and crew scheduling, that we have developed previously. Computational results have shown that our approach can be applied to problems of practical size. However, application of the approach to the actual problems that one encounters in practice, is not always straightforward. This is mainly due to the existence of particular constraints that can be regarded as \\house rules" of the public transport company under consideration. In this paper we apply our approach to problems of individual bus lines of the RET, the Rotterdam public transport company, where particular constraints should be satisfied. Furthermore, we investigate the impact of allowing drivers to change vehicle during a break. Currently, the rule at the RET is that such changeovers are only allowed in split duties; they are never allowed in other type of duties. We show that it is already possible to save crews if for the non-split duties, restricted changeovers are allowed. http://repub.eur.nl/res/pub/23/ 2000-05-19T00:00:00Z 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.