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Railway Delay Management with Passenger Rerouting Considering Train Capacity Constraints
Abstract
Delay management for railways is concerned with the question of whether a train should wait for a delayed feeder train or depart on time. The answer should not only depend on the length of the delay but also consider other factors, such as capacity restrictions. We present an optimization model for delay management in railway networks that accounts for capacity constraints on the number of passengers that a train can effectively carry. While limited capacities of tracks and stations have been considered in delay management models, passenger train capacity has been neglected in the literature so far, implicitly assuming an infinite train capacity. However, even in open systems where no seat reservation is required and passengers may stand during the journey if all seats are occupied, physical space is naturally limited, and the number of standing seats is constrained for passenger safety reasons. We present a mixed-integer nonlinear programming formulation for the delay management problem with passenger rerouting and capacities of trains. Our model allows the rerouting of passengers missing their connection due to delays or capacity constraints. We linearize the model in exact and approximate ways and experimentally compare the different approaches with the solution of a reference model from the literature that neglects capacity constraints. The results demonstrate that there is a significant impact of considering train capacity restrictions in decisions to manage delays.
... To compute delays, first the starting point of a train schedule has to be included by the parameter e for the planned arrival or departure times of an event e ∈ E arr ∪ E dep . The earliest possible arrival time for a passenger of type p ∈ P without delays, denoted by t p , can be computed in a preprocessing step with a shortest path algorithm (see König and Schön 2020 for an explicit formulation). The preprocessing model corresponds to the DM problem where all delays are set to zero, i.e., the preprocessing model only consists of a modified objective function (Eq. ...
... The complete model looks as follows (see e.g., Dollevoet et al. 2012;König and Schön 2020): ...
... The delay can spread through the network and repercussions will get visible in other parts of the network. In König and Schön (2020), the emergence of new connections due to delays is also possible, i.e., passengers can jump on late trains for which in an undelayed case no connection was planned. ...
Passengers traveling by train may need to change trains on their route. If the focal train of a passenger is late, the passenger might miss his connection and has to decide how to continue his trip. Delay management addresses the question whether the connecting train should wait (or not) for the delayed passengers. If the connecting train waits, delays would get transferred through the network. In literature, several works consider delays and their impact on railways and how to reschedule disturbed plans. We focus on works, aiming to minimize passenger inconvenience as it is done in delay management. In the last two decades, dozens of works considering the delay management problem have emerged, tackling the problem in different ways. In this paper, an overview on the existing literature is given, and a new classification is introduced. We provide a taxonomy scheme for railway problems at an operational level and show how the field of delay management fits to other parts of the planning process. Moreover, limitations of the delay management approaches are discussed and future research opportunities are suggested.
... Schasfoort et al. studied the real-time train assignment problem and modelled it as a mixed integer program that strove to minimize the total weighted delay of trains [49]. Königa and Schöna (2020) presented an optimization model for delay management in railway networks, taking limited capacities of tracks and stations into consideration [50]. Vansteenwegen et al. (2019) proposed a conflict prevention strategy for large and complex networks in real-time railway traffic management based on the analysis of the impact of the unexpected events such as overcrowded platforms or small mechanical defects can cause conflicts [51]. ...
... Schasfoort et al. studied the real-time train assignment problem and modelled it as a mixed integer program that strove to minimize the total weighted delay of trains [49]. Königa and Schöna (2020) presented an optimization model for delay management in railway networks, taking limited capacities of tracks and stations into consideration [50]. Vansteenwegen et al. (2019) proposed a conflict prevention strategy for large and complex networks in real-time railway traffic management based on the analysis of the impact of the unexpected events such as overcrowded platforms or small mechanical defects can cause conflicts [51]. ...
Both train rescheduling and station track assignment have become hot topics in recent years. It is fundamentally important to do the rescheduling and track assignment work at the same time to avoid the feasibility risk of the re‐scheduled timetable. The purpose of this paper is to design an integrated model for train rescheduling and track assignment in order to provide an integrative plan for the trains to run on the railway sections and go through stations. Based on the existing train rescheduling model, the model is designed by adding the constraints and the optimization goal of track assignment. The goal of track assignment is to maximize the equilibrium of the track usage time, and the constraint is that two trains cannot occupy a same track at the same time. An artificial bee colony algorithm is used to solve the model to get the operation plan. A computing experiment was carried out to prove the effectiveness of the model and the efficiency of the algorithm. The approach presented in this paper can provide a reference for the developers of a railway dispatching system.
... Despite the progress made in both operationoriented and passenger-oriented research, there exists a notable gap in the literature addressing passenger connections, particularly regarding the optimization of platform selection during train rerouting. Existing studies, such as those by Dollevoet et al. [26] and König and Schön [27], have explored the possibility of rerouting passengers in the network to let them reach to their destinations in case of disruption, but overlook train rerouting to different platforms within the station to constrain minimum connection time. However, optimizing platform selection during train rerouting can help prevent delay propagation: if the chosen platforms allow for a short minimum connection time, the receiving train may experience less waiting time when the feeder train is VOLUME 11, 2023 3 This article has been accepted for publication in IEEE Access. ...
This paper addresses the real-time Railway Traffic Management Problem (rtRTMP), which involves adjusting train timetables during perturbations. Perturbations in railway networks often lead to significant delays, necessitating strategies to minimize their propagation. An important objective of traffic management is to facilitate passenger transfers through connecting trains, which may become difficult when traffic is disturbed. Pursuing this objective, the paper focuses on mitigating train delays by reducing connection times during transfers without compromising connections. To achieve this, we extend an existing Mixed-Integer Linear Programming (MILP) formulation for the rtRTMP by introducing two alternative enhancements. Moreover, we pursue the same delay mitigation by extending an Ant Colony Optimization algorithm for the Train Routing Selection Problem (TRSP): this problem reduces the number of alternative routes to be considered for trains, making rtRTMP instances tractable. We assess the efficiency of the proposed enhancements in reducing the total train delay while preserving passenger connections in multiple instances representing traffic in the Lille-Flandres station control area, located in the north of France. The results demonstrate that the integration of these enhancements, in both the TRSP and the rtRTMP, results in a significant reduction in delay propagation.
... microclimatic conditions as well as strong opinions about urban greenery itself. Further, we wished to avoid the distortion effect of participants prioritising some unrelated factor such as improvements in punctuality (jso/dpa, 2022;König & Schön, 2021) over the issue of greenery. ...
The increasing density of urban spaces and buildings is undermining public health. To compensate, there is a growing trend towards biophilic design, including at one of the most frequented and highly functional sites: railway stations. Previous studies have confirmed the economic feasibility of station greenery and users' preference for this but also their reluctance to pay for greenery compared to other services. One research gap is the lack of consideration given to the full range and dose-response correlation of urban cultural ecosystem services provided by station greenery. To fill this gap, we present the development and implementation of a method using static 2D representations of virtual reality scenes generated from a digital twin. In a between-subjects experiment (N = 352), participants were randomly assigned to assess one of three levels of greenery by means of a six-item semantic differential. Supported by statistically significant differences between groups, we could identify improvements in well-being, aesthetics, stress reduction, perception of safety, psychological noise reduction and identity. Further, women were found to prefer higher levels of greenery than men. Based on our results, we recommend applying the method to evaluate planning options and that (more) greenery be introduced at metropolitan stations as part of biophilic design.
... Regarding the studies related to the modeling of passengers' behaviors, Uematsu et al. [4], Landex et al. [5], Dollevoet et al. [6], Jian et al. [7], Iwakura et al. [8], Kobayashi et al. [9] [10], Kunimatsu et al. [11], Corman [12] and König et al. [13] developed their original simulation models and conducted train delay simulations. Additionally, Kanai et al. [14] proposed an optimal train delays management from passengers' viewpoints considering the whole railway network. ...
... This assumption prohibits the usage of such approaches in the case of large passenger flows. In the literature, only a few approaches include the train capacity, for the rolling stock rescheduling problem (Cadarso, Marín, and Maróti 2013;Kroon, Maróti, and Nielsen 2015), for the train (re-)scheduling problem (Niu, Zhou, and Gao 2015;Binder, Maknoon, and Bierlaire 2017;Meng et al. 2020), and recently for the delay management problem (König and Schön 2020). To handle large passenger flows, the consideration of the train capacity and the free-split of passengers in each group is essential. ...
This paper focuses on adjusting the offline-planned schedules for urban rail networks in the case of large passenger demand. We simultaneously reschedule train services, adjust rolling stock plans, and find the best route for passengers in the updated train schedule. The goal is to improve transport performance for passengers and to balance it with operating cost, while respecting operational constraints. A mixed-integer nonlinear programming (MINLP) model is first proposed. Approximate and exact methods are further introduced to reformulate the nonlinear term in the MINLP model, resulting in mixed-integer linear programming (MILP) models. In the models, emergency train services can be added if necessary. Short-turning and stop-pattern adaptation can speed up the circulation of rolling stock (i.e. metro vehicles). Passengers with the same characteristics are gathered into a group, and the passengers of a group may follow different routes, depending on resource availability. Experimental results on a small-scale case study demonstrate the better performance of three exact reformulation methods, i.e. they can find the first feasible solution much faster (within 180 s) and obtain solutions with much higher quality within a certain computation time, in comparison with the other proposed approximate and exact methods. Moreover, the results identify the improved performance of the operation for passengers, up to 13% improvement when properly shortening the headway time and up to 69% if operating emergency trains.
... There is a large amount of literature on train timetabling and scheduling problems for railway transportation systems (Caprara et al., 2002;Zhou and Zhong, 2005;D'Ariano et al., 2007;Liu and Kozan, 2009;Mesa et al., 2014;Pellegrini et al., 2014;Fischetti and Monaci, 2017;Veelenturf et al., 2017;Corman et al., 2017;König and Schön, 2021). An overview on different models and solution methodologies is given by Cordeau et al. (1998); Cacchiani and Toth (2012); Corman and Meng (2014). ...
With the expansion of urban rail networks and the increase of passengers demand, the coordination of strongly connected lines becomes more and more important, because passengers transfer several times during their trips and major transfer stations in the rail network often suffer from over-crowdedness, especially during peak-hours. In this paper, we study the optimization of coordinated train timetables for an urban rail network, which is a tactical timetabling problem and includes several operational constraints and time-dependent passenger-related data. We propose a mathematical formulation with the objective of minimizing the crowdedness of stations during peak hours to synchronously generate the optimal coordinated train timetables. By introducing several sets of passenger flow variables, the timetable coordination problem is formulated as a mixed-integer linear programming problem, that is possible to solve to optimum. To capture the train carrying capacity constraints, we explicitly incorporate the number of in-vehicle passengers in the modelling framework by considering the number of boarding and alighting passengers as passenger flow variables. To improve the computational efficiency of large-scale instances, we develop an Adaptive Large Neighborhood Search (ALNS) algorithm with a set of destroying and repairing operators and a decomposition-based ALNS algorithm. Real-world case studies based on the operational data of Beijing urban rail network are conducted to verify the effectiveness of timetable coordination. The computational results illustrate that the proposed approaches reduce the level of crowdedness of metro stations by around 8% in comparison with the current practical timetable of the investigated Beijing urban rail network.
... Passengers selected rail transport over individual passenger car transport. This directly impacted a decrease of the transport congestion phenomenon (Bai et al., 2020;König and Schön, 2020). ...
Purpose
Omnichannel sales have provided new impetus for the development of catering merchants. The authors thus focus on how catering merchants should manage capacities at the ordering, production and delivery stages to meet customers’ needs in different channels under third-party platform delivery and merchant self-delivery. This is of great significance for the development of the omnichannel catering industry.
Design/methodology/approach
This paper formulates the capacity decisions of omnichannel catering merchants under the third-party platform delivery and merchant self-delivery mode. The authors mainly use queuing theory to analyze the queuing behavior of online and offline customers, and the impact of waiting time on customer shopping behavior. In addition, the authors also characterize the merchant’s capacity by the rate in queuing model.
Findings
The authors find that capacities at ordering stage and food production stage are composed of base capacities and safety capacities, but the delivery capacities only have the latter. And in the self-delivery mode, merchants can develop higher safety capacities by charging delivery fees. The authors prove that regardless of the delivery mode, omnichannel sales can bring higher profits to merchants by integrating demand.
Originality/value
The authors focus on analyzing the capacity management of omnichannel catering merchants at the ordering, production and delivery stages. And the authors also add the delivery process into the omnichannel for analysis, so as to solve the problem of capacity decision-making under different delivery modes. The management of delivery capacity and its impact on other stages’ capacities are not covered in other literature studies, which is one of the main innovations of this paper.
The paper focuses on the possible capacity improvement of a segment between two stations of a single-track railway line by using of extended station switch point area and on methods assessing the capacity of such railway infrastructure, where a part of a single-track line segment being not equipped itself with e.g. line blocks becomes partially double-tracked. These methods can extend state-or-art general capacity assessment methods and allow more detailed assessment in this specific case. The research was conducted on three levels. The first is only analytic, the second is based on the developed own mesoscopic stochastic simulation model and the third is based on a stochastic microsimulation model elaborated by using the OpenTrack software. Divided solutions on each level can provide assessments with different demands on computation and model development. Stepwise solutions at the individual level may rationalize capacity assessment.
This study presents a comprehensive review of different problem models for managing railway operations by problem-type classification. Railway terminology was used to identify the studies that encompass the existing body of knowledge. The 28 articles analyzed showed that existing studies are focused on the individual schedule components, such as rolling stock, schedules, crews, and passengers. Few studies have adopted a broader scope by covering several of those components. Two of the most popular approaches include the integer linear program and the mixed integer linear program variant. The difference between them is that integer programming uses discrete decision-making variable data, while mixed integer programming also admits continuous variable data. In contrast, few studies involve combining computational algorithms with human knowledge-based approaches. This analysis reveals that the most significant variables for managing disruptive events are related to verifying suppressed circulation and the discrete events of real-time traffic, such as departures and arrivals at stations.
In public transport, e.g., railways, crowding is of major influence on passenger satisfaction and also on system performance. We study the passenger-oriented traffic control problem by means of integrated optimization, particularly considering the crowding effects on passenger route choices and on train traffic. The goal is to find the system optimum solution by adapting train schedules and rerouting passengers. A mixed-integer nonlinear programming (MINLP) model is proposed, identifying the train orders and departure and arrival times, as well as finding the best route for passengers, with the objective of minimizing passenger disutility and train delay. In the model, we allow free splits of the passengers in a group onto different routes and reasonable passenger transfers between trains. We value train crowding by using time multiplier, which is defined as a piecewise constant function of the train crowding ratio (also called load factor), indicating that passengers perceive a longer travel time on a more crowded train. Moreover, we assume variations of the minimum train dwell time, caused by the alighting and boarding passengers. The nonlinear terms in the MINLP model are linearized by using an exact reformulation method and three transformation properties, resulting in an equivalent mixed-integer linear programming (MILP) model. In the experiences, we adopt a real-world railway network, i.e., the urban railway network in Zürich city, to examine the proposed approach. The results demonstrate the effectiveness of the model. The results show that, by considering the crowding effects, some passengers are forced to choose the routes that are less crowded but have larger travel/delay times, which leads to the improved passenger comfort and makes the planned train timetable less affected (in terms of delays). We also find that flexibility in train schedules brings more possibilities to serve better the passengers. Moreover, it is observed that if the train dwell time is highly sensitive to the alighting and boarding passengers, then the transport network will become vulnerable and less reliable, which should be avoided in real operations.
As a tour agency plans a tour schedule with rail transport, it is necessary to evaluate the capacity of the rail transport network to determine the number of passengers in the tour group that can be served. This study develops a stochastic rail transport network (SRTN) according to the train timetable and tour schedule, such that each available train’s loading capacity (that is, the number of cars) may be fully and partially reserved for other requests. Under the consideration of a tour group including q passengers, the network reliability accordingly means the probability that the q-passenger group can successfully depart from a source station for a sink station via the SRTN. In addition, the passengers might not punctually change trains at a transfer station owing to train arrival delay. Because the travel agency cannot control the situation of train arrival delay while planning a tour schedule, the uncertainty of train arrival delay results in an acceptable delay probability that the passengers traveling by non-direct trains can successfully change trains and this must be considered for the network reliability evaluation. An algorithm integrating the minimal paths and the modified Recursive Sum of Disjoint Product are integrated to solve the addressed problem. A real case of a rail transport network in Taiwan is adopted to demonstrate the applicability of the proposed approach. The travel agency can view the network reliability as a reference indicator to evaluate the number of passengers in the group that can be served.
We propose a novel algorithm for the capacitated passenger assignment problem in public transportation where exogenous priority lists define the order in which passengers are assigned. Separating explicitly theses rules from the assignment procedure allows for a great deal of flexibility to model various priority rules. When the actual rules are endogenous, the framework can easily be embedded in a fixed-point specification. Computational experiments are performed on a realistic case study based on the morning rush hours of the timetable of Canton Vaud, Switzerland. The algorithm is able to assign the demand in very low computational times. The results provide evidences that the ordering of the passengers does not have a significant impact on aggregate performance indicators (such as average delay and level of unsatisfied demand), but that the variability at the individual passenger level is substantial. Thanks to its flexibility, our framework can easily be implemented by a railway operator who wishes to evaluate the effects of different policies in terms of passenger priorities.
Trains movements on a railway network are regulated by official timetables. Deviations and delays occur quite often in practice, demanding fast rescheduling and rerouting decisions in order to avoid conflicts and minimize overall delay. This is the real-time train dispatching problem. In contrast with the classic "holistic" approach, we show how to decompose the problem into smaller sub-problems associated with the line and the stations. This decomposition is the basis for a master-slave solution algorithm, in which the master problem is associated with the line and the slave problem is associated with the stations. The two sub-problems are modeled as mixed integer linear programs, with specic sets of variables and constraints. Similarly to the classical Benders' decomposition approach, slave and master communicate through suitable feasibility cuts in the variables of the master. Extensive tests on real-life instances from single and double-track lines in Italy showed significant improvements over current dispatching performances. A decision support system based on this exact approach has been in operation in Norway since February 2014, and represents one of the first operative applications of mathematical optimization to train dispatching.
We introduce the decision support tool PANDA (Passenger Aware Novel Dispatching Assistance). Our web-based tool is designed to provide train dispatchers with detailed real-time information about the current passenger flow and the multi-dimensional impact of waiting decisions in case of train delays. After presenting the algorithmic background and PANDA’s main features, we show how it can be utilized in a typical use case scenario for train dispatchers. Besides its practical value for train dispatchers, the framework can be used to systematically study scientific questions. Exemplarily, we use our software to experimentally analyse the influence of waiting decisions on realistic passenger flows of Deutsche Bahn. In a first experiment, we evaluate PANDA’s potential benefit for passengers. Our findings indicate that a remarkable reduction in total delay might be possible in comparison to current practice. In two additional experiments, we investigate the timing aspect of waiting decisions. Our observations suggest that the timing of waiting decisions is of crucial importance and that a carefully implemented early rerouting strategy has a significant potential to reduce resulting delays of passengers.
Train movements in railway lines are generally controlled by human dispatchers. As disruptions often occur, dispatchers take real-time scheduling and routing decisions in the attempt to minimize deviations from the offi cial timetable. This optimization problem is called Train Dispatching. We represent it as a Mixed Integer Linear Programming model, and solve it by a Benders'-like decomposition within a suitable master/slave scheme. Interestingly, the master and the slave problems correspond to a macroscopic and microscopic representation of the railway, recently exploited in heuristic approaches to the problem. The decomposition,
along with some new modeling ideas, allowed us to solve real-life instances of practical interest to optimality in short computing time. Automatic dispatching systems based on our macro/micro decomposition - in which both master and slave are solved heuristically - have been in operation in several Italian lines since
year 2011. The exact approach described in this paper outperforms such systems on our test-bed of real-life instances. Furthermore, a system based on another version of the exact decomposition approach has been in operation since February 2014 on a line in Norway.
The effects of high passenger density at bus stops, at rail stations, inside buses and trains are diverse. This paper examines the multiple dimensions of passenger crowding related to public transport demand, supply and operations, including effects on operating speed, waiting time, travel time reliability, passengers' wellbeing, valuation of waiting and in- vehicle time savings, route and bus choice, and optimal levels of frequency, vehicle size and fare. Secondly, crowding externalities are estimated for rail and bus services in Sydney, in order to show the impact of crowding on the estimated value of in-vehicle time savings and demand prediction. Using Multinomial Logit (MNL) and Error Components (EC) mod- els, we show that alternative assumptions concerning the threshold load factor that trig- gers a crowding externality effect do have an influence on the value of travel time (VTTS) for low occupancy levels (all passengers sitting); however, for high occupancy lev- els, alternative crowding models estimate similar VTTS. Importantly, if demand for a public transport service is estimated without explicit consideration of crowding as a source of dis- utility for passengers, demand will be overestimated if the service is designed to have a number of standees beyond a threshold, as analytically shown using a MNL choice model. More research is needed to explore if these findings hold with more complex choice models and in other contexts.
Railway traffic is operated according to a detailed schedule, specifying for each train its path through the network plus arrival and departure times at its scheduled stops. During daily operations, disturbances perturb the plan and dispatchers take action in order to keep operations feasible and to limit delay propagation. This article presents a thorough assessment of the possible application of an optimization-based framework for the evaluation of different timetables and proactive railway traffic management over a large network, considering stochastic disturbances. Two types of timetables are evaluated in detail: “ regular” and “ shuttle” timetables. The former is the regular plan of operations for normal traffic conditions, while the latter plan is designed to be robust against widespread disturbances, such as adverse weather, track blockage, and other operational failures. A test case is presented on a large Dutch railway network with heavy traffic, for which we compute by microsimulation detailed train movements at the level of block signals and at a precision of seconds. When comparing the timetables, a trade-off is found between the minimization of train delays, due to potential conflicts and due to delayed rolling stock and crew duties, and the minimization of passenger travel time between given origins and destinations.
Deregulation has opened up many opportunities and challenges in the transportation industry—opportunities to increase profits and challenges to keep from being outflanked by competition. A goal of particular interest to the scheduled airlines is to set prices more adaptively and to change them more rapidly. A difficult problem arises when many passengers with different itineraries compete for a limited number of seats on a single-flight segment. The problem is complicated by the existence of different fare classes, many flight segments, and different demands across time. For any given set of prices, flight-segment capacities, and passenger-carrying demand, there is some number of passengers at each fare class on each flight segment that will optimize revenue. Knowledge of such an optimum can be used not only in pricing analysis but also in setting policies to influence the passenger fare-class mix so that the optimum will be more nearly achieved in actual practice.
We describe a method for identifying the optimum fare-class mix and the design of a system for that purpose which we built and implemented for Frontier Airlines. The recognition and formulation of the problem has become even more important as the number of aircraft in the sky has been reduced and the competition for a limited number of seats has become more intense.
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.
We consider (small) disturbances of a railway system. In case of such delays, one has to decide if connecting trains should
wait for delayed feeder trains or if they should depart on time, i.e. which connections should be maintained and which can
be dropped. Finding such wait-depart decisions (minimizing e.g. the average delay of the passengers) is called the delay management problem. In the literature, the limited capacity of the tracks (meaning that no two trains can use the same piece of track at the
same time) has so far been neglected in the delay management problem. In this paper we present models and first results integrating
these important constraints. We develop algorithmic approaches that have been tested at a real-world example provided by Deutsche Bahn AG.
The delay management problem deals with reactions in case of delays in public transportation. More specifically, the aim is to decide if connecting vehicles should wait for delayed feeder vehicles or if it is better to depart on time. As objective we consider the convenience over all customers, expressed as the average delay of a customer when arriving at his or her destination.
We present path-based and activity-based integer programming models for the delay management problem and show the equivalence of these formulations. Based on these, we present a simplification of the (cubic) activity-based model which results in an integer linear program. We identify cases in which this linearization is correct, namely if the so-called never-meet property holds. We analyze this property using real-world railway data. Finally, we show how to find an optimal solution in linear time if the never-meet property holds.
Delay management is an important issue in the daily operations of any railway company. The task is to update the planned timetable to a disposition timetable in such a way that the inconvenience for the passengers is as small as possible. The two main decisions that have to be made in this respect are the wait-depart decisions, to decide which connections should be maintained in case of delays, and the priority decisions, which determine the order in which trains are allowed to pass a specific piece of track. The latter are necessary to take the limited capacity of the track system into account. While the wait-depart decisions have been intensively studied in the literature, the priority decisions in the capacitated case have been neglected so far in delay management optimization models.
In the current paper, we add the priority decisions to the integer programming formulation of the delay management problem and are hence able to deal with the capacitated case. The corresponding constraints are disjunctive constraints leading to cycles in the resulting event-activity network. Nevertheless, we are able to derive reduction techniques for the network that enable us to extend the formulation of the never-meet property from the uncapacitated delay management problem to the capacitated case. We then use our results to derive exact and heuristic solution procedures for solving the delay management problem.
The results of the algorithms are evaluated both from a theoretical and a numerical point of view. The latter has been done within a case study using the railway network in the region of Harz, Germany.
Traffic controllers regulate railway traffic by sequencing train movements and setting routes with the aim of ensuring smooth train behaviour and limiting, as much as possible, train delays. In this paper, we describe the implementation of a real-time traffic management system, called ROMA (Railway traffic Optimization by Means of Alternative graphs), to support controllers in the everyday task of managing disturbances. We make use of a branch-and-bound algorithm for sequencing train movements, while a local search algorithm is developed for rerouting optimization purposes. The compound problem of routing and sequencing trains is approached iteratively, computing an optimal train sequencing for given train routes and then improving this solution by locally rerouting some trains. An extensive computational study is carried out, based on a dispatching area of the Dutch railway network. We study practical size instances, and include in the model important operational constraints, including rolling stock and passenger connections. Different types of disturbances are analysed, including train delays and blocked tracks. Comparison with common dispatching practice shows the high potential of the system as an effective support tool to improve punctuality.
Constructing a profitable schedule is of utmost importance to an airline because its profitability is critically influenced by its flight offerings. We focus our attention on the steps of the airline schedule planning process involving schedule design and fleet assignment. Airline schedule design involves determining when and where to offer flights such that profits are maximized, and fleet assignment involves assigning aircraft types to flight legs to maximize revenue and minimize operating cost. We present integrated models and solution algorithms that simultaneously optimize the selection of flight legs for and the assignment of aircraft types to the selected flight legs. Preliminary results, based on data from a major U.S. airline, suggest that significant benefits can be achieved.
We consider the airline fleet assignment problem involving the profit maximizing assignment of aircraft types to flight legs. Although several basic formulations have been proposed, important network considerations are insufficiently treated in these formulations and the resulting solutions are often suboptimal. We propose a new formulation and solution approach that captures network effects and generates superior solutions. We quantify the benefits of our proposed approach in a case study using data from a major United States airline.
Dealing with delayed vehicles is a necessary issue in the dispositive work of a public transportation company. If a vehicle arrives at some station with a delay, it has to be decided if the connecting vehicles should wait for changing passengers or if they should depart in time. A possible objective function is to minimize the sum of all delays over all customers using the transportation network. In this paper the delay management problem is formulated as a mixed integer linear program, and solution approaches based on this formulation are indicated.
In this chapter we describe facility location models where consumers generate streams of stochastic demands for service, and service times are stochastic. This combination leads to congestion, where some of the arriving demands cannot be served immediately and must either wait in queue or be lost to the system. These models have applications that range from emergency service systems (fire, ambulance, police) to networks of public and private facilities. One key issue is whether customers travel to facilities to obtain service, or mobile servers travel to customer locations (e.g., in case of police cars). For the most part, we focus on models with static (fixed) servers, as the underlying queueing systems are more tractable and thus a richer set of analytical results is available. After describing the main components of the system (customers, facilities, and the objective function), we focus on the customer-facility interaction, developing a classification of models based on the how customer demand is allocated to facilities and whether the demand is elastic or not. We use our description of system components and customer-response classification to organize the rich variety of models considered in the literature into four thematic groups that share common assumptions and structural properties. For each group we review the solution approaches and outline the main difficulties. We conclude with a review of some important open problems. We specifically outline the advances and new approaches that have been developed since the previous edition of this volume.
Railway delay management considers the question of whether a train should wait for a delayed feeder train. Several works in the literature analyze these so-called wait-depart decisions. The underlying models range from rules of thumb to complete network optimizations. Almost none of them account for uncertainties regarding future delays. In this paper, we present a multi-stage stochastic dynamic programming (SDP) model to make wait-depart decisions in the presence of uncertain future delays. The SDP approach explicitly accounts for potential recourse actions at later stations in a look-ahead manner when making the decision in the current stage. The objective is to minimize the total delay experienced by passengers at their final station by recursively solving Bellman equations. We focus on a single train line but consider the effects on direct feeder and connecting trains. In an extensive numerical study, we compare the solution quality and computational effort of the SDP to other optimization approaches and simple heuristic decision rules that are frequently used in delay management. The SDP approach outperforms the other approaches in almost every scenario with regard to solution quality in reasonable time and seems to be a promising starting point for stochastic dynamic delay management with interesting future research opportunities.
This paper focuses on how to coordinate a critical set of assignment and routing decisions in a class of multiple-depot transit vehicle scheduling problems. The assignment decision aims to assign a set of transit vehicles from their current locations to trip tasks in a given timetable, where the routing decision needs to route different vehicles to perform the assigned tasks and return to the depot or designated layover locations. When applying the general purpose solvers and task-oriented Lagrangian relaxation framework for real world instances, a thorny issue is that different but indistinguishable vehicles from the same depot or similar locations could commit to the same set of tasks. This inherent solution symmetry property causes extremely difficult computational barriers for effectively eliminating identical solutions, and the lower bound solutions could contain many infeasible vehicle-to-task matches, leading to large optimality gaps. To systematically coordinate the assignment and routing decisions and further dynamically break symmetry during the solution search process, we adopt a variable-splitting approach to introduce task-specific and vehicle-distinguishable Lagrangian multipliers and then propose a sequential assignment process in order to enhance the solution quality for the augmented models with tight formulations. We conduct the numerical experiments to offer the managerial interpretation and examine solution quality of the proposed approach in a wider range of applications.
Operators and passengers need to adjust their plans in case of large scale disruptions in railway networks. Where most previous research has focused on the operators, this paper studies the combined support of both in a system where passengers have free route choice. In case of a disruption passengers receive route advice, which they are not required to follow: passenger's route choice depends on the route advice and the timetable information available to them. Simultaneous to providing advice, rolling stock is rescheduled in order to accommodate the anticipated passenger demand. The duration of the disruption is uncertain and passenger flows arise from a complex interaction between the passengers' route choices and the seat capacity allocated to the trains.
We present an optimization based algorithm that aims to minimize passenger inconvenience through provision of route advice and rolling stock rescheduling, where the advice optimization and rolling stock rescheduling modules are supported by a passenger simulation model. The algorithm aims to include and evaluate solutions under realistic passenger behavior assumptions. Our computational tests on realistic instances of Netherlands Railways (NS) indicate that the addition of the travel advice effectively improves the service quality to the passengers more than only rescheduling rolling stock, even when not all passengers follow the advice.
Very often, a train passenger must meet a deadline at the destination, for example, to catch a plane or to arrive at an important meeting on time. Train delays and broken connections let the passenger arrive later than scheduled. Events of this kind are usually not foreseeable before the journey commences. To be on the safe side, a connection should be prebooked such that, in case the connection breaks anywhere, alternative continuations guarantee arrival prior to the deadline with acceptably high probability. For busy people, the challenge is to commence the journey as late as possible, provided the risk of failing to meet the deadline is negligible. This scenario translates into the problem to find the latest connection plus alternative continuations such that the probability of meeting the deadline is not lower than a given required probability of success (close to 100%). We present a dynamic-programming approach to this optimization problem and report on an empirical study based on comprehensive real-world data from Deutsche Bahn AG, the German national railways company. Our algorithm efficiently computes optimal results.
Real-time timetable information and delay management in public transportation systems are two challenging applications which can be modeled as optimization problems on dynamically changing, large and complex graphs, so-called event-activity networks. We describe both applications in detail, review the state-of-the-art and explain the requirements for systems solving these problems in a productive environment. Focussing on recent research on decision support for train dispatchers, we sketch the system architecture for the software prototype PANDA.
In this paper we describe the Traveler’s Route Choice Problem (TRCP). This is the problem of a traveler in a railway system who plans to take the fastest route to a destination but is faced with a disruption of unknown length on this route. In that case, he can wait until the disruption is over or take a detour route as an alternative. Since the duration of the disruption is not known in advance, he is left with a decision problem under uncertainty. In this paper we model the problem and describe the strategies that may be used in such a situation. Instead of finding optimal strategies for a specialized quality measure, we consider dominance relations between strategies and show that dominated strategies are nonoptimal for the common quality measures. We then analyze which strategies for the TRCP are dominated. In general, the set of nondominated strategies is strongly reduced. We also show that, under certain assumptions, only a small set of strategies is nondominated and conclude that in this case the TRCP can be solved by enumeration for any of the quality measures.
The e-companion is available at https://doi.org/10.128/opre.2016.1564 .
We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.
Frequent train delays make passenger-oriented train dispatching a task of high practical relevance. In case of delays, dispatchers have to decide whether trains should wait for one or several delayed feeder trains or should depart on time. To support dispatchers, we have recently introduced the train dispatching framework PANDA (CASPT 2015).
In this paper, we present and evaluate two enhancements which are also of general interest.
First, we study the sensitivity of waiting decisions with respect to the accuracy of passenger flow data. More specifically, we develop an integer linear programming formulation for the following optimization problem: Given a critical transfer, what is the minimum number of passengers we have to add or to subtract from the given passenger flow such that the decision would change from waiting to non-waiting or vice versa?
Based on experiments with realistic passenger flows and delay data from 2015 in Germany, an important empirical finding is that a significant fraction of all decisions is highly sensitive to small changes in passenger flow composition. Hence, very accurate passenger flows are needed in these cases.
Second, we investigate the practical value of more sophisticated simulations. A simple strategy evaluates the effect of a waiting decision of some critical transfer on passenger delay subject to the assumption that all subsequent decisions are taken according to standard waiting time rules, as usually employed by railway companies like Deutsche Bahn. Here we analyze the impact of a higher level of simulation where waiting decisions for a critical transfer are considered jointly with one or more other decisions for subsequent transfers. We learn that such "coupled decisions" lead to improved solution in about 6.3% of all considered cases.
On a daily basis, large-scale disruptions require infrastructure managers and railway operators to reschedule their railway timetables together with their rolling stock and crew schedules. This research focuses on timetable rescheduling for passenger train services on a macroscopic level in a railway network. An integer linear programming model is formulated for solving the timetable rescheduling problem, which minimizes the number of cancelled and delayed train services while adhering to infrastructure and rolling stock capacity constraints. The possibility of rerouting train services to reduce the number of cancelled and delayed train services is also considered. In addition, all stages of the disruption management process (from the start of the disruption to the time the normal situation is restored) are taken into account. Computational tests of the described model on a heavily used part of the Dutch railway network show that the model is able to find optimal solutions in short computation times. This makes the approach applicable for use in practice.
Optimization models for railway traffic rescheduling tackle the problem of determining, in real-time, control actions to reducing the effect of disturbances in railway systems. In this field, mainly two research streams can be identified. On the one hand, train scheduling models are designed to include all conditions relevant to feasible and efficient operation of rail services, from the viewpoint of operations managers. On the other hand, delay management models focus on the impact of rescheduling decisions on the quality of service perceived by the passengers. Models in the first stream are mainly microscopic, while models in the second stream are mainly macroscopic.This paper aims at merging these two streams of research by developing microscopic passenger-centric models, solution algorithms and lower bounds. Several fast heuristic methods are proposed, based on alternative decompositions of the model. A lower bound is proposed, consisting of the resolution of a set of min-cost flow problems with activation constraints. Computational experiments, based on multiple test cases of the real-world Dutch railway network, show that good quality solutions and lower bounds can be found within a limited computation time.
In this chapter we describe facility location models where consumers generate streams of stochastic demands for service, and service times are stochastic. This combination leads to congestion, where some of the arriving demands cannot be served immediately and must either wait in queue or be lost to the system. These models have applications that range from emergency service systems (fire, ambulance, police) to networks of public and private facilities. One key issue is whether customers travel to facilities to obtain service, or mobile servers travel to customer locations (e.g., in case of police cars). For the most part, we focus on models with static (fixed) servers, as the underlying queueing systems are more tractable and thus a richer set of analytical results is available. After describing the main components of the system (customers, facilities, and the objective function), we focus on the customer-facility interaction, developing a classification of models based on the how customer demand is allocated to facilities and whether the demand is elastic or not. We use our description of system components and customer-response classification to organize the rich variety of models considered in the literature into four thematic groups that share common assumptions and structural properties. For each group we review the solution approaches and outline the main difficulties. We conclude with a review of some important open problems.
We consider the Online Delay Management Problem (ODMP) on a network with a path topology that is served by one train. In this problem the number of delayed passengers who want to board the train is not known beforehand but revealed in an online fashion once the train arrives at the corresponding station. The goal is to decide at which station a train should wait in order to minimize the total delay of all passengers.
Competitive analysis has become one of the standard tools to evaluate the performance of algorithms in the presence of incomplete information from a theoretical point of view. The ODMP has been analyzed by means of classical competitive analysis, where one compares the output of an online algorithm with that of an optimal offline algorithm which has complete knowledge about the input data. In this paper we use different approaches to overcome the often criticized pessimism of standard competitive analysis: lookahead, comparative analysis and average-case analysis. Each of these approaches extends the classical worst-case approach of competitive analysis in different aspects. We complement these extensions by addressing the problem from the viewpoint of stochastic optimization. We discuss the theoretical benefits of the concepts and provide a case-study on real world data.
The delay management problem asks
how to react to exogenous delays in public railway traffic such that the overall passenger delay is minimized. Such source delays occur in the operational business of public transit and easily make the scheduled timetable infeasible. The delay management problem is a real-time problem further complicated by its online nature. Source delays are not known in advance, hence decisions have to be taken quickly and without exactly knowing the future. This work focuses on online delay management. We enhance established offline models and gain a generic model that is able to cover complex realistic memoryless delay scenarios. We introduce and experimentally evaluate online strategies for delay management that are practical, easily applicable, and robust. Our experiments show that the most promising approach is based on simulation and a learning strategy which is able to deal very well with the wait-depart decisions. Finally, by analyzing the solutions found, we gain interesting insights in the structure of good delay management strategies for real-world railway data.
In the last decade simulation models and optimization environments have been developed that are able to address the complexity of real-time railway dispatching. Nevertheless, actual implementations of these systems in practice are scarce. Essential for implementation of an advanced dispatching system is the trust of traffic controllers into a stable working of the system. Nervous systems might change advice suddenly, and even switch back to a solution previously discarded, as time and knowledge of the perturbation progress. To this end, we propose several metrics and a framework to assess the stability of railway dispatching solutions under incomplete knowledge, and report on the evaluation of the state-of-the-art dispatching system ROMA, coupled with the simulation environment EGTRAIN, here considered as a surrogate of the real field. Rescheduling plans calculated at different control stages have been compared for different prediction horizons of the rescheduling tool. This setup has been applied to the Dutch Utrecht–Den Bosch corridor. Results show that the instability increases as stochastic disturbances propagate. Shorter prediction horizons give plans which are more stable over time in terms of train reordering, but tend to manage perturbations mostly by retiming. Larger horizons instead allow to manage traffic essentially by reordering trains but lead to more unstable plans. Enlarging the prediction horizon over a given threshold does not alter neither the structure of plans nor their variation over time.
This paper deals with the development of decision support systems for traffic management of large and busy railway networks in case of severe disturbances. Railway operators typically structure the control of complicated networks into the coordinated control of several local dispatching areas. A dispatcher takes rescheduling decisions on the trains running on its local area while a coordinator addresses global issues that may arise between areas. While several advanced train dispatching models and algorithms have been proposed to support the dispatchers' task, the coordination problem did not receive much attention in the literature on train scheduling. This paper presents new heuristic algorithms for both local dispatching and coordination and compares centralized and distributed procedures to support the task of dispatchers and coordinators. We adopt dispatching procedures driven by optimization algorithms and based on local or global information and decisions. Computational experiments on a Dutch railway network, actually controlled by ten dispatchers, assess the performance of the centralized and distributed procedures. Various traffic disturbances, including entrance delays and blocked tracks, are analyzed on various time horizons of traffic prediction. Results show that the new heuristics clearly improve the global performance of the network with respect to the state of the art.
The task of delay management is to decide whether connecting trains should wait for delayed feeder trains or depart on time in order to minimize the passengers’ delay. To estimate the effect of the wait-depart decisions on the travel times, most delay management models assume that passengers’ routes are predefined. However, in practice, passengers can adapt their routes to the wait-depart decisions and arising changes in the timetable. For this reason, in this paper we assume that passengers’ demand is given in form of pairs of origins and destinations (OD-pairs) and take wait-depart decisions and decisions on passengers’ routes simultaneously.
This approach, called delay management with re-routing, was introduced in Dollevoet et al. (Transp. Sci. 46(1):74–89, 2012) and we build our research upon the results obtained there. We show that the delay management problem with re-routing is strongly NP-hard even if there is only one OD-pair. Furthermore, we prove that even if there are only two OD-pairs, the problem cannot be approximated with constant approximation ratio unless P=NP. However, for the case of only one OD-pair we propose a polynomial-time algorithm. We show that our algorithm finds an optimal solution if there is no reasonably short route from origin to destination which requires a passenger to enter the same train twice. Otherwise, the solution found by the algorithm is a 2-approximation of an optimal solution and the estimated travel time is a lower bound on the objective value.
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.
We propose a new formulation for the assignment problem over congested transit networks. The congestion effects due to insufficient capacity of system elements (transit lines) are considered to be concentrated at transit stops. Waiting times on access links are therefore dependent on passenger flows. A special formulation of the transit network is used in order to model correctly the congestion effects. Finally, algorithms for solution are analyzed.
Based on an approach recently proposed for obtaining global optimal solution of general 0–1 fractional programming (G-FP) problem, a theorem is presented in this research. Through this theorem, the nonlinear terms appearing in the formulation transformed from G-FP can be directly replaced by a set of linear inequalities. The G-FP problem can hence be easily and more efficiently solved as a mixed integer program.
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.
After a major service disruption on a single-track rail line, dispatchers need to generate a series of train meet-pass plans at different decision times of the rescheduling stage. The task is to recover the impacted train schedule from the current and future disturbances and minimize the expected additional delay under different forecasted operational conditions. Based on a stochastic programming with recourse framework, this paper incorporates different probabilistic scenarios in the rolling horizon decision process to recognize (1) the input data uncertainty associated with predicted segment running times and segment recovery times and (2) the possibilities of rescheduling decisions after receiving status updates. The proposed model periodically optimizes schedules for a relatively long rolling horizon, while selecting and disseminating a robust meet-pass plan for every roll period. A multi-layer branching solution procedure is developed to systematically generate and select meet-pass plans under different stochastic scenarios. Illustrative examples and numerical experiments are used to demonstrate the importance of robust disruption handling under a dynamic and stochastic environment. In terms of expected total train delay time, our experimental results show that the robust solutions are better than the expected value-based solutions by a range of 10-30%.
The railway systems in various European countries adopt regular timetables, in which the trains arrive and depart at constant intervals. In fact, their simple structure provides several advantages both to the passengers and to the management of the service. The design of such timetables has recently received a certain attention in the literature, but the standard model aims to optimize the service for a fixed demand. We relax this unrealistic assumption, taking into account the reciprocal influence between the quality of the timetable and the amount of transport demand captured by the railway. This results into a mixed-integer non linear model with a non-convex continuous relaxation. We solve it by a branch-and-bound algorithm based on a piecewise-linear overestimate of the objective function and a heuristic algorithm which iteratively applies the standard fixed-demand model and a demand-estimation model, feeding each one with data based on the solution obtained from the other one at the previous iteration. The computational results presented concern both random instances and a real-world regional network located in Northwestern Italy.
The task of finding global optima to general classes of nonconvex optimization problem is attracting increasing attention. McCormick [4] points out that many such problems can conveniently be expressed in separable form, when they can be tackled by the special methods of Falk and Soland [2] or Soland [6], or by Special Ordered Sets. Special Ordered Sets, introduced by Beale and Tomlin [1], have lived up to their early promise of being useful for a wide range of practical problems. Forrest, Hirst and Tomlin [3] show how they have benefitted from the vast improvements in branch and bound integer programming capabilities over the last few years, as a result of being incorporated in a general mathematical programming system.
Nevertheless, Special Ordered Sets in their original form require that any continuous functions arising in the problem be approximated by piecewise linear functions at the start of the analysis. The motivation for the new work described in this paper is the relaxation of this requirement by allowing automatic interpolation of additional relevant points in the course of the analysis.
This is similar to an interpolation scheme as used in separable programming, but its incorporation in a branch and bound method for global optimization is not entirely straightforward. Two by-products of the work are of interest. One is an improved branching strategy for general special-ordered-set problems. The other is a method for finding a global minimum of a function of a scalar variable in a finite interval, assuming that one can calculate function values and first derivatives, and also bounds on the second derivatives within any subinterval.
The paper describes these methods, their implementation in the UMPIRE system, and preliminary computational experience.
For nonlinear programming problems which are factorable, a computable procedure for obtaining tight underestimating convex programs is presented. This is used to exclude from consideration regions where the global minimizer cannot exist.
To improve the robustness of timetables for a network of passenger train services, this paper seeks to minimize a waiting cost function that includes running time supplements and different types of waiting times and late arrivals. The approach is applied to the whole intercity (IC) network of the Belgian railways. The IC network consists of 14 fast trains connecting all major cities in Belgium. In the first phase of the approach, ideal running time supplements are calculated to safeguard connections when the feeder train is late. These supplements are based on the delay distributions of the trains, the passenger counts and on the weighting of different types of waiting times. In a second phase, continuous Linear Programming (LP) is used to construct an improved timetable with well-scheduled connections and, whenever possible, with ideal running time supplements. Simulation evaluates different timetables and makes further improvement of the LP timetable possible. For the case of the IC network, the final result is a timetable with suitable transfer times and a waiting cost, that is, 40% lower than the current timetable. Since continuous LP modelling is applied, the proposed technique is very promising for developing better timetables – even for very extensive railway networks.
The paper studies a train scheduling problem faced by railway infrastructure managers during real-time traffic control. When train operations are perturbed, a new conflict-free timetable of feasible arrival and departure times needs to be re-computed, such that the deviation from the original one is minimized. The problem can be viewed as a huge job shop scheduling problem with no-store constraints. We make use of a careful estimation of time separation among trains, and model the scheduling problem with an alternative graph formulation. We develop a branch and bound algorithm which includes implication rules enabling to speed up the computation. An experimental study, based on a bottleneck area of the Dutch rail network, shows that a truncated version of the algorithm provides proven optimal or near optimal solutions within short time limits.
Disposition management solves the decision problem whether a train should wait for incoming delayed trains or not. This problem has a highly dynamic nature due to a steady stream of update information about delayed trains. A dispatcher has to solve a global optimization problem since his decisions have an effect on the whole network, but he takes only local decisions for subnetworks (for few stations and only for departure events in the near future). In this paper, we introduce a new model for an optimization tool. Our implementation includes as building blocks (1) routines for the permanent update of our graph model subject to incoming delay messages, (2) routines for forecasting future arrival and departure times, (3) the update of passenger flows subject to several rerouting strategies (including dynamic shortest path queries), and (4) the simulation of passenger flows. The general objective is the satisfaction of passengers. We propose three different formalizations of objective functions to capture this goal. Experiments on test data with the train schedule of German Railways and real delay messages show that our disposition tool can compute waiting decisions within a few seconds. In a test with artificial passenger flows it is fast enough to handle the typical amount of decisions which have to be taken within a period of 15 minutes in real time.
Assume that a train reaches a station with delay. At the station there is a bus ready to depart. The question of whether the bus should wait for the delayed train or depart on time is called the delay management problem. Different single objective functions for this problem have been introduced and analyzed. In this paper, we present a bicriteria model for the delay management problem, taking into account both the delay of the vehicles and the number of passengers who miss a connection. Our model does not depend on detailed data about the passengers and hence can be easily implemented in practice.
To analyze the problem, we present an integer programming formulation and a graph-theoretic approach that is based on discrete time/cost trade-off project networks. Using results of project planning, we develop an efficient solution method. We tested our procedure using real-world data. The results show the applicability of the approach.
The correct estimation of spill, or passenger demand turned away, is an integral part of the determination of optimal aircraft capacities in the airline fleet assignment process. While making advances in the solution of the large-scale fleet assignment optimization problem, airlines have continued to use an aggregate approach to spill estimation. This aggregate approach ignores the effects of yield management practices that have been widely implemented by airlines during the past decade. In this paper, we illustrate the importance of incorporating the effects of yield management booking limits into the methodology used to estimate both the number of passengers spilled at a given aircraft capacity and their associated revenue value. We describe an approach to spill estimation that makes use of the detailed demand information provided by yield management systems, and we present recursive algorithms that can be used to obtain more accurate spill estimates in cases when multiple booking classes are used. Numerical examples are presented to illustrate the extent to which the outcomes of the different estimation approaches differ, suggesting that these differences can be large enough to have an impact on optimal fleet assignment.
Unavoidable disruptions induce the necessity of delay management in timetable-driven passenger rail traffic. Minimizing the negative consequences of delays becomes one of the most relevant challenges for the economic success, as it directly affects the timeliness of passengers, which is a core indicator of customer satisfaction. In this article, we evaluate and compare various delay management strategies in a passenger railway network. A simulator has been implemented to generate delays and perform operations control decisions to resolve connection conflicts induced through passenger connections involving delayed trains. We compare dispatching strategies based on mathematical optimization with simple rule-based strategies. Simulation runs with a timetable from the long-distance passenger traffic of German Railways show that, due to the online nature of this decision problem, a simple waiting time rule strategy can outperform a strategy where the operations are reoptimized online after each disruption. © 2010 Wiley Periodicals, Inc. NETWORKS, 2011 © 2011 Wiley Periodicals, Inc.