An optimization model for line planning and timetabling in automated urban metro subway networks

In this paper we present a Mixed Integer Nonlinear Programming model that we developed as part of a pilot study requested by the R&D company Metrolab in order to design tools for finding solutions for line planning and timetable situations in automated urban metro subway networks. Our model incorporates important factors in public transportation systems from both, a cost-oriented and a passenger-oriented perspective, as time-dependent demands, interchange stations, short-turns and technical features of the trains in use. The incoming flows of passengers are modeled by means of piecewise linear demand functions which are parameterized in terms of arrival rates and bulk arrivals. Decisions about frequencies, train capacities, short-turning and timetables for a given planning horizon are jointly integrated to be optimized in our model. Finally, a novel Math-Heuristic approach is proposed to solve the problem. The results of extensive computational experiments are reported to show its applicability and effectiveness to handle real-world subway networksComment: 30 pages, 6 figures, 9 table

Train scheduling with application to the UK rail network

Nowadays, transforming the railway industry for better performance and making the best usage of the current capacity are the key issues in many countries. Operational research methods and in particular scheduling techniques have a substantial potential to offer algorithmic solutions to improve railway operation and control. This thesis looks at train scheduling and rescheduling problems in a microscopic level with regard to the track topology. All of the timetable components are fixed and we aim to minimize delay by considering a tardiness objective function and only allowing changes to the order and to the starting times of trains on blocks. Various operational and safety constraints should be considered. We have achieved further developments in the field including generalizations to the existing models in order to obtain a generic model that includes important additional constraints. We make use of the analogy between the train scheduling problem and job shop scheduling problem. The model is customized to the UK railway network and signaling system. Introduced solution methods are inspired by the successful results of the shifting bottleneck to solve the job shop scheduling problems. Several solution methods such as mathematical programming and different variants of the shifting bottleneck are investigated. The proposed methods are implemented on a real-world case study based on London Bridge area in the South East of the UK. It is a dense network of interconnected lines and complicated with regard to stations and junctions structure. Computational experiments show the efficiency and limitations of the mathematical programming model and one variant of the proposed shifting bottleneck algorithms. This study also addresses train routing and rerouting problems in a mesoscopic level regarding relaxing some of the detailed constraints. The aim is to make the best usage of routing options in the network to minimize delay propagation. In addition to train routes, train entry times and orders on track segment are defined. Hence, the routing and scheduling decisions are combined in the solutions arising from this problem. Train routing and rerouting problems are formulated as modified job shop problems to include the main safety and operational constraints. Novel shifting bottleneck algorithms are provided to solve the problem. Computational results are reported on the same case study based on London Bridge area and the results show the efficiency of one variant of the developed shifting bottleneck algorithms in terms of solution quality and runtime

A branch-and-price approach for trip sequence planning of high-speed train units

In high-speed railway operations, a trip sequence plan is made once the timetable is determined, and serves as a reference in the subsequent operations of train units scheduling. In light of the maintenance requirements of train units and periodicity characteristics of trip sequences, we introduce a trip sequence graph to describe the train units’ movement and coupling/splitting in a railway network. Based on the trip sequence graph, two integer linear programming models are then formulated, namely a path-based model and an arc-based model. Integrated with the characteristics of the trip sequence graph, a customized branch-and-price algorithm is developed to solve the path-based model. The two models are applied to the high-speed railway network in eastern China, and through numerical experiments, the effectiveness and applicability of the models are discussed

Port Rail Shunting Optimization Problems

openThe work focuses on a particular section of the intermodal chain of freight transportation, which is the link between rail and sea transportation modes and happens in the maritime port area. Among this field, the study deals with the management of rail operations, called here rail shunting operations, that have to be performed in the port area. Two optimization problems arises in this context. The first concerns the scheduling of the rail shunting operations, here called Port Rail Shunting Scheduling Problem (PRSSP). The second deals with the re-scheduling of the same operations in case of unpredictable events, here called Port Rail Shunting Re-Scheduling Problem (PRSRP). After a literature overview on the concerning studies, we concentrate on an innovative way to use the well known space-time networks as solution approach structure for both the above mentioned problems. The innovative structure has been called operation-time-space network and is deeply analyzed in a dedicated chapter. A network flow model based on an operation-time-space network for solving PRSSP has been developed. It has been tested using random generated instances providing good results. The same model has been extended in order to solve PRSRP and it has been tested giving good results as well. Finally, the models have been used to solve the real case of a port area located in Italy in order to test the applicability of the developed models to a real context. The tests have been executed using real data and provided good results confirming the possibility to apply the proposed approach in similar real problems.openXXXIII CICLO - LOGISTICA E TRASPORTIAsta, Veronic

Operations Research Modeling of Cyclic Train Timetabling, Cyclic Train Platforming, and Bus Routing Problems

Public transportation or mass transit involves the movement of large numbers of people between a given numbers of locations. The services provided by this system can be classified into three groups: (i) short haul: a low-speed service within small areas with high population; (ii) city transit: transporting people within a city; and (iii) long haul: a service with long trips, few stops, and high speed (Khisty and Lall, 2003). It can be also classified based on local and express services. The public transportation planning includes five consecutive steps: (i) the network design and route design; (ii) the setting frequencies or line plan; (iii) the timetabling; (iv) the vehicle scheduling; and (v) the crew scheduling and rostering (Guihaire and Hao, 2008; Schöbel, 2012). The first part of this dissertation considers three problems in passenger railway transportation. It has been observed that the demand for rail travel has grown rapidly over the last decades and it is expected that the growth continues in the future. High quality railway services are needed to accommodate increasing numbers of passengers and goods. This is one of the key factors for economic growth. The high costs of railway infrastructure ask for an increased utilization of the existing infrastructure. Attractive railway services can only be offered with more reliable rolling stock and a more reliable infrastructure. However, to keep a high quality standard of operations, smarter methods of timetable construction are indispensable, since existing methods have major shortcomings. The first part of this dissertation, comprising Chapters 1-6, aims at developing a cyclic (or periodic) timetable for a passenger railway system. Three different scenarios are considered and three mixed integer linear programs, combined with heuristics for calculating upper and lower bounds on the optimal value for each scenario, will be developed. The reason of considering a periodic timetable is that it is easy to remember for passengers. The main inputs are the line plan and travel time between and minimum dwell time at each station. The output of each model is an optimal periodic timetable. We try to optimize the quality of service for the railway system by minimizing the length of cycle by which trains are dispatched from their origin. Hence, we consider the cycle length as the primary objective function. Since minimizing travel time is a key factor in measuring service quality, another criterion--total dwell time of the trains--is considered and added to the objective function. The first problem, presented in Chapter 3, has already been published in a scholarly journal (Heydar et al., 2013). This chapter is an extension of the work of Bergmann (1975) and is the simplest part of this research. In this problem, we consider a single-track unidirectional railway line between two major stations with a number of stations in between. Two train types--express and local--are dispatched from the first station in an alternate fashion. The express train stops at no intermediate station, while the local train should make a stop at every intermediate station for a minimum amount of dwell time. A mixed integer linear program is developed in order to minimize the length of the dispatching cycle and minimize the total dwell time of the local train at all stations combined. Constraints include a minimum dwell time for the local train at each station, a maximum total dwell time for the local train, and headway considerations on the main line an in stations. Hundreds of randomly generated problem instances with up to 70 stations are considered and solved to optimality in a reasonable amount of time. Instances of this problem typically have multiple optimal solutions, so we develop a procedure for finding all optimal solutions of this problem. In the second problem, presented in Chapter 4, we present the literature\u27s first mixed integer linear programming model of a cyclic, combined train timetabling and platforming problem which is an extension of the model presented in Chapter 3 and Heydar et al. (2013). The work on this problem has been submitted to a leading transportation journal (Petering et al., 2012). From another perspective, this work can be seen as investigating the capacity of a single track, unidirectional rail line that adheres to a cyclic timetable. In this problem, a set of intermediate stations lies between an origin and destination with one or more parallel sidings at each station. A total of T train types--each with a given starting and finishing point and a set of known intermediate station stops--are dispatched from their respective starting points in cyclic fashion, with one train of each type dispatched per cycle. A mixed integer linear program is developed in order to schedule the train arrivals and departures at the stations and assign trains to tracks (platforms) in the stations so as to minimize the length of the dispatching cycle and/or minimize the total stopping (dwell) time of all train types at all stations combined. Constraints include a minimum dwell time for each train type in each of the stations in which it stops, a maximum total dwell time for each train type, and headway considerations on the main line and on the tracks in the stations. This problem belongs to the class of NP-hard problems. Hundreds of randomly generated and real-world problem instances with 4-35 intermediate stations and 2-11 train types are considered and solved to optimality in a reasonable amount of time using IBM ILOG CPLEX. Chapter 5 expands upon the work in Chapter 4. Here, we present a mixed integer linear program for cyclic train timetabling and routing on a single track, bi-directional rail line. There are T train types and one train of each type is dispatched per cycle. The decisions include the sequencing of the train types on the main line and the assignment of train types to station platforms. Two conflicting objectives--(1) minimizing cycle length (primary objective) and (2) minimizing total train journey time (secondary objective)--are combined into a single weighted sum objective to generate Pareto optimal solutions. Constraints include a minimum stopping time for each train type in each station, a maximum allowed journey time for each train type, and a minimum headway on the main line and on platforms in stations. The MILP considers five aspects of the railway system: (1) bi-directional train travel between stations, (2) trains moving at different speeds on the main line, (3) trains having the option to stop at stations even if they are not required to, (4) more than one siding or platform at a station, and (5) any number of train types. In order to solve large scale instances, various heuristics and exact methods are employed for computing secondary parameters and for finding lower and upper bounds on the primary objective. These heuristics and exact methods are combined with the math model to allow CPLEX 12.4 to find optimal solutions to large problem instances in a reasonable amount of time. The results show that it is sometimes necessary for (1) a train type to stop at a station where stopping is not required or (2) a train type to travel slower than its normal speed in order to minimize timetable cycle time. In the second part of this dissertation, comprising Chapters 7-9, we study a transit-based evacuation problem which is an extension of bus routing problem. This work has been already submitted to a leading transportation journal (Heydar et al., 2014). This paper presents a mathematical model to plan emergencies in a highly populated urban zone where a certain numbers of pedestrians depend on transit for evacuation. The proposed model features a two-level operational framework. The first level operation guides evacuees through urban streets and crosswalks (referred to as the pedestrian network ) to designated pick-up points (e.g., bus stops), and the second level operation properly dispatches and routes a fleet of buses at different depots to those pick-up points and transports evacuees to their destinations or safe places. In this level, the buses are routed through the so-called vehicular network. An integrated mixed integer linear program that can effectively take into account the interactions between the aforementioned two networks is formulated to find the maximal evacuation efficiency in the two networks. Since the large instances of the proposed model are mathematically difficult to solve to optimality, a two-stage heuristic is developed to solve larger instances of the model. Over one hundred numerical examples and runs solved by the heuristic illustrate the effectiveness of the proposed solution method in handling large-scale real-world instances

Verfahren zum Einfügen der zusätzlichen non-zyklischen Pfade in die bestehenden zyklischen Fahrpläne

With the development of high-speed railway (HSR), cyclic timetable shows many advantages. However, the pure cyclic timetable is not suitable in China's HSR. Consequently, a hybrid timetable concept named "cyclic + non-cyclic" timetable is proposed, with a cyclic core timetable in which some trains are inserted as non-cyclic trains. Nowadays, the cyclic timetables have been well developed but the technique of inserting additional train paths is still a significant demand for research. The Adding Train Paths (ATP) problem firstly is an integration of timetable scheduling and rescheduling problem. Therefore it is considered involving many general constraints, such as flexible running time, dwell time and headways. Based on an event-activity graph, a general mixed integer program model for the ATP problem is formulated. In addition, several real-world constraints that concerning the acceleration and deceleration time, priority for overtaking, station capacity, allowed adjustments, periodic structure and frequency of services are incorporated into the general model. In order to get a new timetable that with low deviations to the initial services and high quality of the performance to the additional trains, objective functions of minimizing travel time, minimizing total adjustments, minimizing the makespan and maximizing the robustness of the new timetable are discussed in this thesis. More importantly, many additional trains may not be inserted because of a shortage of train-sets. So how to cover the entire trains with minimum train-sets must be also taken into account in this problem. The train-set circulation in the ATP problem is decomposed to two sub-problems. (i) For initial trains, the initial train-set route is assumed to be fixed; it is solved as a rescheduling problem of a tight constraint to keep the current circulation. (ii) For additional trains, it is a train-set planning problem to cover all the additional trains with minimal number of train-sets. In order to solve the problem in a reasonable time, we start from fixed train-set route, and then apply flexible train-set route that provides possible alternative turning activities to decrease the waiting time of a train-set in an overnight turn-around. Case studies based on Shanghai-Hangzhou HSR line in China investigate the proposed framework and associated techniques. Meanwhile, the performances of various settings are compared to analyse the affecting factors to this specific problem.Zusammen mit der Entwicklung von Hochgeschwindigkeitsverkehr (HGV) hat der zyklische Fahrplan als sehr vorteilhaft bewiesen. Allerdings ist der zyklische Fahrplan für HGV in China nicht geeignet. Demzufolge wird ein Hybrid-Fahrplan Konzept mit „zyklisch + non-zyklisch“ vorgeschlagen. Mit dem zyklischen Fahrplan als Basis werden neue non-zyklischen Pfade eingefügt. Der zyklische Fahrplan wird bereits intensiv geforscht. Beim Einfügen von zusätzlicher non-zyklischen Pfade besteht jedoch großer Forschungsbedarf. Dieses Problem umfasst sowohl den Bereich der Planung als auch der Umplanung von Fahrplan. Mehrere Restriktionen werden berücksichtigt, z.B.: flexibel Fahrzeit, Haltezeit und Zugfolgezeit. Basiert auf Event-Activity-Graph, ein generisches gemischtes integrales Modell wird entwickelt. Zusätzlich werden die praxisrelevanten Restriktionen wie Beschleunigungszeit, Bremszeit, Priorität der Züge, Anzahl der Bahnhofsgleise, zulässige Verschiebung der Abfahrtszeit, periodische Struktur und Taktfrequenz mitbetrachtet. Um ein neuer Fahrplan mit einer geringen Verschiebung der Abfahrtszeit und zugleich eine hohe Qualität der zusätzlichen Züge zu ermöglichen, wird in dieser Arbeit die folgenden Kriterien als Zielfunktionen untersucht: Reisezeit, Summe der gesamten Zeitverschiebung, Spannbreite der Zeitverschiebung und Robustheit der Fahrplan. Die Anzahl der zusätzlichen non-zyklischen Pfade hängt wesentlich von der Anzahl der Züge ab, welche noch verfügbar sind. Daher ist ein optimaler Fahrzeugumlaufplan für die zusätzlichen Zugfahrten ein wichtiges Zielkriterium. Umlauf der bestehenden Zugfahrten und der zusätzlichen Zugfahrten werden separat betrachtet. (i) Bei der bestehenden Zugfahrten wird keine Änderung an Fahrzeugumlauf vorgenommen, auch nach Verschiebung der Abfahrtszeit bleibt der Umlauf unverändert. (ii) Für die zusätzlichen Zugfahrten wird die Anzahl der benötigen Züge minimiert. Um die Aufgabe in einer annehmbaren Rechenzeit zu lösen, werden anfangs die zusätzlichen Zugfahrten, deren Laufweg mit den zyklischen Zugfahrten identisch ist, untersucht. Anschließend werden weitere Zugfahrten mit flexiblen Laufweg eingefügt, welche durch Wenden im Unterwegsbahnhof die Wartezeit bzw. Aufenthaltszeit über Nacht am Endbahnhof möglichst reduzieren kann. Als Fallstudie wird HGV Shanghai-Hangzhou in China untersucht. Die Rechenzeiten von der unterschiedlichen Parametereinstellungen werden während der Untersuchung getestet, analysiert und verglichen

Combinatorial optimization and vehicle fleet planning : perspectives and prospects

Bibliography : p.52-60.Research supported in part by the National Science Foundation under grant 79-26225-ECS.by Thomas L. Magnanti