Integer programming based solution approaches for the train dispatching problem

Railroads face the challenge of competing with the trucking industry in a fastpaced environment. In this respect, they are working toward running freight trains on schedule and reducing travel times. The planned train schedules consist of departure and arrival times at main stations on the rail network. A detailed timetable, on the other hand, consists of the departure and arrival times of each train in each track section of its route. The train dispatching problem aims to determine detailed timetables over a rail network in order to minimize deviations from the planned schedule. We provide a new integer programming formulation for this problem based on a spacetime network; we propose heuristic algorithms to solve it and present computational results of these algorithms. Our approach includes some realistic constraints that have not been previously considered as well as all the assumptions and practical issues considered by the earlier works

A mixed integer linear programming model with heuristic improvements for single-track railway rescheduling problem

A rescheduling algorithm for trains on a single-track railway was developed in case of disturbances that would cause conflicts between trains. This algorithm is based on mixed integer linear programming (MILP) with speed-up routines. The model considers station capacities explicitly (i.e., the number of available tracks for meeting and overtaking operations). Because the model is too hard for the solvers (CPLEX in this study) to tackle, three speed-up routines were devised when rescheduling trains. These routines are a greedy heuristic to reduce the solution space, using the lazy constraint attribute of the solver and a multiobjective approach to find a good initial feasible solution that conforms to actual railway operation. The algorithm was tested on a hypothetical rail line for different sizes of timetable instances with disturbed trains in a maximum two-hour time horizon. It managed to solve the hardest instances within a three-minute time limit thus minimizing the total weighted delay of rescheduled trains. The optimality gap metric is used to show the effectiveness and efficiencies of the speed-up heuristics developed

TIMETABLE MANAGEMENT TECHNIQUE IN RAILWAY CAPACITY ANALYSIS: DEVELOPMENT OF THE HYBRID OPTIMIZATION OF TRAIN SCHEDULES (HOTS) MODEL

There are two general approaches to improve the capacity in a rail corridor, either by applying new capital infrastructure investment or by improving the operation of the rail services. Techniques to evaluate the railway operation include modeling and optimization through the use of commercial timetable management and rail simulation tools. However, only a few of the existing tools include complete features of timetable management techniques (e.g. timetable compression) are equipped with an optimization model for rescheduling and timetable improvement and this is especially true when it comes to the U.S. rail environment that prevalently uses unstructured operation practices. This dissertation explores an application of timetable (TT) management techniques (e.g. rescheduling and timetable compression techniques) in the U.S. rail environment and their effect on capacity utilization and level of service (LOS) parameters. There are many tools and simulation packages used for capacity analysis, by both European and the U.S. rail industry, but due to the differences in the operating philosophy and network characteristics of these two rail systems, European studies tend to use timetable-based simulation tools (e.g. RailSys, OpenTrack) while the non-timetable based tools (e.g. RTC) are commonly used in the U.S. (Chapter 1). This research study investigated potential benefits of using a “Hybrid Simulation” approach that would combine the advantages of both the U.S. and European tools. Two case studies (a single track and a multiple-track case study) were developed to test the hybrid simulation approach, and it was concluded that applying timetable management techniques (e.g. timetable compression technique) is promising when implemented in a single track corridor (Chapter 2), but it is only applicable for the multiple track corridors under directional operation pattern (Chapter 3). To address this, a new heuristic rescheduling and rerouting technique was developed as part of the research to convert a multiple track case study from non-directional operation pattern to a fully directional operation pattern (Chapter 4). The knowledge and skills of existing software, obtained during the development and testing of “Hybrid Simulation”, was used to develop an analytical rescheduling/optimization model called “Hybrid Optimization of Train Schedules” (HOTS) (Chapter 5). While the results of the “Hybrid simulation approach” are promising, the method was also time consuming and challenging, as all respective details and database of the given corridors had to be replicated in both simulation tools. The “HOTS Model” could provide the same functions and features of train rescheduling, but with much less efforts and challenges as in the hybrid simulation. The HOTS model works in conjunction with any commercial rail simulation software and it can reschedule an initial timetable (with or without conflict) to provide a “Conflict-Free” timetable based on user-defined criteria. The model is applicable to various types of rail operations, including single, double and multiple-track corridors, under both directional and nondirectional operation patterns. The capabilities of the HOTS model were tested for the two case studies developed in the research, and its outcomes were compared to those obtained from the commercial software. It was concluded that the HOTS model performed satisfactorily in each of the test scenarios and the model results either improved or maintained the initial timetable characteristics. The results are promising for the future development of the model, but limitations in the current model structure, such as station capacity limits, should be addressed to improve the potential of applying the model for industrial applications

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

Analytical Models in Rail Transportation: An Annotated Bibliography

Not AvailableThis research has been supported, in part, by the U.S. Department of Transportation under contract DOT-TSC-1058, Transportation Advanced Research Program (TARP)

Estimation of Railroad Capacity Using Parametric Methods

This paper reviews different methodologies used for railroad capacity estimation and presents a user-friendly method to measure capacity. The objective of this paper is to use multivariate regression analysis to develop a continuous relation of the discrete parameters identified for capacity estimation. The algorithm developed in this paper can be used for managerial decision making regarding railroad capacity by various state agencies and state DOTs. This paper illustrates the relationship between the parameters and section capacities, which can be used to improve the throughput of the transportation system. The paper also illustrates the application of the model to estimate capacity of a statewide railroad network

Development of a prototype for the automated generation of timetable scenarios specified by the transport service intention

Within the next 5 to 10 years, public transport in Switzerland as well as in other European countries will experience major technological and organisational changes. However, changes will also take place on the customer side, resulting in different mobility behaviour and demand patterns. These changes will lead to additional challenges for transport service providers in private as well as public domains. Time to market will be a key success factor and it is unnecessary to mention that due to these factors the speed and flexibility of business processes in freight as well as in passenger transport industry have to be increased significantly. Within the railway value chain (line planning, timetabling and vehicle scheduling etc.) the coordination of the individual planning steps is a key success factor. SBB as the leading service provider in public transport in Switzerland has recognized this challenge and, together with various partners, initiated the strategic project Smart Rail 4.0. The ZHAW and especially the Institute for Data Analysis and Process Design (IDP) of the School of Engineering wants to be part of this transformation process and to contribute with research and educational activities. The IDP research therefore aims for the transformation of academic and scientific know-how to practical applicability. In a first step this concerns directly the current Smart Rail 4.0 TMS-PAS project activities, that concentrate on timetabling issues. The IDP project team considers the integration of the line planning and the timetabling process as crucial for practical applications. To address this in the current research project, we present an application concept that enables the integration of these two major process steps in the transport service value-chain. Although it turns out from our research, that the technical requirements for the integration of the process can be satisfied, rules and conditions for a closer cooperation of the involved business units, the train operating companies and the infrastructure operating company, have to be improved and to be worked out in more detail. In addition to a detailed application concept with use cases for the timetabling process we propose a methodology for computer aided timetable generation based on the central planning object known as ‘service intention’. The service intention can be used to iteratively develop the timetable relying on a ‘progressive feasibility assessment’, a feature that is requested in practice. Our proposed model is based on the ‘track-choice’ and line rotation extension of the commonly known method for the generation of periodic event schedules ‘PESP’. The extension makes use of the track infrastructure representation which is also used in the line planning and timetabling system Viriato. This system that is widely used by public transport planners and operators. With the help of Viriato, it is rather easy to configure the timetabling problem in sufficient detail. On the other side, the level of detail of the considered data is light enough to algorithmically solve practical timetabling problems of realistic sizes. Taking into consideration the technical and operational constraints given by rolling stock, station and track topology data on one hand, and the commercial requirements defined by a given line concept on the other, the method presented generates periodic timetables including train-track assignments. In the first step, the standardized data structure ‘service intention’ represents the line concept consisting of train paths and frequencies. Due to the utilization of infrastructure-based track capacities, we are also able to assess the feasibility of the line concept given. Additionally, the method allows for handling temporary resource restrictions (e.g. caused by construction sites or operational disturbances). In order to assess the performance of the resulting timetable we present a framework for performance measurement that addresses the customer convenience (in terms of start-to-end travel time) as well as operational stability requirements (in terms of delay sensitivity and critical relations)

Improvement of maintenance timetable stability based on iteratively assigning event flexibility in FPESP

In the operational management of railway networks, an important requirement is the fast adaptation of timetable scenarios, in which operational disruptions or time windows with temporary unavailability of infrastructure, for instance during maintenance time windows, are taken into consideration. In those situations, easy and fast reconfiguration and recalculation of timetable data is of central importance. This local and temporal rescheduling results in shifted departure and arrival times and sometimes even in modified stop patterns at intermediate stations of train runs. In order to generate reliable timetabling results it is a prerequisite that train-track assignments, as well as operational and commercial dependencies are taken into consideration. In order to refer to the right level of detail for modelling track infrastructure and train dynamics in the computer aided planning process we present a generic model that we call Track-Choice FPESP (TCFPESP), as it implements suitable extensions of the established PESP-model. We show, how the service intention (the data structure for timetable specification) together with resource capacity information entered into a standard timetabling tool like Viriato can be utilized in order to configure the TCFPESP model. In addition, we are able to calculate quantitative performance measures for assessing timetable quality aspects. In order to achieve this we present a method for evaluating travel times based on passenger routings and a method for evaluating timetable robustness based on max-plus algebra. This approach supports the planner to generate integrated periodic timetable solutions in iterative development cycles and taking into account intervals for local maintenance work