Showing papers in "Public Transport in 2009"

An overview on vehicle scheduling models

Abstract: The vehicle scheduling problem, arising in public transport bus companies, addresses the task of assigning buses to cover a given set of timetabled trips with consideration of practical requirements such as multiple depots and vehicle types as well as further extensions. An optimal schedule is characterized by minimal fleet size and/or minimal operational costs. Various publications were released as a result of extensive research in the last decades on this topic. Several modeling approaches as well as specialized solution strategies were presented for the problem and its extensions. This paper discusses the modeling approaches for different kinds of vehicle scheduling problems and gives an up-to-date and comprehensive overview on the basis of a general problem definition. Although we concentrate on the presentation of modeling approaches, also the basic ideas of solution approaches are given.

The bus bridging problem in metro operations: conceptual framework, models and algorithms

Abstract: Metro networks provide efficient transportation services to large numbers of travelers in urban areas around the World; any unexpected operational disruption can lead to rapid degradation of the provided level of service by a city’s public transportation system. In such instances, quick and efficient substitution of services is necessary for accommodating metro passengers including the widely used practice of “bridging” metro stations using bus services. Despite its widespread application, bus bridging is largely done ad-hoc and not as part of an integrated optimization procedure. In this paper we propose a methodological framework for planning and designing an efficient bus bridging network. Furthermore, we offer a set of structured steps and optimization models and algorithms for handling bus bridging problems.

Capacity constraints in delay management

Abstract: 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.

Integrating line planning, timetabling, and vehicle scheduling: a customer-oriented heuristic

Abstract: Given an existing public transportation network, the classic planning process in public transportation is as follows: In a first step, the lines are designed; in a second step a timetable is calculated and finally the vehicle and crew schedules are planned. The drawback of this sequence is that the main factors for the costs (i.e. the number of vehicles and drivers needed) are only determined in a late stage of the planning process. We hence suggest to reorder the classic sequence of the planning steps: In our new approach we first design the vehicle routes, then split them to lines and finally calculate a (periodic) timetable. The advantage is that costs can be controlled during the whole process while the objective in all three steps is customer-oriented. In the paper we formulate an integrated model from which we develop this new approach, discuss the complexity of the resulting problems, and present a heuristic which we applied within a case study, optimizing the local bus system in Gottingen, Germany.

Automated timetable design for demand-oriented service on suburban railways

Abstract: Economic and attractive operation of suburban railways can only be realised by flexibilisation of headways, adaptation of the network and capacity of the different lines Under those circumstances, the computation of optimal operation programmes is very complex This contribution presents a two-level approach (computation of transport offer, timetable design) and shows the results obtained from fully-automatic offer planning and timetabling for a suburban railway

A multi-objective metaheuristic approach for the Transit Network Design Problem

Abstract: We study the problem of the optimal design of routes and frequencies in urban public transit systems, the Transit Network Design Problem (TNDP), which is modeled as a multi-objective combinatorial optimization problem. A new heuristic based on the GRASP metaheuristic is proposed to solve the TNDP. As a multi-objective metaheuristic, it produces in a single run a set of non-dominated solutions representing different trade-off levels between the conflicting objectives of users and operators. Previous approaches have dealt with the multi-objective nature of the problem by weighting the different objectives into a single objective function. The case proposed by Mandl is used to show that the multi-objective metaheuristic is capable of producing a diverse set of solutions, which are compared with solutions obtained by other authors. We show that the proposed algorithm produces more non-dominated solutions than the Weighted Sum Method with the same computational effort, using the case of Mandl and another real test case.

The Integrated Dial-a-Ride Problem

Abstract: In this paper we present a formulation of the Integrated Dial-a-Ride (IDARP). This problem is to schedule dial-a-ride requests, where some part of each journey may be carried out by a fixed route service. The IDARP is a generalization of the Dial-a-Ride Problem. An arc-based formulation is proposed, and it is shown how the model can be made easier to solve by arc elimination, variable substitution and the introduction of subtour elimination constraints. Small instances of the IDARP can be solved using an exact solution method, and one such instance is studied. We also describe how input and output data can be created and visualized in a geographic information system.

Regularity analysis for optimizing urban transit network design

Abstract: Transit network planners often propose network structures that either assume a certain level of regularity or are even especially focused on improving service reliability, such as networks in which parts of lines share a common route or the introduction of short-turn services. The key idea is that travelers on that route will have a more frequent transit service. The impact of such network designs on service regularity is rarely analyzed in a quantitative way. This paper presents a tool that can be used to assess the impact of network changes on the regularity on a transit route and on the level of transit demand. The tool can use actual data on the punctuality of the transit system. The application of such a tool is illustrated in two ways. A case study on introducing coordinated services shows that the use of such a tool leads to more realistic estimates than the traditional approach. Second, a set of graphs is developed which can be used for a quick scan when considering network changes. These graphs can be used to assess the effect of coordinating the schedules and of improving the punctuality.

Delay resistant timetabling

Abstract: In public transport punctuality has prominent influence on the customers’ satisfaction. Our task is to support a management decision to optimally invest passengers’ nominal travel time to secure the nominal schedule against delay. For aperiodic scheduling we clarify the notion and use of a fixed amount of time supplements, so-called buffers, both theoretically and by realistic examples. The general tool to solve such optimization problems is a sampling approach. We show how this approach is mathematically justified. As its applicability to large networks is limited, we show an efficient alternative for the case of series-parallel graphs. For periodic timetabling we propose two heuristic approaches to ensure a certain level of delay resistance at the least expense of slightly increased nominal passengers travel time, and analyze in detail their advantages and drawbacks.

Optimality conditions for public transport schedules with timepoint holding

Abstract: Holding buses to scheduled departure time at timepoints involves a tradeoff between reliability and speed, with impacts on user and operating cost. Two new measures of user cost, excess waiting time and potential travel time, are proposed. They relate to the early extreme of a bus’s departure time distribution from a passenger’s origin stop, and the late extreme of a bus’s arrival time distribution at the destination stop. A route with long headway service is modeled assuming that segment running times are independently distributed. Operating impacts of unreliability are captured by requiring enough recovery time that delay does not systematically grow with each cycle. Based on an objective of minimizing a sum of operating cost and user costs, optimality conditions are derived for the strictness of a timepoint and for dispatching reliability at the terminal, which are related to the amount of slack within the running time schedule and within the scheduled layover. It is shown that a timepoint’s optimal strictness (probability of holding) increases with the demand for boardings at the timepoint, with the effect diminishing as stops become farther from the start of the route; however, welfare benefits compared to using a uniform percentage of slack across the route may be small. It is also shown that there is no universally optimal dispatch reliability; the more slack is built into the running time schedule, the less reliable should be the dispatch from the terminal. Up to a point, as scheduled running time increases, the optimal recovery time decreases, and slack time spent holding en route substitutes one-to-one for slack time spent holding at the terminal, so that holding at timepoints does not necessarily increase operating cost.

Decision support for crew rostering at NS

Abstract: This paper describes a method for solving the cyclic crew rostering problem (CCRP). This is the problem of cyclically ordering a set of duties for a number of crew members, such that several complex constraints are satisfied and such that the quality of the obtained roster is as high as possible. The described method was tested on a number of instances of NS, the largest operator of passenger trains in the Netherlands. These instances involve the generation of rosters for groups of train drivers or conductors of NS. The tests show that high quality solutions for practical instances of the CCRP can be generated in an acceptable amount of computing time. Finally, we describe an experiment where we constructed rosters in an automatic way for a group of conductors. They preferred our—generated—rosters over their own manually constructed rosters.

An examination of take-off scheduling constraints at London Heathrow airport

Abstract: In this paper, we focus upon the departure system for London Heathrow airport, one of the busiest airports in the world. Decreasing the delay for aircraft awaiting take-off with their engines running would decrease fuel usage and have consequent cost and pollution benefits. We explain how the departure system at Heathrow currently works and we describe the various constraints that apply to take-off schedules. A model for the take-off order problem is presented from the point of view of the runway controller, the person who is responsible for the take-off scheduling. We investigate the effects of each constraint and combination of constraints, using a simulation of the Heathrow departure system. The role of the runway controller in the simulation is performed by a search which was designed to form the basis of an online decision support system. Both the simulation and the decision support system are fully described. We use the results to evaluate the effect upon delay that we would expect from various changes that could be made to the departure system. We end the paper by drawing conclusions about the predicted effectiveness of different changes that could be made to the departure system and focus upon a further opportunity for decision support research.

Driver scheduling problem modelling

Abstract: The Drivers Scheduling Problem (DSP) consists of selecting a set of duties for vehicle drivers, for example buses, trains, plane or boat drivers or pilots, for the transportation of passengers or goods. This is a complex problem because it involves several constraints related to labour and company rules and can also present different evaluation criteria and objectives. Being able to develop an adequate model for this problem that can represent the real problem as close as possible is an important research area.The main objective of this research work is to present new mathematical models to the DSP problem that represent all the complexity of the drivers scheduling problem, and also demonstrate that the solutions of these models can be easily implemented in real situations. This issue has been recognized by several authors and as important problem in Public Transportation. The most well-known and general formulation for the DSP is a Set Partition/Set Covering Model (SPP/SCP). However, to a large extend these models simplify some of the specific business aspects and issues of real problems. This makes it difficult to use these models as automatic planning systems because the schedules obtained must be modified manually to be implemented in real situations. Based on extensive passenger transportation experience in bus companies in Portugal, we propose new alternative models to formulate the DSP problem. These models are also based on Set Partitioning/Covering Models; however, they take into account the bus operator issues and the perspective opinions and environment of the user.We follow the steps of the Operations Research Methodology which consist of: Identify the Problem; Understand the System; Formulate a Mathematical Model; Verify the Model; Select the Best Alternative; Present the Results of the Analysis and Implement and Evaluate. All the processes are done with close participation and involvement of the final users from different transportation companies. The planner?s opinion and main criticisms are used to improve the proposed model in a continuous enrichment process. The final objective is to have a model that can be incorporated into an information system to be used as an automatic tool to produce driver schedules. Therefore, the criteria for evaluating the models is the capacity to generate real and useful schedules that can be implemented without many manual adjustments or modifications. We have considered the following as measures of the quality of the model: simplicity, solution quality and applicability. We tested the alternative models with a set of real data obtained from several different transportation companies and analyzed the optimal schedules obtained with respect to the applicability of the solution to the real situation. To do this, the schedules were analyzed by the planners to determine their quality and applicability. The main result of this work is the proposition of new mathematical models for the DSP that better represent the realities of the passenger transportation operators and lead to better schedules that can be implemented directly in real situations.

Branching approaches for integrated vehicle and crew scheduling

Abstract: The integrated multi-depot vehicle and crew scheduling problem simultaneously builds vehicle blocks and crew duties. We present an integer mathematical formulation that combines a multi-commodity flow model with a mixed set partitioning/covering model. We propose solution approaches that start by solving the linear programming relaxation of the model. Whenever the resulting linear programming solution is not integer, three branching alternative strategies can be applied: a branch-and-bound algorithm and two branch-and-price schemes. The branch-and-bound algorithm performs branching over the set of feasible crew duties generated while solving the linear relaxation. In the first branch-and-price scheme the linear programming relaxation is solved approximately, while in the second one it is solved exactly. Computational experience is reported over two different types of problems: randomly generated data publicly available for benchmarking in the Internet and data from a bus company operating in Lisbon.

Bi-objective evolutionary heuristics for bus driver rostering

Abstract: The Bus Driver Rostering Problem (BRP) refers to the assignment of drivers to the daily crew duties that cover a set of schedules for buses of a company during a planning period of a given duration, e.g., a month. An assignment such as this, denoted as roster, must comply with legal and institutional rules, namely Labour Law, labour agreements and the company’s regulations. This paper presents a new bi-objective model for the BRP, assuming a non-cyclic rostering context. One such model is appropriate to deal with the specific and diverse requirements of individual drivers, e.g. absences. Two evolutionary heuristics, differing as to the strategies adopted to approach the Pareto frontier, are described for the BRP. The first one, following a utopian strategy, extends elitism to include an infeasible (utopic) and two potential lexicographic individuals in the population, and the second one is an adapted version of the well known SPEA2 (Strength Pareto Evolutionary Algorithm). The heuristics’ empirical performance was studied through computational tests on BRP instances generated from the solution of integrated vehicle-crew scheduling problems, along with the rules of a public transit company operating in Portugal. This research shows that both methodologies are adequate to tackle these instances. However, the second one is, in general, the more favourable. In reasonable computation times they provide the company’s planning department with several rosters that satisfy all the constraints, an achievement which is very difficult to obtain manually. In addition, among these rosters they identify the potentially efficient ones with respect to the BRP model’s two objectives, one concerning the interests of administration, the other the interests of the workers. Both heuristics have advantages and drawbacks. This suggests that they should be used complementarily. On the other hand, the heuristics can, with little effort, be adapted to a wide variety of rostering rules.

Congested Multimodal Transit Network Design

Abstract: The planning of transit services is vital to transit-oriented metropolises. It is a complex, multi-objective decision process, especially for services operated by the private sector. Traveler’s desire for direct, affordable, and quality services often conflicts with the profit-making objective of private operators. In a multi-modal network, partly collaborative and partly competitive interactions among transit modes further complicate the problem. To simplify the planning problem, existing studies generally consider transit network design from the perspective of a single mode while neglecting the modal interactions. The lack of a comprehensive approach across transit modes may result in an unbalanced supply of transit services, weakening the financial viability of the services and, more importantly, adding unnecessarily to congestion, especially in already congested districts. This study explicitly considers these interactions in a multi-modal network framework. We develop a systematic phase-wise methodology for multi-modal network design, considering both the effect of congestion and integration of modal transfers. Inter-route and inter-modal transfers are modeled through the State Augmented Multi-modal (SAM) network approach developed in earlier studies. An illustrative example is included to demonstrate the design procedure and its salient features.

Critical time windowed train driver relief opportunities

Abstract: Train driver scheduling is the problem of constructing an efficient schedule of driver shifts, each of which contains a sequence of work on one or more trains separated by breaks. Relief opportunities (ROs) occur when trains stop at a station. While relieving on arrival at a train station is the preferred practice in the UK rail industry, considering relieving at other times within the full window of relief opportunities (WRO) at a stop might allow for a schedule optimization algorithm to build better schedules. However, simply expanding each WRO into ROs at individual minutes within the WRO would exponentially increase the complexity of the combinatorial optimization problem. A rational approach would be to be selective in considering the WROs when applying Generate-and-Select (GaS); this could either take the form of a pre-processing stage to GaS, or that of augmenting (or even replacing) the generation phase of GaS. In this paper we first show a simple example where approximating WROs by a single relief point results in inefficient schedules, and hints at the complexity of exploiting WROs. We then study the potential of WROs in terms of the new spells and/or shifts they may allow to be created. We propose a heuristic extension to the GaS generation phase, where WROs are analysed in relation to individual scheduling constraints; ROs within WROs that are deemed useful are added to the set of arrival-time ROs. Results show an improvement over the traditional approach in a number of real-life instances from UK operations. We also present a constructive method to analyse a combination of scheduling constraints. Results show that the method is effective in exploiting constraints that may be skipped or difficult to consider by non-constructive approaches.