eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2018-08-28
65
0
0
10.4230/OASIcs.ATMOS.2018
article
OASIcs, Volume 65, ATMOS'18, Complete Volume
Borndörfer, Ralf
Storandt, Sabine
OASIcs, Volume 65, ATMOS'18, Complete Volume
https://drops.dagstuhl.de/storage/01oasics/oasics-vol065-atmos2018/OASIcs.ATMOS.2018/OASIcs.ATMOS.2018.pdf
Theory of computation, Design and analysis of algorithms, Mathematics of computing, Discrete mathematics, Mathematics of computing, Combinatorics
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2018-08-28
65
0:i
0:x
10.4230/OASIcs.ATMOS.2018.0
article
Front Matter, Table of Contents, Preface, Conference Organization
Borndörfer, Ralf
Storandt, Sabine
Front Matter, Table of Contents, Preface, Conference Organization
https://drops.dagstuhl.de/storage/01oasics/oasics-vol065-atmos2018/OASIcs.ATMOS.2018.0/OASIcs.ATMOS.2018.0.pdf
Front Matter
Table of Contents
Preface
Conference Organization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2018-08-28
65
1:1
1:10
10.4230/OASIcs.ATMOS.2018.1
article
Reformulations for Integrated Planning of Railway Traffic and Network Maintenance
Lidén, Tomas
1
https://orcid.org/0000-0002-1643-6365
Linköping University, Department of Science and Technology, Norrköping SE-601 74, Sweden
This paper addresses the capacity planning problem of coordinating train services and network maintenance windows for a railway system. We present model reformulations, for a mixed integer linear optimization model, which give a mathematically stronger model and substantial improvements in solving performance - as demonstrated with computational experiments on a set of synthetic test instances. As a consequence, more instances can be solved to optimality within a given time limit and the optimality gap can be reduced quicker.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol065-atmos2018/OASIcs.ATMOS.2018.1/OASIcs.ATMOS.2018.1.pdf
Railway scheduling
Maintenance planning
Optimization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2018-08-28
65
2:1
2:9
10.4230/OASIcs.ATMOS.2018.2
article
Large Scale Railway Renewal Planning with a Multiobjective Modeling Approach
Sousa, Nuno
1
https://orcid.org/0000-0002-2681-5035
Alçada-Almeida, Luis
2
https://orcid.org/0000-0003-1272-9053
Coutinho-Rodrigues, João
3
https://orcid.org/0000-0001-9311-5584
INESC-Coimbra, Coimbra, Portugal, Department of Sciences and Technology, Open University, Lisbon, Portugal, R. da Escola Politécnica 141-147, 1269-001 Lisboa, Portugal. Phone +351 213 916 300
INESC-Coimbra, Coimbra, Portugal , Faculty of Economics, University of Coimbra, Coimbra, Portugal, Av. Dr. Dias da Silva 165, 3004-512 Coimbra, Portugal. Phone: +351 239 790 500
INESC-Coimbra, Coimbra, Portugal, Department of Civil Engineering, Faculty of Sciences and Technology, University of Coimbra, Coimbra, Portugal, Rua Luís Reis Santos - Polo II, 3030-788 Coimbra, Portugal. Phone +351 239 797 100
A multiobjective modeling approach for managing large scale railway infrastructure asset renewal is presented. An optimized intervention project schedule is obtained considering operational constraints in a three objectives model: evenly spreading investment throughout multiple years, minimizing total cost, minimizing work start postponements on higher priority railway sections. The MILP model was based on a real world case study; the objectives and constraints specified by an infrastructure management company. Results show that investment spreading greatly influences the other objectives and that total cost fluctuations depend on the overall condition of the railway infrastructure. The model can produce exact efficient solutions in reasonable time, even for very large-sized instances (a test network of similar size to the USA railway network, the largest in the world). The modeling approach is therefore a very useful, practical methodology, for generating optimized solutions and analyzing trade-offs among objectives, easing the task of ultimately selecting a solution and produce the works schedule for field implementation.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol065-atmos2018/OASIcs.ATMOS.2018.2/OASIcs.ATMOS.2018.2.pdf
Rail infrastructure
Renewal maintenance
Multiobjective modeling
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2018-08-28
65
3:1
3:13
10.4230/OASIcs.ATMOS.2018.3
article
How to Measure the Robustness of Shunting Plans
van den Broek, Roel
1
Hoogeveen, Han
1
van den Akker, Marjan
1
Department of Computer Science, Utrecht University, Utrecht, The Netherlands
The general problem of scheduling activities subject to temporal and resource constraints as well as a deadline emerges naturally in numerous application domains such as project management, production planning, and public transport. The schedules often have to be implemented in an uncertain environment, where disturbances cause deviations in the duration, release date or deadline of activities. Since these disruptions are not known in the planning phase, we must have schedules that are robust, i.e., capable of absorbing the disturbances without large deteriorations of the solution quality. Due to the complexity of computing the robustness of a schedule directly, many surrogate robustness measures have been proposed in literature. In this paper, we propose new robustness measures, and compare these and several existing measures with the results of a simulation study to determine which measures can be applied in practice to obtain good approximations of the true robustness of a schedule with deadlines. The experiments are performed on schedules generated for real-world scheduling problems at the shunting yards of the Dutch Railways (NS).
https://drops.dagstuhl.de/storage/01oasics/oasics-vol065-atmos2018/OASIcs.ATMOS.2018.3/OASIcs.ATMOS.2018.3.pdf
robustness
resource-constrained project scheduling
partial order schedule
uncertainty
Monte Carlo simulation
train shunting
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2018-08-28
65
4:1
4:17
10.4230/OASIcs.ATMOS.2018.4
article
Robustness as a Third Dimension for Evaluating Public Transport Plans
Friedrich, Markus
1
Müller-Hannemann, Matthias
2
https://orcid.org/0000-0001-6976-0006
Rückert, Ralf
2
Schiewe, Alexander
3
Schöbel, Anita
3
Institut für Straßen- und Verkehrswesen, Universität Stuttgart, Pfaffenwaldring 7, D 70569 Stuttgart, Germany
Institut für Informatik, Martin-Luther-Universität Halle-Wittenberg, Von-Seckendorff-Platz 1, D 06120 Halle (Saale), Germany
Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Lotzestr. 16-18, D 37083 Göttingen, Germany
Providing attractive and efficient public transport services is of crucial importance due to higher demands for mobility and the need to reduce air pollution and to save energy. The classical planning process in public transport tries to achieve a reasonable compromise between service quality for passengers and operating costs. Service quality mostly considers quantities like average travel time and number of transfers. Since daily public transport inevitably suffers from delays caused by random disturbances and disruptions, robustness also plays a crucial role.
While there are recent attempts to achieve delay-resistant timetables, comparably little work has been done to systematically assess and to compare the robustness of transport plans from a passenger point of view. We here provide a general and flexible framework for evaluating public transport plans (lines, timetables, and vehicle schedules) in various ways. It enables planners to explore several trade-offs between operating costs, service quality (average perceived travel time of passengers), and robustness against delays. For such an assessment we develop several passenger-oriented robustness tests which can be instantiated with parameterized delay scenarios. Important features of our framework include detailed passenger flow models, delay propagation schemes and disposition strategies, rerouting strategies as well as vehicle capacities.
To demonstrate possible use cases, our framework has been applied to a variety of public transport plans which have been created for the same given demand for an artificial urban grid network and to instances for long-distance train networks. As one application we study the impact of different strategies to improve the robustness of timetables by insertion of supplement times. We also show that the framework can be used to optimize waiting strategies in delay management.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol065-atmos2018/OASIcs.ATMOS.2018.4/OASIcs.ATMOS.2018.4.pdf
robustness
timetabling
vehicle schedules
delays
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2018-08-28
65
5:1
5:21
10.4230/OASIcs.ATMOS.2018.5
article
Fast Robust Shortest Path Computations
Hansknecht, Christoph
1
Richter, Alexander
1
Stiller, Sebastian
1
Institute for Mathematical Optimization, Technical University Braunschweig, Germany
We develop a fast method to compute an optimal robust shortest path in large networks like road networks, a fundamental problem in traffic and logistics under uncertainty.
In the robust shortest path problem we are given an s-t-graph D(V,A) and for each arc a nominal length c(a) and a maximal increase d(a) of its length. We consider all scenarios in which for the increased lengths c(a) + bar{d}(a) we have bar{d}(a) <= d(a) and sum_{a in A} (bar{d}(a)/d(a)) <= Gamma. Each path is measured by the length in its worst-case scenario. A classic result [Bertsimas and Sim, 2003] minimizes this path length by solving (|A| + 1)-many shortest path problems. Easily, (|A| + 1) can be replaced by |Theta|, where Theta is the set of all different values d(a) and 0. Still, the approach remains impractical for large graphs.
Using the monotonicity of a part of the objective we devise a Divide and Conquer method to evaluate significantly fewer values of Theta. This methods generalizes to binary linear robust problems. Specifically for shortest paths we derive a lower bound to speed-up the Divide and Conquer of Theta. The bound is based on carefully using previous shortest path computations. We combine the approach with non-preprocessing based acceleration techniques for Dijkstra adapted to the robust case.
In a computational study we document the value of different accelerations tried in the algorithm engineering process. We also give an approximation scheme for the robust shortest path problem which computes a (1 + epsilon)-approximate solution requiring O(log(d^ / (1 + epsilon))) computations of the nominal problem where d^ := max d(A) / min (d(A)\{0}).
https://drops.dagstuhl.de/storage/01oasics/oasics-vol065-atmos2018/OASIcs.ATMOS.2018.5/OASIcs.ATMOS.2018.5.pdf
Graph Algorithms
Shortest Paths
Robust Optimization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2018-08-28
65
6:1
6:13
10.4230/OASIcs.ATMOS.2018.6
article
Tree Decomposition Methods for the Periodic Event Scheduling Problem
van Heuven van Staereling, Irving
1
Centrum Wiskunde & Informatica, Science Park 123, Amsterdam, Netherlands
This paper proposes an algorithm that decomposes the Periodic Event Scheduling Problem (PESP) into trees that can efficiently be solved. By identifying at an early stage which partial solutions can lead to a feasible solution, the decomposed components can be integrated back while maintaining feasibility if possible. If not, the modifications required to regain feasibility can be found efficiently. These techniques integrate dynamic programming into standard search methods.
The performance of these heuristics are very satisfying, as the problem using publicly available benchmarks can be solved within a reasonable amount of time, in an alternative way than the currently accepted leading-edge techniques. Furthermore, these heuristics do not necessarily rely on linearity of the objective function, which facilitates the research of timetabling under nonlinear circumstances.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol065-atmos2018/OASIcs.ATMOS.2018.6/OASIcs.ATMOS.2018.6.pdf
Dynamic Programming
Trees
Periodic Event Scheduling Problem
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2018-08-28
65
7:1
7:13
10.4230/OASIcs.ATMOS.2018.7
article
A Bilevel Approach to Frequency Optimization in Public Transportation Systems
Arizti, Agustin
1
Mauttone, Antonio
1
Urquhart, Maria E.
1
Universidad de la República, J. Herrera y Reissig 565, Montevideo, Uruguay
We consider the problem of frequency optimization in transit systems, whose objective is to determine the time interval between subsequent buses for a set of public transportation lines. We extend an existing single level model by adding a constraint on bus capacities, while maintaining user choice on routes by means of an assignment sub-model. The resulting formulation is bilevel, and is transformed into a mixed integer linear programming formulation (MILP) that can be solved to optimality for small-sized problem instances, using standard MILP techniques. We study different variants of the same formulation to better understand the bilevel nature of the model and its application to real settings.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol065-atmos2018/OASIcs.ATMOS.2018.7/OASIcs.ATMOS.2018.7.pdf
transportation
public transport capacity
transit frequency optimization
mixed integer linear programming
bilevel programming
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2018-08-28
65
8:1
8:22
10.4230/OASIcs.ATMOS.2018.8
article
Cost-Minimal Public Transport Planning
Pätzold, Julius
1
Schiewe, Alexander
1
Schöbel, Anita
1
University of Goettingen, Lotzestr. 16-18, 37083 Göttingen, Germany
In this paper we discuss what a cost-optimal public transport plan looks like, i.e., we determine a line plan, a timetable and a vehicle schedule which can be operated with minimal costs while, at the same time, allowing all passengers to travel between their origins and destinations. We are hereby interested in an exact solution of the integrated problem. In contrast to a passenger-optimal transport plan, in which there is a direct connection for every origin-destination pair, the structure or model for determining a cost-optimal transport plan is not obvious and has not been researched so far.
We present three models which differ with respect to the structures we are looking for. If lines are directed and may contain circles, we prove that a cost-optimal schedule can (under weak assumptions) already be obtained by first distributing the passengers in a cost-optimal way. We are able to streamline the resulting integer program such that it can be applied to real-world instances. The model gives bounds for the general case. In the second model we look for lines operated in both directions, but allow only simplified vehicle schedules. This model then yields stronger bounds than the first one. Our most realistic model looks for lines operated in both directions, and allows all structures for the vehicle schedules. This model, however, is only computable for small instances. Finally, the results of the three models and their respective bounds are compared experimentally.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol065-atmos2018/OASIcs.ATMOS.2018.8/OASIcs.ATMOS.2018.8.pdf
Public Transport Planning
Integer Optimization
Line Planning
Vehicle Scheduling
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2018-08-28
65
9:1
9:15
10.4230/OASIcs.ATMOS.2018.9
article
Changing Lanes on a Highway
Petig, Thomas
1
Schiller, Elad M.
2
Suomela, Jukka
3
Qamcom Research and Technology AB, Sweden
Chalmers University of Technology, Sweden
Aalto University, Finland
We study a combinatorial optimization problem that is motivated by the scenario of autonomous cars driving on a multi-lane highway: some cars need to change lanes before the next intersection, and if there is congestion, cars need to slow down to make space for those who are changing lanes. There are two natural objective functions to minimize: (1) how long does it take for all traffic to clear the road, and (2) the total number of maneuvers. In this work, we present an approximation algorithm for solving these problems in the two-lane case and a hardness result for the multi-lane case.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol065-atmos2018/OASIcs.ATMOS.2018.9/OASIcs.ATMOS.2018.9.pdf
Collaborative agents
vehicle scheduling
traffic optimization
approximation algorithms
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2018-08-28
65
10:1
10:19
10.4230/OASIcs.ATMOS.2018.10
article
Parameterized Algorithms and Data Reduction for Safe Convoy Routing
van Bevern, René
1
2
https://orcid.org/0000-0002-4805-218X
Fluschnik, Till
3
Tsidulko, Oxana Yu.
2
1
Department of Mechanics and Mathematics, Novosibirsk State University, Ulitsa Pirogova 2, 630090 Novosibirsk, Russian Federation
Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Prospekt Akademika Koptyuga 4, 630090 Novosibirsk, Russian Federation
Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Ernst-Reuter-Platz 7, 10587 Berlin, Germany
We study a problem that models safely routing a convoy through a transportation network, where any vertex adjacent to the travel path of the convoy requires additional precaution: Given a graph G=(V,E), two vertices s,t in V, and two integers k,l, we search for a simple s-t-path with at most k vertices and at most l neighbors. We study the problem in two types of transportation networks: graphs with small crossing number, as formed by road networks, and tree-like graphs, as formed by waterways. For graphs with constant crossing number, we provide a subexponential 2^O(sqrt n)-time algorithm and prove a matching lower bound. We also show a polynomial-time data reduction algorithm that reduces any problem instance to an equivalent instance (a so-called problem kernel) of size polynomial in the vertex cover number of the input graph. In contrast, we show that the problem in general graphs is hard to preprocess. Regarding tree-like graphs, we obtain a 2^O(tw) * l^2 * n-time algorithm for graphs of treewidth tw, show that there is no problem kernel with size polynomial in tw, yet show a problem kernel with size polynomial in the feedback edge number of the input graph.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol065-atmos2018/OASIcs.ATMOS.2018.10/OASIcs.ATMOS.2018.10.pdf
NP-hard problem
fixed-parameter tractability
problem kernelization
shortest path
secluded solution
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2018-08-28
65
11:1
11:15
10.4230/OASIcs.ATMOS.2018.11
article
A Neighborhood Search and Set Cover Hybrid Heuristic for the Two-Echelon Vehicle Routing Problem
Amarouche, Youcef
1
Guibadj, Rym N.
2
Moukrim, Aziz
1
Sorbonne universités, Université de technologie de Compiègne, CNRS, Heudiasyc UMR 7253, CS 60 319, 60 203 Compiègne cedex, France
LISIC, Laboratoire d'Informatique Signal et Image de la Côte d'Opale, ULCO, Université Lille Nord-de-France, France
The Two-Echelon Vehicle Routing Problem (2E-VRP) is a variant of the classical vehicle routing problem arising in the context of city logistics. In the 2E-VRP, freight from a main depot is delivered to final customers using intermediate facilities, called satellites. In this paper, we propose a new hybrid heuristic method for solving the 2E-VRP that relies on two components. The first component effectively explores the search space in order to discover a set of interesting routes. The second recombines the discovered routes into high-quality solutions. Experimentations on benchmark instances show the performance of our approach: our algorithm achieves high-quality solutions in short computational times and improves the current best known solutions for several large scale instances.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol065-atmos2018/OASIcs.ATMOS.2018.11/OASIcs.ATMOS.2018.11.pdf
Two-Echelon Vehicle Routing Problem
City Logistics
hybrid method
integer programming
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2018-08-28
65
12:1
12:20
10.4230/OASIcs.ATMOS.2018.12
article
Multi-Source Multi-Sink Nash Flows over Time
Sering, Leon
1
Skutella, Martin
1
Institute of Mathematics, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
Nash flows over time describe the behavior of selfish users eager to reach their destination as early as possible while traveling along the arcs of a network with capacities and transit times. Throughout the past decade, they have been thoroughly studied in single-source single-sink networks for the deterministic queuing model, which is of particular relevance and frequently used in the context of traffic and transport networks. In this setting there exist Nash flows over time that can be described by a sequence of static flows featuring special properties, so-called `thin flows with resetting'. This insight can also be used algorithmically to compute Nash flows over time. We present an extension of these results to networks with multiple sources and sinks which are much more relevant in practical applications. In particular, we come up with a subtle generalization of thin flows with resetting, which yields a compact description as well as an algorithmic approach for computing multi-terminal Nash flows over time.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol065-atmos2018/OASIcs.ATMOS.2018.12/OASIcs.ATMOS.2018.12.pdf
Network congestion
Nash equilibrium
dynamic routing game
deterministic queuing model
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2018-08-28
65
13:1
13:22
10.4230/OASIcs.ATMOS.2018.13
article
Oligopolistic Competitive Packet Routing
Peis, Britta
1
Tauer, Bjoern
1
Timmermans, Veerle
1
Vargas Koch, Laura
1
Department of Management Science, RWTH Aachen, Kackertstraße 7, 52072 Aachen, Germany
Oligopolistic competitive packet routing games model situations in which traffic is routed in discrete units through a network over time. We study a game-theoretic variant of packet routing, where in contrast to classical packet routing, we are lacking a central authority to decide on an oblivious routing protocol. Instead, selfish acting decision makers ("players") control a certain amount of traffic each, which needs to be sent as fast as possible from a player-specific origin to a player-specific destination through a commonly used network. The network is represented by a directed graph, each edge of which being endowed with a transit time, as well as a capacity bounding the number of traffic units entering an edge simultaneously. Additionally, a priority policy on the set of players is publicly known with respect to which conflicts at intersections are resolved. We prove the existence of a pure Nash equilibrium and show that it can be constructed by sequentially computing an integral earliest arrival flow for each player. Moreover, we derive several tight bounds on the price of anarchy and the price of stability in single source games.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol065-atmos2018/OASIcs.ATMOS.2018.13/OASIcs.ATMOS.2018.13.pdf
Competitive Packet Routing
Nash Equilibrium
Oligopoly
Efficiency of Equilibria
Priority Policy
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2018-08-28
65
14:1
14:11
10.4230/OASIcs.ATMOS.2018.14
article
The Path&Cycle Formulation for the Hotspot Problem in Air Traffic Management
Mannino, Carlo
1
Sartor, Giorgio
1
SINTEF, Forskningsveien 1, Oslo, Norway
The Hotspot Problem in Air Traffic Management consists of optimally rescheduling a set of airplanes that are forecast to occupy an overcrowded region of the airspace, should they follow their original schedule. We first provide a MILP model for the Hotspot Problem using a standard big-M formulation. Then, we present a novel MILP model that gets rid of the big-M coefficients. The new formulation contains only simple combinatorial constraints, corresponding to paths and cycles in an associated disjunctive graph. We report computational results on a set of randomly generated instances. In the experiments, the new formulation consistently outperforms the big-M formulation, both in terms of running times and number of branching nodes.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol065-atmos2018/OASIcs.ATMOS.2018.14/OASIcs.ATMOS.2018.14.pdf
Air Traffic Management
Hotspot Problem
Job-shop scheduling
Mixed Integer Linear Programming
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2018-08-28
65
15:1
15:14
10.4230/OASIcs.ATMOS.2018.15
article
Vehicle Scheduling Based on a Line Plan
van Lieshout, Rolf N.
1
Bouman, Paul C.
1
Erasmus University Rotterdam, Econometric Institute, Erasmus University Rotterdam, 3000 DR Rotterdam, The Netherlands
We consider the following problem: given a set of lines in a public transportation network with their round trip times and frequencies, a maximum number of vehicles and a maximum number of lines that can be combined into a vehicle circulation, does there exist a set of vehicle circulations that covers all lines given the constraints. Solving this problem provides an estimate of the costs of operating a certain line plan, without having to compute a timetable first. We show that this problem is NP-hard for any restriction on the number of lines that can be combined into a circulation which is equal to or greater than three. We pay special attention to the case where at most two lines can be combined into a circulation, which is NP-hard if a single line can be covered by multiple circulations. If this is not allowed, a matching algorithm can be used to find the optimal solutions, which we show to be a 16/15-approximation for the case where it is allowed. We also provide an exact algorithm that is able to exploit low tree-width of the so-called circulation graph and small numbers of vehicles required to cover single circulations.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol065-atmos2018/OASIcs.ATMOS.2018.15/OASIcs.ATMOS.2018.15.pdf
Vehicle scheduling
integrated railway planning
(fractional) matching
treewidth
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2018-08-28
65
16:1
16:15
10.4230/OASIcs.ATMOS.2018.16
article
A Simple Way to Compute the Number of Vehicles That Are Required to Operate a Periodic Timetable
Borndörfer, Ralf
1
Karbstein, Marika
1
Liebchen, Christian
2
Lindner, Niels
1
Zuse Institute Berlin (ZIB), Takustr. 7, 14195 Berlin, Germany
Technical University of Applied Sciences Wildau, Hochschulring 1, 15745 Wildau, Germany
We consider the following planning problem in public transportation: Given a periodic timetable, how many vehicles are required to operate it?
In [Julius Paetzold et al., 2017], for this sequential approach, it is proposed to first expand the periodic timetable over time, and then answer the above question by solving a flow-based aperiodic optimization problem.
In this contribution we propose to keep the compact periodic representation of the timetable and simply solve a particular perfect matching problem. For practical networks, it is very much likely that the matching problem decomposes into several connected components. Our key observation is that there is no need to change any turnaround decision for the vehicles of a line during the day, as long as the timetable stays exactly the same.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol065-atmos2018/OASIcs.ATMOS.2018.16/OASIcs.ATMOS.2018.16.pdf
Vehicle Scheduling
Periodic Timetabling
Bipartite Matching