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  • 2018  (14)
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  • 2015-2019  (14)
  • 2000-2004
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  • 1
    Publication Date: 2021-01-22
    Description: We study the problem of finding subpaths with high demand in a given network that is traversed by several users. The demand of a subpath is the number of users who completely cover this subpath during their trip. Especially with large instances, an efficient algorithm for computing all subpaths' demands is necessary. We introduce a path-graph to prevent multiple generations of the same subpath and give a recursive approach to compute the demands of all subpaths. Our runtime analysis shows, that the presented approach compares very well against the theoretical minimum runtime.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 2
    Publication Date: 2021-01-22
    Description: The problem of allocating operating rooms (OR) to surgical cases is a challenging task, involving both combinatorial aspects and uncertainty handling. We formulate this problem as a parallel machines scheduling problem, in which job durations follow a lognormal distribution, and a fixed assignment of jobs to machines must be computed. We propose a cutting-plane approach to solve the robust counterpart of this optimization problem. To this end, we develop an algorithm based on fixed-point iterations that identifies worst-case scenarios and generates cut inequalities. The main result of this article uses Hilbert's projective geometry to prove the convergence of this procedure under mild conditions. We also propose two exact solution methods for a similar problem, but with a polyhedral uncertainty set, for which only approximation approaches were known. Our model can be extended to balance the load over several planning periods in a rolling horizon. We present extensive numerical experiments for instances based on real data from a major hospital in Berlin. In particular, we find that: (i) our approach performs well compared to a previous model that ignored the distribution of case durations; (ii) compared to an alternative stochastic programming approach, robust optimization yields solutions that are more robust against uncertainty, at a small price in terms of average cost; (iii) the \emph{longest expected processing time first} (LEPT) heuristic performs well and efficiently protects against extreme scenarios, but only if a good prediction model for the durations is available. Finally, we draw a number of managerial implications from these observations.
    Language: English
    Type: article , doc-type:article
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  • 3
    Publication Date: 2020-08-05
    Description: Wir beschreiben die Optimierung des Nahverkehrsnetzes der Stadt Karlsruhe im Zusammmenhang mit den Baumaßnahmen der sogenannten Kombilösung.
    Language: German
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 4
    Publication Date: 2022-03-11
    Description: We investigate the relation between Hall’s theorem and Kőnig’s theorem in graphs and hypergraphs. In particular, we characterize the graphs satisfying a deficiency version of Hall’s theorem, thereby showing that this class strictly contains all Kőnig–Egerváry graphs. Furthermore, we give a generalization of Hall’s theorem to normal hypergraphs.
    Language: English
    Type: article , doc-type:article
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  • 5
    Publication Date: 2020-08-05
    Description: Dieses Dokument fasst den Stand der mathematischen Modellierung von Preissystemen des öV mittels eines am ZIB entwickelten Tarifgraphenmodells zusammen. Damit sind sehr einfache und konzise Beschreibungen von Tarifstrukturen möglich, die sich algorithmisch behandeln lassen: Durch das zeitgleiche Tracken eines Pfades im Routinggraphen im Tarifgraphen kann schon während einer Routenberechnung der Preis bestimmt werden. Wir beschreiben zunächst das Konzept. Die konkrete Realisierung wird im Folgenden beispielhaft an den Tarifsystemen der Verkehrsverbünde Warnow, MDV, Vogtland, Bremen/Niedersachsen, Berlin/Brandenburg und Mittelsachsen erläutert. Anschließend folgen Überlegungen zur konkreten Implementierung von Kurzstrecken-Tarifen und zur Behandlung des Verbundübergriffs.
    Language: German
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 6
    Publication Date: 2021-01-22
    Description: We study the problem of finding subpaths with high demand in a given network that is traversed by several users. The demand of a subpath is the number of users who completely cover this subpath during their trip. Especially with large instances, an efficient algorithm for computing all subpaths' demands is necessary. We introduce a path-graph to prevent multiple generations of the same subpath and give a recursive approach to compute the demands of all subpaths. Our runtime analysis shows, that the presented approach compares very well against the theoretical minimum runtime.
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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  • 7
    Publication Date: 2021-01-22
    Description: We investigate a graph theoretical problem arising in the automatic billing of a network toll. Given a network and a family of user paths, we study the graph segmentation problem (GSP) to cover parts of the user paths by a set of disjoint segments. The GSP is shown to be NP-hard but for special cases it can be solved in polynomial time. We also show that the marginal utility of a segment is bounded. Computational results for real-world instances show that in practice the problem is more amenable than the theoretic bounds suggest.
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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  • 8
    Publication Date: 2020-11-16
    Description: We consider the following planning problem in public transportation: Given a periodic timetable, how many vehicles are required to operate it? In [9], 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.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 9
    Publication Date: 2020-08-05
    Description: Running and optimizing transportation systems give rise to very complex and large-scale optimization problems requiring innovative solution techniques and ideas from mathematical optimization, theoretical computer science, and operations research. Since 2000, the series of Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS) workshops brings together researchers and practitioners who are interested in all aspects of algorithmic methods and models for transportation optimization and provides a forum for the exchange and dissemination of new ideas and techniques. The scope of ATMOS comprises all modes of transportation. The 18th ATMOS workshop (ATMOS’18) was held in connection with ALGO’18 and hosted by Aalto University in Helsinki, Finland, on August 23–24, 2018. Topics of interest were all optimization problems for passenger and freight transport, including, but not limited to, demand forecasting, models for user behavior, design of pricing systems, infrastructure planning, multi-modal transport optimization, mobile applications for transport, congestion modelling and reduction, line planning, timetable generation, routing and platform assignment, vehicle scheduling, route planning, crew and duty scheduling, rostering, delay management, routing in road networks, traffic guidance, and electro mobility. Of particular interest were papers applying and advancing techniques like graph and network algorithms, combinatorial optimization, mathematical programming, approximation algorithms, methods for the integration of planning stages, stochastic and robust optimization, online and real-time algorithms, algorithmic game theory, heuristics for real-world instances, and simulation tools. There were twenty-nine submissions from eighteen countries. All of them were reviewed by at least three referees in ninety-one reviews, among them five external ones, and judged on their originality, technical quality, and relevance to the topics of the workshop. Based on the reviews, the program committee selected sixteen submissions to be presented at the workshop (acceptance rate: 55%), which are collected in this volume in the order in which they were presented. Together, they quite impressively demonstrate the range of applicability of algorithmic optimization to transportation problems in a wide sense. In addition, Dennis Huisman kindly agreed to complement the program with an invited talk on Railway Disruption Management: State-of-the-art in practice and new research directions. Based on the reviews, Ralf Borndörfer, Marika Karbstein, Christian Liebchen, and Niels Lindner won the Best Paper Award of ATMOS’18 with their paper A simple way to compute the number of vehicles that Are required to operate a periodic timetable. In addition, we awarded Tomas Lidén the Best VGI Paper Award of ATMOS’18 for his paper Reformulations for railway traffic and maintenance planning. We would like to thank the members of the Steering Committee of ATMOS for giving us the opportunity to serve as Program Chairs of ATMOS’18, all the authors who submitted papers, Dennis Huisman for accepting our invitation to present an invited talk, the members of the Program Committee and the additional reviewers for their valuable work in selecting the papers appearing in this volume, our sponsors MODAL, TomTom, and VGIscience for their support of the prizes, and the local organizers for hosting the workshop as part of ALGO’18. We acknowledge the use of the EasyChair system for the great help in managing the submission and review processes, and Schloss Dagstuhl for publishing the proceedings of ATMOS’18 in its OASIcs series.
    Language: English
    Type: proceedings , doc-type:Other
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  • 10
    Publication Date: 2020-08-05
    Description: Rolling stock optimization is a task that naturally arises by operating a railway system. It could be seen with different level of details. From a strategic perspective to have a rough plan which types of fleets to be bought to a more operational perspective to decide which coaches have to be maintained first. This paper presents a new approach to deal with rolling stock optimisation in case of a (long term) strike. Instead of constructing a completely new timetable for the strike period, we propose a mixed integer programming model that is able to choose appropriate trips from a given timetable to construct efficient tours of railway vehicles covering an optimized subset of trips, in terms of deadhead kilometers and importance of the trips. The decision which trip is preferred over the other is made by a simple evaluation method that is deduced from the network and trip defining data.
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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