TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Klostermeier, Fridolin A1 - Küttner, Christian T1 - Telebus Berlin - Mobilität für Behinderte N2 - Steigendes Mobilitätsbedürfnis der Behinderten bei angespannter Haushaltslage --- diese Situation ergab vor drei Jahren beim Berliner Behindertenfahrdienst {\em Telebus\/} Handlungsbedarf. Gleichzeitig stie\ss{} die verwendete manuelle (Fahrzeug-)Tourenplanung mit damals etwa 1.000 Fahrtwünschen pro Tag an ihre Grenzen. Zur Lösung dieser Probleme war der effiziente Einsatz von Computern und von {\em mathematischen Optimierungsverfahren\/} erforderlich. Ergebnis des daraufhin gestarteten {\em Telebus-Projektes\/} ist die Entwicklung eines neuen, alle Arbeitsabläufe unterstützenden Computersystems, das seit über einem Jahr im Einsatz ist. Herzstück dieses Systems ist ein auf mathematischen Methoden der ganzzahligen Optimierung basierendes Verfahren zur Tourenplanung. Ziel dieses Artikels ist die Beschreibung dieses Verfahrens und seiner Verwendung bei der Behindertenbeförderung. Das Beispiel Telebus zeigt, da\ss{} der Einsatz mathematischer Optimierungstechniken neue Möglichkeiten für Kosteneinsparungen bei gleichzeitiger Serviceverbesserung auch in anderen Bereichen des ÖPNV eröffnet. T3 - ZIB-Report - SC-96-40 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2500 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Grimm, Boris A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - Optimization of Handouts for Rolling Stock Rotations Visualization N2 - A railway operator creates (rolling stock) rotations in order to have a precise master plan for the operation of a timetable by railway vehicles. A rotation is considered as a cycle that multiply traverses a set of operational days while covering trips of the timetable. As it is well known, the proper creation of rolling stock rotations by, e.g., optimization algorithms is challenging and still a topical research subject. Nevertheless, we study a completely different but strongly related question in this paper, i.e.: How to visualize a rotation? For this purpose, we introduce a basic handout concept, which directly leads to the visualization, i.e., handout of a rotation. In our industrial application at DB Fernverkehr AG, the handout is exactly as important as the rotation itself. Moreover, it turns out that also other European railway operators use exactly the same methodology (but not terminology). Since a rotation can have many handouts of different quality, we show how to compute optimal ones through an integer program (IP) by standard software. In addition, a construction as well as an improvement heuristic are presented. Our computational results show that the heuristics are a very reliable standalone approach to quickly find near-optimal and even optimal handouts. The efficiency of the heuristics is shown via a computational comparison to the IP approach. T3 - ZIB-Report - ZR-16-73 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61430 SN - 1438-0064 ER - TY - JOUR A1 - Harrod, Steven A1 - Schlechte, Thomas T1 - A Direct Comparison of Physical Block Occupancy Versus Timed Block Occupancy in Train Timetabling Formulations JF - Transportation Research Part E: Logistics and Transportation Review N2 - Two fundamental mathematical formulations for railway timetabling are compared on a common set of sample problems, representing both multiple track high density services in Europe and single track bidirectional operations in North America. One formulation, ACP, enforces against conflicts by constraining time intervals between trains, while the other formulation, RCHF, monitors physical occupation of controlled track segments. The results demonstrate that both ACP and RCHF return comparable solutions in the aggregate, with some significant differences in select instances, and a pattern of significant differences in performance and constraint enforcement overall. Y1 - 2013 U6 - https://doi.org/10.1016/j.tre.2013.04.003 VL - 54 SP - 50 EP - 66 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Karbstein, Marika A1 - Pfetsch, Marc T1 - Models for Fare Planning in Public Transport JF - Discrete Applied Mathematics Y1 - 2012 U6 - https://doi.org/10.1016/j.dam.2012.02.027 VL - 160 IS - 18 SP - 2591 EP - 2605 ER - TY - GEN A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Schlechte, Thomas T1 - Re-optimizing ICE Rotations after a Tunnel Breakdown near Rastatt N2 - Planning rolling stock movements in industrial passenger railway applications isa long-term process based on timetables which are also often valid for long periods of time. For these timetables and rotation plans, i.e., plans of railway vehicle movements are constructed as templates for these periods. During operation the rotation plans are affected by all kinds of unplanned events. An unusal example for that is the collapse of a tunnel ceiling near Rastatt in southern Germany due to construction works related to the renewal of the central station in Stuttgart. As a result the main railway connection between Stuttgart and Frankfurt am Main, located on top of the tunnel, had to be closed from August 12th to October 2nd 2017. This had a major impact on the railway network in southern Germany. Hence, all rotation plans and train schedules for both passenger and cargo traffic had to be revised. In this paper we focus on a case study for this situation and compute new rotation plans via mixed integer programming for the ICE high speed fleet of DB Fernverkehr AG one of the largest passenger railway companies in Europe. In our approach we take care of some side constraints to ensure a smooth continuation of the rotation plans after the disruption has ended. T3 - ZIB-Report - 19-02 KW - case study KW - re-optimization KW - railway rolling stock optimization KW - mixed integer programming Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73976 SN - 1438-0064 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Grimm, Boris A1 - Schlechte, Thomas T1 - Re-optimizing ICE Rotations after a Tunnel Breakdown near Rastatt T2 - Proceedings of the 8th International Conference on Railway Operations Modelling and Analysis - RailNorrköping 2019 N2 - Planning rolling stock movements in industrial passenger railway applications isa long-term process based on timetables which are also often valid for long periods of time. For these timetables and rotation plans, i.e., plans of railway vehicle movements are constructed as templates for these periods. During operation the rotation plans are affected by all kinds of unplanned events. An unusal example for that is the collapse of a tunnel ceiling near Rastatt in southern Germany due to construction works related to the renewal of the central station in Stuttgart. As a result the main railway connection between Stuttgart and Frankfurt am Main, located on top of the tunnel, had to be closed from August 12th to October 2nd 2017. This had a major impact on the railway network in southern Germany. Hence, all rotation plans and train schedules for both passenger and cargo traffic had to be revised. In this paper we focus on a case study for this situation and compute new rotation plans via mixed integer programming for the ICE high speed fleet of DB Fernverkehr AG one of the largest passenger railway companies in Europe. In our approach we take care of some side constraints to ensure a smooth continuation of the rotation plans after the disruption has ended. Y1 - 2019 UR - http://www.ep.liu.se/ecp/article.asp?issue=069&article=011&volume= SN - 978-91-7929-992-7 SN - 1650-3686 VL - Linköping Electronic Conference Proceedings IS - 069 SP - 160 EP - 168 PB - Linköping University Electronic Press, Linköpings universitet CY - Linköping, Sweden ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Grimm, Boris A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - Optimization of handouts for rolling stock rotations JF - Journal of Rail Transport Planning & Management N2 - A railway operator creates (rolling stock) rotations in order to have a precise master plan for the operation of a timetable by railway vehicles. A rotation is considered as a cycle that multiply traverses a set of operational days while covering trips of the timetable. As it is well known, the proper creation of rolling stock rotations by, e.g., optimization algorithms is challenging and still a topical research subject. Nevertheless, we study a completely different but strongly related question in this paper, i.e.: How to visualize a rotation? For this purpose, we introduce a basic handout concept, which directly leads to the visualization, i.e., handout of a rotation. In our industrial application at DB Fernverkehr AG, the handout is exactly as important as the rotation itself. Moreover, it turns out that also other European railway operators use exactly the same methodology (but not terminology). Since a rotation can have many handouts of different quality, we show how to compute optimal ones through an integer program (IP) by standard software. In addition, a construction as well as an improvement heuristic are presented. Our computational results show that the heuristics are a very reliable standalone approach to quickly find near-optimal and even optimal handouts. The efficiency of the heuristics is shown via a computational comparison to the IP approach. Y1 - 2019 U6 - https://doi.org/10.1016/j.jrtpm.2019.02.001 IS - 10 SP - 1 EP - 8 ER - TY - GEN A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Schulz, Christof A1 - Weider, Steffen T1 - The Rolling Stock Rotation Planning Problem under Revenue Considerations N2 - In many railway undertakings a railway timetable is offered that is valid for a longer period of time. At DB Fernverkehr AG, one of our industrial partners, this results in a summer and a winter timetable. For both of these timetables rotation plans, i.e., a detailed plan of railway vehicle movements is constructed as a template for this period. Sometimes there are be periods where you know for sure that vehicle capacities are not sufficient to cover all trips of the timetable or to transport all passenger of the trips. Reasons for that could be a heavy increase of passenger flow, a heavy decrease of vehicle availability, impacts from nature, or even strikes of some employees. In such events the rolling stock rotations have to be adapted. Optimization methods are particularly valuable in such situations in order to maintain a best possible level of service or to maximize the expected revenue using the resources that are still available. In most cases found in the literature, a rescheduling based on a timetable update is done, followed by the construction of new rotations that reward the recovery of parts of the obsolete rotations. We consider a different, novel, and more integrated approach. The idea is to guide the cancellation of the trips or reconfiguration of the vehicle composition used to operate a trip of the timetable by the rotation planning process, which is based on the mixed integer programming approach presented in Reuther (2017). The goal is to minimize the operating costs while cancelling or operating a trip with an insufficient vehicle configuration in sense of passenger capacities inflicts opportunity costs and loss of revenue, which are based on an estimation of the expected number of passengers. The performance of the algorithms presented in two case studies, including real world scenarios from DB Fernverkehr AG and a railway operator in North America. T3 - ZIB-Report - 19-01 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-71339 SN - 1438-0064 ER - TY - CHAP A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Schulz, Christof A1 - Weider, Steffen T1 - The Rolling Stock Rotation Planning Problem under Revenue Considerations T2 - Proceedings of the Rail Transport Demand Management Conference N2 - In many railway undertakings a railway timetable is offered that is valid for a longer period of time. At DB Fernverkehr AG, one of our industrial partners, this results in a summer and a winter timetable. For both of these timetables rotation plans, i.e., a detailed plan of railway vehicle movements is constructed as a template for this period. Sometimes there are be periods where you know for sure that vehicle capacities are not sufficient to cover all trips of the timetable or to transport all passenger of the trips. Reasons for that could be a heavy increase of passenger flow, a heavy decrease of vehicle availability, impacts from nature, or even strikes of some employees. In such events the rolling stock rotations have to be adapted. Optimization methods are particularly valuable in such situations in order to maintain a best possible level of service or to maximize the expected revenue using the resources that are still available. In most cases found in the literature, a rescheduling based on a timetable update is done, followed by the construction of new rotations that reward the recovery of parts of the obsolete rotations. We consider a different, novel, and more integrated approach. The idea is to guide the cancellation of the trips or reconfiguration of the vehicle composition used to operate a trip of the timetable by the rotation planning process, which is based on the mixed integer programming approach presented in Reuther (2017). The goal is to minimize the operating costs while cancelling or operating a trip with an insufficient vehicle configuration in sense of passenger capacities inflicts opportunity costs and loss of revenue, which are based on an estimation of the expected number of passengers. The performance of the algorithms presented in two case studies, including real world scenarios from DB Fernverkehr AG and a railway operator in North America. Y1 - 2018 ER - TY - GEN A1 - Beckenbach, Isabel A1 - Hatzel, Meike A1 - Wiederrecht, Sebastian T1 - The Tight Cut Decomposition of Matching Covered Uniformable Hypergraphs N2 - The perfect matching polytope, i.e. the convex hull of (incidence vectors of) perfect matchings of a graph is used in many combinatorial algorithms. Kotzig, Lovász and Plummer developed a decomposition theory for graphs with perfect matchings and their corresponding polytopes known as the tight cut decomposition which breaks down every graph into a number of indecomposable graphs, so called bricks. For many properties that are of interest on graphs with perfect matchings, including the description of the perfect matching polytope, it suffices to consider these bricks. A key result by Lovász on the tight cut decomposition is that the list of bricks obtained is the same independent of the choice of tight cuts made during the tight cut decomposition procedure. This implies that finding a tight cut decomposition is polynomial time equivalent to finding a single tight cut. We generalise the notions of a tight cut, a tight cut contraction and a tight cut decomposition to hypergraphs. By providing an example, we show that the outcome of the tight cut decomposition on general hypergraphs is no longer unique. However, we are able to prove that the uniqueness of the tight cut decomposition is preserved on a slight generalisation of uniform hypergraphs. Moreover, we show how the tight cut decomposition leads to a decomposition of the perfect matching polytope of uniformable hypergraphs and that the recognition problem for tight cuts in uniformable hypergraphs is polynomial time solvable. T3 - ZIB-Report - 18-61 KW - uniform hypergraphs KW - perfect matchings KW - tight cuts Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-71149 SN - 1438-0064 ER - TY - GEN A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Olthoff, Mats T1 - A Solution Approach to the Vehicle Routing Problem with Perishable Goods N2 - This paper focuses on a special case of vehicle routing problem where perishable goods are considered. Deliveries have to be performed until a due date date, which may vary for different products. Storing products is prohibited. Since late deliveries have a direct impact on the revenues for these products, a precise demand prediction is important. In our practical case the product demands and vehicle driving times for the product delivery are dependent on weather conditions, i.e., temperatures, wind, and precipitation. In this paper the definition and a solution approach to the Vehicle Routing Problem with Perishable Goods is presented. The approach includes a procedure how historical weather data is used to predict demands and driving times. Its run time and solution quality is evaluated on different data sets given by the MOPTA Competition 2018. T3 - ZIB-Report - 20-03 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-77020 SN - 1438-0064 ER - TY - CHAP A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Olthoff, Mats T1 - A Solution Approach to the Vehicle Routing Problem with Perishable Goods T2 - Operations Research 2019 Proceedings N2 - This paper focuses on a special case of vehicle routing problem where perishable goods are considered. Deliveries have to be performed until a due date date, which may vary for different products. Storing products is prohibited. Since late deliveries have a direct impact on the revenues for these products, a precise demand prediction is important. In our practical case the product demands and vehicle driving times for the product delivery are dependent on weather conditions, i.e., temperatures, wind, and precipitation. In this paper the definition and a solution approach to the Vehicle Routing Problem with Perishable Goods is presented. The approach includes a procedure how historical weather data is used to predict demands and driving times. Its run time and solution quality is evaluated on different data sets given by the MOPTA Competition 2018. Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-77020 ER - TY - GEN A1 - Sagnol, Guillaume A1 - Blanco, Marco A1 - Sauvage, Thibaut T1 - The Cone of Flow Matrices: Approximation Hierarchies and Applications N2 - Let G be a directed acyclic graph with n arcs, a source s and a sink t. We introduce the cone K of flow matrices, which is a polyhedral cone generated by the matrices $\vec{1}_P\vec{1}_P^T\in\RR^{n\times n}$, where $\vec{1}_P\in\RR^n$ is the incidence vector of the (s,t)-path P. We show that several hard flow (or path) optimization problems, that cannot be solved by using the standard arc-representation of a flow, reduce to a linear optimization problem over $\mathcal{K}$. This cone is intractable: we prove that the membership problem associated to $\mathcal{K}$ is NP-complete. However, the affine hull of this cone admits a nice description, and we give an algorithm which computes in polynomial-time the decomposition of a matrix $X\in \operatorname{span} \mathcal{K}$ as a linear combination of some $\vec{1}_P\vec{1}_P^T$'s. Then, we provide two convergent approximation hierarchies, one of them based on a completely positive representation of~K. We illustrate this approach by computing bounds for the quadratic shortest path problem, as well as a maximum flow problem with pairwise arc-capacities. T3 - ZIB-Report - 17-32 KW - Flows in graphs KW - Approximation Hierarchies KW - Copositive Programming KW - Semidefinite Programming Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64399 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Karbstein, Marika T1 - A Primal-Dual Approximation Algorithm for the Steiner Connectivity Problem N2 - We extend the primal-dual approximation technique of Goemans and Williamson to the Steiner connectivity problem, a kind of Steiner tree problem in hypergraphs. This yields a (k+1)-approximation algorithm for the case that k is the minimum of the maximal number of nodes in a hyperedge minus 1 and the maximal number of terminal nodes in a hyperedge. These results require the proof of a degree property for terminal nodes in hypergraphs which generalizes the well-known graph property that the average degree of terminal nodes in Steiner trees is at most 2. T3 - ZIB-Report - 13-54 KW - Primal-Dual Approximation KW - Steiner Connectivity Problem KW - Degree Property KW - Hypergraph Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42430 SN - 1438-0064 ER - TY - THES A1 - Löbel, Fabian T1 - Solving Integrated Timetabling and Passenger Routing Problems Using the Modulo Network Simplex Algorithm N2 - Common models and solving approaches for the problem of periodic timetabling, that is, determining periodic arrival and departure times of a given public transportation network’s lines so that the total weighted travel time of all passengers is minimized, fail to take passenger behavior into account. Current research is attempting to resolve this issue and first results show a positive impact on solution quality. This thesis aims to give a brief overview of literature on the topic of timetabling and to then state a heuristic approach to Integrated Timetabling by blending passenger behavior into the Modulo Network Simplex algorithm, which is part of the research carried out by the author’s study group at the Zuse Institut Berlin in the framework of MATHEON’s research project MI-3 supported by the Einstein Foundation Berlin. Y1 - 2017 ER - TY - GEN A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - A Cut Separation Approach for the Rolling Stock Rotation Problem with Vehicle Maintenance T2 - 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019) N2 - For providing railway services the company’s railway rolling stock is one if not the most important ingredient. It decides about the number of passenger or cargo trips the company can offer, about the quality a passenger experiences the train ride and it is often related to the image of the company itself. Thus, it is highly desired to have the available rolling stock in the best shape possible. Moreover, in many countries, as Germany where our industrial partner DB Fernverkehr AG (DBF) is located, laws enforce regular vehicle inspections to ensure the safety of the passengers. This leads to rolling stock optimization problems with complex rules for vehicle maintenance. This problem is well studied in the literature for example see Maroti and Kroon 2005, or Cordeau et. al. 2001 for applications including vehicle maintenance. The contribution of this paper is a new algorithmic approach to solve the Rolling Stock Rotation Problem for the ICE high speed train fleet of DBF with included vehicle maintenance. It is based on a relaxation of a mixed integer linear programming model with an iterative cut generation to enforce the feasibility of a solution of the relaxation in the solution space of the original problem. The resulting mixed integer linear programming model is based on a hypergraph approach presented in Borndörfer et. al. 2015. The new approach is tested on real world instances modeling different scenarios for the ICE high speed train network in Germany and compared to the approaches of Reuther 2017 that are in operation at DB Fernverkehr AG. The approach shows a significant reduction of the run time to produce solutions with comparable or even better objective function values. T3 - ZIB-Report - 19-61 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-75501 SN - 1438-0064 ER - TY - CHAP A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas ED - Cacchiani, Valentina ED - Marchetti-Spaccamela, Alberto T1 - A Cut Separation Approach for the Rolling Stock Rotation Problem with Vehicle Maintenance T2 - 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019) N2 - For providing railway services the company's railway rolling stock is one if not the most important ingredient. It decides about the number of passenger or cargo trips the company can offer, about the quality a passenger experiences the train ride and it is often related to the image of the company itself. Thus, it is highly desired to have the available rolling stock in the best shape possible. Moreover, in many countries, as Germany where our industrial partner DB Fernverkehr AG (DBF) is located, laws enforce regular vehicle inspections to ensure the safety of the passengers. This leads to rolling stock optimization problems with complex rules for vehicle maintenance. This problem is well studied in the literature for example see [Maróti and Kroon, 2005; Gábor Maróti and Leo G. Kroon, 2007], or [Cordeau et al., 2001] for applications including vehicle maintenance. The contribution of this paper is a new algorithmic approach to solve the Rolling Stock Rotation Problem for the ICE high speed train fleet of DBF with included vehicle maintenance. It is based on a relaxation of a mixed integer linear programming model with an iterative cut generation to enforce the feasibility of a solution of the relaxation in the solution space of the original problem. The resulting mixed integer linear programming model is based on a hypergraph approach presented in [Ralf Borndörfer et al., 2015]. The new approach is tested on real world instances modeling different scenarios for the ICE high speed train network in Germany and compared to the approaches of [Reuther, 2017] that are in operation at DB Fernverkehr AG. The approach shows a significant reduction of the run time to produce solutions with comparable or even better objective function values. Y1 - 2019 UR - https://drops.dagstuhl.de/opus/volltexte/2019/11413/ U6 - https://doi.org/10.4230/OASIcs.ATMOS.2019.1 VL - 75 SP - 1:1 EP - 1:12 PB - Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik CY - Dagstuhl, Germany ER - TY - GEN A1 - Tesch, Alexander T1 - A Nearly Exact Propagation Algorithm for Energetic Reasoning in O(n^2 log n) N2 - In constraint programming, energetic reasoning constitutes a powerful start time propagation rule for cumulative scheduling problems (CuSP). In this paper, we first present an improved time interval checking algorithm that is derived from a polyhedral model. In a second step, we extend this algorithm to an energetic reasoning propagation algorithm with complexity O(n^2 log n) where n denotes the number of jobs. The key idea is based on a new sweep line subroutine that efficiently evaluates the relevant time intervals for all jobs. In particular, our algorithm yields at least one possible energetic reasoning propagation for each job. Finally, we show that on the vast number of relevant time intervals our approach yields the maximum possible propagation according to the energetic reasoning rule. T3 - ZIB-Report - 16-25 KW - Cumulative Scheduling KW - Energetic Reasoning KW - Sweep Line Algorithm Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-59332 SN - 1438-0064 ER - TY - JOUR A1 - Sagnol, Guillaume A1 - Blanco, Marco A1 - Sauvage, Thibaut T1 - The Cone of Flow Matrices: Approximation Hierarchies and Applications JF - Networks N2 - Let G be a directed acyclic graph with n arcs, a source s and a sink t. We introduce the cone K of flow matrices, which is a polyhedral cone generated by the matrices $\vec{1}_P\vec{1}_P^T\in\RR^{n\times n}$, where $\vec{1}_P\in\RR^n$ is the incidence vector of the (s,t)-path P. We show that several hard flow (or path) optimization problems, that cannot be solved by using the standard arc-representation of a flow, reduce to a linear optimization problem over $\mathcal{K}$. This cone is intractable: we prove that the membership problem associated to $\mathcal{K}$ is NP-complete. However, the affine hull of this cone admits a nice description, and we give an algorithm which computes in polynomial-time the decomposition of a matrix $X\in \operatorname{span} \mathcal{K}$ as a linear combination of some $\vec{1}_P\vec{1}_P^T$'s. Then, we provide two convergent approximation hierarchies, one of them based on a completely positive representation of~K. We illustrate this approach by computing bounds for the quadratic shortest path problem, as well as a maximum flow problem with pairwise arc-capacities. Y1 - 2018 U6 - https://doi.org/10.1002/net.21820 VL - 72 IS - 1 SP - 128 EP - 150 ER - TY - JOUR A1 - Beckenbach, Isabel A1 - Borndörfer, Ralf T1 - Hall’s and Kőnig’s theorem in graphs and hypergraphs JF - Discrete Mathematics N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1016/j.disc.2018.06.013 VL - 341 IS - 10 SP - 2753 EP - 2761 ER - TY - GEN A1 - Sagnol, Guillaume A1 - Blanco, Marco A1 - Sauvage, Thibaut T1 - Approximation Hierarchies for the cone of flow matrices N2 - Let $G$ be a directed acyclic graph with $n$ arcs, a source $s$ and a sink $t$. We introduce the cone $K$ of flow matrices, which is a polyhedral cone generated by the matrices $1_P 1_P^T \in R^{n\times n}$, where $1_P\in R^n$ is the incidence vector of the $(s,t)$-path $P$. Several combinatorial problems reduce to a linear optimization problem over $K$. This cone is intractable, but we provide two convergent approximation hierarchies, one of them based on a completely positive representation of $K$. We illustrate this approach by computing bounds for a maximum flow problem with pairwise arc-capacities. T3 - ZIB-Report - 18-20 KW - Flows in graphs KW - Approximation hierarchies KW - Copositive programming Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-68424 SN - 1438-0064 ER - TY - CHAP A1 - Sagnol, Guillaume A1 - Blanco, Marco A1 - Sauvage, Thibaut T1 - Approximation Hierarchies for the cone of flow matrices T2 - INOC 2017 – 8th International Network Optimization Conference N2 - Let $G$ be a directed acyclic graph with $n$ arcs, a source $s$ and a sink $t$. We introduce the cone $K$ of flow matrices, which is a polyhedral cone generated by the matrices $1_P 1_P^T \in R^{n\times n}$, where $1_P\in R^n$ is the incidence vector of the $(s,t)$-path $P$. Several combinatorial problems reduce to a linear optimization problem over $K$. This cone is intractable, but we provide two convergent approximation hierarchies, one of them based on a completely positive representation of $K$. We illustrate this approach by computing bounds for a maximum flow problem with pairwise arc-capacities. Y1 - 2018 U6 - https://doi.org/10.1016/j.endm.2018.02.002 VL - 64 SP - 275 EP - 284 ER - TY - CHAP A1 - Schade, Stanley A1 - Schlechte, Thomas A1 - Witzig, Jakob T1 - Structure-based Decomposition for Pattern-Detection for Railway Timetables T2 - Operations Research Proceedings 2017 N2 - We consider the problem of pattern detection in large scale railway timetables. This problem arises in rolling stock optimization planning in order to identify invariant sections of the timetable for which a cyclic rotation plan is adequate. We propose a dual reduction technique which leads to an decomposition and enumeration method. Computational results for real world instances demonstrate that the method is able to produce optimal solutions as fast as standard MIP solvers. Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-89920-6_95 SP - 715 EP - 721 PB - Springer International Publishing ER - TY - GEN A1 - Borndörfer, Ralf A1 - Euler, Ricardo A1 - Karbstein, Marika A1 - Mett, Fabian T1 - Ein mathematisches Modell zur Beschreibung von Preissystemen im öV N2 - 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. T3 - ZIB-Report - 18-47 Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-70564 SN - 1438-0064 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Breuer, Matthias A1 - Grimm, Boris A1 - Reuther, Markus A1 - Schade, Stanley A1 - Schlechte, Thomas T1 - Timetable Sparsification by Rolling Stock Rotation Optimization T2 - Operations Research 2017 N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-89920-6_96 SP - 723 EP - 728 PB - Springer International Publishing ER - TY - CHAP A1 - Beckenbach, Isabel ED - Kliewer, Natalia ED - Ehmke, Jan Fabian ED - Borndörfer, Ralf T1 - A Hypergraph Network Simplex Algorithm T2 - Operations Research Proceedings 2017 N2 - We describe a network simplex algorithm for the minimum cost flow problem on graph-based hypergraphs which are directed hypergraphs of a particular form occurring in railway rotation planning. The algorithm is based on work of Cambini, Gallo, and Scutellà who developed a hypergraphic generalization of the network simplex algorithm. Their main theoretical result is the characterization of basis matrices. We give a similar characterization for graph-based hypergraphs and show that some operations of the simplex algorithm can be done combinatorially by exploiting the underlying digraph structure. Y1 - 2018 VL - Operations Research Proceedings 2017 SP - 309 EP - 316 PB - Springer CY - Cham ER - TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Pfetsch, Marc T1 - Models for Line Planning in Public Transport N2 - The \emph{line planning problem} is one of the fundamental problems in strategic planning of public and rail transport. It consists of finding lines and corresponding frequencies in a public transport network such that a given travel demand can be satisfied. There are (at least) two objectives. The transport company wishes to minimize its operating cost; the passengers request short travel times. We propose two new multi-commodity flow models for line planning. Their main features, in comparison to existing models, are that the passenger paths can be freely routed and that the lines are generated dynamically. T3 - ZIB-Report - 04-10 KW - line planning KW - column generation Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7854 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc ED - Barnhart, Cynthia ED - Clausen, Uwe ED - Lauther, Ulrich ED - Möhring, Rolf T1 - Line Planning and Connectivity T2 - Models and Algorithms for Optimization in Logistics Y1 - 2009 IS - 09261 PB - Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany CY - Dagstuhl, Germany ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Klostermeier, Fridolin A1 - Küttner, Christian T1 - Berliner Telebussystem bietet Mobilität für Behinderte JF - Der Nahverkehr Y1 - 1997 VL - 1/2 SP - 20 EP - 22 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc ED - Haasis, Hans-Dietrich ED - Kopfer, Herbert ED - Schönberger, Jörn T1 - Optimal Fares for Public Transport T2 - Operations Research Proceedings 2005 Y1 - 2006 UR - {http://opus.kobv.de/zib/volltexte/2005/869/} SP - 29 EP - 36 PB - Springer-Verlag ER - TY - CHAP A1 - Neumann, Marika ED - Waldmann, Karl-Heinz ED - Stocker, Ulrike T1 - Fare Planning for Public Transport T2 - Operations Research Proceedings 2006 Y1 - 2007 UR - {http://opus.kobv.de/zib/volltexte/2009/1160/} SP - 61 EP - 66 PB - Springer-Verlag ER - TY - JOUR A1 - Neumann, Marika T1 - Mathematische Preisplanung im ÖPNV JF - OR News Y1 - 2007 IS - 30 SP - 29 EP - 31 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Klostermeier, Fridolin A1 - Küttner, Christian T1 - Optimierung des Berliner Behindertenfahrdienstes JF - DMV-Mitteilungen Y1 - 1997 VL - 2 SP - 38 EP - 43 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - Railway Track Allocation by Rapid Branching N2 - The track allocation problem, also known as train routing problem or train timetabling problem, is to find a conflict-free set of train routes of maximum value in a railway network. Although it can be modeled as a standard path packing problem, instances of sizes relevant for real-world railway applications could not be solved up to now. We propose a rapid branching column generation approach that integrates the solution of the LP relaxation of a path coupling formulation of the problem with a special rounding heuristic. The approach is based on and exploits special properties of the bundle method for the approximate solution of convex piecewise linear functions. Computational results for difficult instances of the benchmark library TTPLIB are reported. T3 - ZIB-Report - 10-22 KW - Trassenallokationsproblem KW - Ganzzahlige Programmierung KW - Rapid-Branching-Heuristik KW - Proximale Bündelmethode KW - Optimization KW - Railway Track Allocation KW - Bundle Method KW - Rapid Branching Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11864 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Karbstein, Marika T1 - Metric Inequalities for Routings on Direct Connections N2 - We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We show that the concept of metric inequalities to characterize capacities that support a multi-commodity flow can be generalized to deal with direct connections. T3 - ZIB-Report - 14-04 KW - metric inequalities KW - direct connection KW - multi-commodity flow problem Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-44219 SN - 1438-0064 ER - TY - CHAP A1 - Heismann, Olga A1 - Borndörfer, Ralf T1 - The Random Hypergraph Assignment Problem T2 - Proceedings of the 16th International Multiconference INFORMATION SOCIETY - IS 2013 N2 - The analysis of random instances of a combinatorial optimization problem, especially their optimal values, can provide a better insight into its structure. Such an extensive analysis was theoretically and practically done for the assignment problem ("random assignment problem") and several of its generalizations. For a recent generalization of the assignment problem to bipartite hypergraphs, the hypergraph assignment problem, such results do not exist so far. We consider a random version of the hypergraph assignment problem for the simplest possible complete bipartite hypergraphs. They have only edges and proper hyperedges of size four and follow a special structure, but the hypergraph assignment problem for this type of hypergraphs is, however, already NP-hard. It can be viewed as a combination of two assignment problems. For random hyperedge costs exponentially i.i.d. with mean 1 we show computational results that suggest that the expected value of minimum cost hyperassignments converges to some value around 1.05 with a small standard deviation. The computational results also suggest that the optimal value is most probably attained with half of the maximum possible number of proper hyperedges. The main result of this paper is the proof that the expected value of a minimum cost hyperassignment which uses exactly half the possible maximum number of proper hyperedges if the vertex number tends to infinity lies between 0.3718 and 1.8310 when hyperedge costs are exponentially i.i.d. with mean 1. Y1 - 2013 SP - 599 EP - 602 ER - TY - CHAP A1 - Sagnol, Guillaume T1 - Network-related problems in optimal experimental design and second order cone programming T2 - Proceedings of PROBASTAT'2011, Tatra Mountains Mathematical Publications N2 - In the past few years several applications of optimal experimental designs have emerged to optimize the measurements in communication networks. The optimal design problems arising from this kind of applications share three interesting properties: (i) measurements are only available at a small number of locations of the network; (ii) each monitor can simultaneously measure several quantities, which can be modeled by ``multiresponse experiments"; (iii) the observation matrices depend on the topology of the network. In this paper, we give an overview of these experimental design problems and recall recent results for the computation of optimal designs by Second Order Cone Programming (SOCP). New results for the network-monitoring of a discrete time process are presented. In particular, we show that the optimal design problem for the monitoring of an AR1 process can be reduced to the standard form and we give experimental results. Y1 - 2012 U6 - https://doi.org/10.2478/v10127-012-0016-x VL - 51 SP - 161 EP - 171 ER - TY - JOUR A1 - Sagnol, Guillaume T1 - On the semidefinite representation of real functions applied to symmetric matrices JF - Linear Algebra and its Applications N2 - We present a new semidefinite representation for the trace of a real function f applied to symmetric matrices, when a semidefinite representation of the convex function f is known. Our construction is intuitive, and yields a representation that is more compact than the previously known one. We also show with the help of matrix geometric means and the Riemannian metric of the set of positive definite matrices that for a rational number p in the interval (0,1], the matrix X raised to the exponent p is the largest element of a set represented by linear matrix inequalities. We give numerical results for a problem inspired from the theory of experimental designs, which show that the new semidefinite programming formulation yields a speed-up factor in the order of 10. Y1 - 2013 U6 - https://doi.org/10.1016/j.laa.2013.08.021 VL - 439 IS - 10 SP - 2829 EP - 2843 ER - TY - CHAP A1 - Hildenbrandt, Achim A1 - Reinelt, Gerhard A1 - Heismann, Olga T1 - Integer Programming Models for the Target Visitation Problem T2 - Proceedings of the 16th International Multiconference INFORMATION SOCIETY - IS 2013 N2 - The target visitation problem (TVP) is concerned with finding a route to visit a set of targets starting from and returning to some base. In addition to the distance traveled a tour is evaluated by taking also preferences into account which address the sequence in which the targets are visited. The problem thus is a combination of two well-known combinato- rial optimization problems: the traveling salesman and the linear ordering problem. In this paper we present several possible IP-Models for this problem and compared them to their usability for branch-and-cut approaches. Y1 - 2013 SP - 569 EP - 572 ER - TY - CHAP A1 - Heismann, Olga A1 - Borndörfer, Ralf T1 - Minimum Cost Hyperassignments with Applications to ICE/IC Rotation Planning T2 - Operations Research Proceedings 2011 N2 - Vehicle rotation planning is a fundamental problem in rail transport. It decides how the railcars, locomotives, and carriages are operated in order to implement the trips of the timetable. One important planning requirement is operational regularity, i.e., using the rolling stock in the same way on every day of operation. We propose to take regularity into account by modeling the vehicle rotation planning problem as a minimum cost hyperassignment problem (HAP). Hyperassignments are generalizations of assignments from directed graphs to directed hypergraphs. Finding a minimum cost hyperassignment is NP-hard. Most instances arising from regular vehicle rotation planning, however, can be solved well in practice. We show that, in particular, clique inequalities strengthen the canonical LP relaxation substantially. Y1 - 2012 SP - 59 EP - 64 ER - TY - JOUR A1 - Langenhan, Andreas A1 - Borndörfer, Ralf A1 - Löbel, Andreas A1 - Schulz, Christof A1 - Weider, Steffen ED - Muñoz, J. C. ED - Voß, S. T1 - Duty Scheduling Templates JF - Proceedings of Conference on Advanced Systems for Public Transport 2012 (CASPT12) N2 - We propose duty templates as a novel concept to produce similar duty schedules for similar days of operation in public transit. Duty templates can conveniently handle various types of similarity requirements, and they can be implemented with ease using standard algorithmic techniques. They have produced good results in practice. Y1 - 2012 ER - TY - THES A1 - Karbstein, Marika T1 - Line Planning and Connectivity N2 - This thesis introduces the Steiner connectivity problem. It is a generalization of the well known Steiner tree problem. Given a graph G = (V, E) and a subset T ⊆ V of the nodes, the Steiner tree problem consists in finding a cost minimal set of edges connecting all nodes in T . The Steiner connectivity problem chooses, instead of edges, from a given set of paths a subset to connect all nodes in T . We show in the first part of this thesis that main results about complexity, approximation, integer programming formulations, and polyhedra can be generalized from the Steiner tree problem to the Steiner connectivity problem. An example for a straightforward generalization are the Steiner partition inequalities, a fundamental class of facet defining inequalities for the Steiner tree problem. They can be defined for the Steiner connectivity problem in an analogous way as for the Steiner tree problem. An example for a generalization that needs more effort is the definition of a directed cut formulation and the proof that this dominates the canonical undirected cut formulation enriched by all Steiner partition inequalities. For the Steiner connectivity problem this directed cut formulation leads to extended formulations, a concept that is not necessary for the Steiner tree problem. There are also major differences between both problems. For instance, the case T = V for the Steiner connectivity problem is equivalent to a set covering problem and, hence, not a polynomial solvable case as in the Steiner tree problem. The Steiner connectivity problem is not only an interesting generalization of the Steiner tree problem but also the underlying connectivity problem in line planning with inte- grated passenger routing. The integrated line planning and passenger routing problem is an important planning problem in service design of public transport and the topic of the second part. Given is the infrastructure network of a public transport system where the edges correspond to streets and tracks and the nodes correspond to stations/stops of lines. The task is to find paths in the infrastructure network for lines and passengers such that the capacities of the lines suffice to transport all passengers. Existing models in the literature that integrate a passenger routing in line planning either treat transfers in a rudimentary way and, hence, neglect an important aspect for the choice of the pas- senger routes, or they treat transfers in a too comprehensive way and cannot be solved for large scale real world problems. We propose a new model that focuses on direct connections. The attractiveness of transfer free connections is increased by introducing a transfer penalty for each non-direct connection. In this way, a passenger routing is computed that favors direct connections. For the computation of this model we also implemented algorithms influenced by the results for the Steiner connectivity problem. We can compute with our model good solutions that minimize a weighted sum of line operating costs and passengers travel times. These solutions improve the solutions of an existing approach, that does not consider direct connections, by up to 17%. In contrast to a comprehensive approach, that considers every transfer and for which we could not even solve the root LP within 10 hours for large instances, the solutions of the new model, computed in the same time, are close to optimality (<1%) or even optimal for real world instances. In a project with the Verkehr in Potsdam GmbH to compute the line plan for 2010 we showed that our approach is applicable in practice and can be used to solve real world problems. Y1 - 2013 UR - www.zib.de/karbstein/scplpp.pdf SN - 978-3-8439-1062-0 ER - TY - JOUR A1 - Hiller, Benjamin A1 - Klug, Torsten A1 - Tuchscherer, Andreas T1 - An Exact Reoptimization Algorithm for the Scheduling of Elevator Groups JF - Flexible Services and Manufacturing Journal Y1 - 2013 U6 - https://doi.org/10.1007/s10696-013-9175-6 SP - 1 EP - 24 ER - TY - CHAP A1 - Schlechte, Thomas T1 - Railway Track Allocation BT - Selected Papers of the International Annual Conference of the German Operations Research Society (GOR), Leibniz University of Hannover, Germany, September 5-7, 2012 T2 - Operations Research Proceedings Y1 - 2012 U6 - https://doi.org/10.1007/978-3-319-00795-314 SP - 15 EP - 20 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Karbstein, Marika A1 - Pfetsch, Marc T1 - The Steiner connectivity problem JF - Mathematical Programming A Y1 - 2013 U6 - https://doi.org/10.1007/s10107-012-0564-5 VL - 142 IS - 1 SP - 133 EP - 167 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Klostermeier, Fridolin A1 - Küttner, Christian T1 - Telebus-Disposition: Ein Konzept zur Serviceverbesserung bei gleichzeitiger Kostensenkung.[nur hausintern] N2 - "`Telebus"' ist der soziale Behindertenfahrdienst im Land Berlin. Das Telebus-Forschungsprojekt des Konrad-Zuse-Zentrums für Informationstechnik (ZIB) hat das Ziel, den Fahrdienst (insbesondere die Disposition der Telebusse) zu verbessern, d.h. kundenfreundlicher zu gestalten und gleichzeitig billiger zu machen. In diesem Bericht werden die bisherigen Ergebnisse dargestellt und weitere Möglichkeiten zur Verbesserung des Service und zur Reduzierung der Kosten skizziert. \originalTeX T3 - ZIB-Report - TR-93-03 Y1 - 1993 N1 - Volltext nur Hausintern ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen ED - Muñoz, J. C. ED - Voß, S. T1 - Vehicle Rotation Planning for Intercity Railways JF - Proceedings of Conference on Advanced Systems for Public Transport 2012 (CASPT12) N2 - This paper provides a generic formulation for rolling stock planning problems in the context of intercity passenger traffic. The main contributions are a graph theoretical model and a Mixed-Integer-Programming formulation that integrate all main requirements of the considered Vehicle-Rotation-Planning problem (VRPP). We show that it is possible to solve this model for real-world instances provided by our industrial partner DB Fernverkehr AG using modern algorithms and computers. Y1 - 2012 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Löbel, Andreas A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen ED - Muñoz, J. C. ED - Voß, S. T1 - Rapid Branching JF - Public Transport N2 - We propose rapid branching (RB) as a general branch-and-bound heuristic for solving large scale optimization problems in traffic and transport. The key idea is to combine a special branching rule and a greedy node selection strategy in order to produce solutions of controlled quality rapidly and efficiently. We report on three successful applications of the method for integrated vehicle and crew scheduling, railway track allocation, and railway vehicle rotation planning. Y1 - 2013 VL - 5 IS - 1 SP - 3 EP - 23 PB - Springer Berlin Heidelberg ER - TY - CHAP A1 - Scheumann, René A1 - Fügenschuh, Armin A1 - Schenker, Sebastian A1 - Vierhaus, Ingmar A1 - Borndörfer, Ralf A1 - Finkbeiner, Matthias ED - Seliger, Günther T1 - Global Manufacturing: How to Use Mathematical Optimisation Methods to Transform to Sustainable Value Creation BT - (GCSM 2012) T2 - Proceedings of the 10th Global Conference on Sustainable Manufacturing Y1 - 2012 SN - 978-605-63463-1-6 SP - 538 EP - 545 ER - TY - JOUR A1 - Sagnol, Guillaume T1 - Approximation of a maximum-submodular-coverage problem involving spectral functions, with application to experimental designs JF - Discrete Applied Mathematics N2 - We study a family of combinatorial optimization problems defined by a parameter $p\in[0,1]$, which involves spectral functions applied to positive semidefinite matrices, and has some application in the theory of optimal experimental design. This family of problems tends to a generalization of the classical maximum coverage problem as $p$ goes to $0$, and to a trivial instance of the knapsack problem as $p$ goes to $1$. In this article, we establish a matrix inequality which shows that the objective function is submodular for all $p\in[0,1]$, from which it follows that the greedy approach, which has often been used for this problem, always gives a design within $1-1/e$ of the optimum. We next study the design found by rounding the solution of the continuous relaxed problem, an approach which has been applied by several authors. We prove an inequality which generalizes a classical result from the theory of optimal designs, and allows us to give a rounding procedure with an approximation factor which tends to $1$ as $p$ goes to $1$. Y1 - 2013 U6 - https://doi.org/10.1016/j.dam.2012.07.016 VL - 161 IS - 1-2 SP - 258 EP - 276 ER - TY - JOUR A1 - Sagnol, Guillaume T1 - A class of Semidefinite Programs with rank-one solutions JF - Linear Algebra and its Applications N2 - We show that a class of semidefinite programs (SDP) admits a solution that is a positive semidefinite matrix of rank at most $r$, where $r$ is the rank of the matrix involved in the objective function of the SDP. The optimization problems of this class are semidefinite packing problems, which are the SDP analogs to vector packing problems. Of particular interest is the case in which our result guarantees the existence of a solution of rank one: we show that the computation of this solution actually reduces to a Second Order Cone Program (SOCP). We point out an application in statistics, in the optimal design of experiments. Y1 - 2011 U6 - https://doi.org/10.1016/j.laa.2011.03.027 VL - 435 IS - 6 SP - 1446 EP - 1463 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Schlechte, Thomas A1 - Swarat, Elmar T1 - Railway Track Allocation -- Simulation, Aggregation, and Optimization JF - Proc. 1st International Workshop on High-speed and Intercity Railways (IWHIR 2011) N2 - Today the railway timetabling process and the track allocation is one of the most challenging problems to solve by a railway company. Especially due to the deregulation of the transport market in the recent years several suppliers of railway traffic have entered the market in Europe. This leads to more potential conflicts between trains caused by an increasing demand of train paths. Planning and operating railway transportation systems is extremely hard due to the combinatorial complexity of the underlying discrete optimization problems, the technical intricacies, and the immense size of the problem instances. In order to make best use of the infrastructure and to ensure economic operation, efficient planning of the railway operation is indispensable. Mathematical optimization models and algorithms can help to automatize and tackle these challenges. Our contribution in this paper is to present a renewed planning process due to the liberalization in Europe and an associated concept for track allocation, that consists of three important parts, simulation, aggregation, and optimization. Furthermore, we present results of our general framework for real world data. Y1 - 2012 U6 - https://doi.org/10.1007/978-3-642-27963-8 VL - 2 IS - 148 SP - 53 EP - 70 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - A Hypergraph Model for Railway Vehicle Rotation Planning JF - 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems N2 - We propose a model for the integrated optimization of vehicle rotations and vehicle compositions in long distance railway passenger transport. The main contribution of the paper is a hypergraph model that is able to handle the challenging technical requirements as well as very general stipulations with respect to the ``regularity'' of a schedule. The hypergraph model directly generalizes network flow models, replacing arcs with hyperarcs. Although NP-hard in general, the model is computationally well-behaved in practice. High quality solutions can be produced in reasonable time using high performance Integer Programming techniques, in particular, column generation and rapid branching. We show that, in this way, large-scale real world instances of our cooperation partner DB Fernverkehr can be solved. Y1 - 2011 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2011.146 VL - OpenAccess Series in Informatics (OASIcs) IS - 20 SP - 146 EP - 155 ER - TY - JOUR A1 - Schlechte, Thomas T1 - Railway Track Allocation - Simulation and Optimization JF - Proceedings of 4th International Seminar on Railway Operations Modelling and Analysis (IAROR) N2 - Today the railway timetabling process and the track allocation is one of the most challenging problems to solve by a railway infrastructure provider. Especially due to the deregulation of the transport market in the recent years several suppliers of railway traffic have entered the market. This leads to an increase of slot requests and then it is natural that conflicts occur among them. Furthermore, railway infrastructure networks consist of very expensive assets, even more they are rigid due to the long-term upgrade process. In order to make best use of these valuable infrastructure and to ensure economic operation, efficient planning of the railway operation is indispensable. Mathematical optimization models and algorithmic methodology can help to automatize and tackle these challenges. Our contribution in this paper is to present a renewed planning process due to the liberalization in Europe and a general framework to support the integration of simulation and optimization for railway capacity allocation. Y1 - 2011 VL - 4 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Neumann, Marika T1 - Linienoptimierung - reif für die Praxis? T2 - Heureka '11 : Optimierung in Verkehr und Transport N2 - Wir stellen in dieser Arbeit ein mathematisches Optimierungsmodell zur Bestimmung eines optimalen Linienplans vor, das sowohl die Fahrzeiten und die Anzahl der Umstiege berücksichtigt als auch die Kosten des Liniennetzes. Dieses Modell deckt wichtige praktische Anforderungen ab, die in einem gemeinsamen Projekt mit den Verkehrsbetrieben in Potsdam (ViP) formuliert wurden. In diesem Projekt wurde der Linienplan 2010 für Potsdam entwickelt. Unsere Berechnungen zeigen, dass die mathematische Optimierung in nichts einer "Handplanung" des Liniennetzes nachsteht. Im Gegenteil, mit Hilfe des Optimierungsprogramms ist es möglich, durch Veränderung der Parameter mehrere verschiedene Szenarien zu berechnen, miteinander zu vergleichen und Aussagen über minimale Kosten und Fahrzeiten zu machen. Y1 - 2011 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika ED - Frigioni, Daniele ED - Stiller, Sebastian T1 - A Configuration Model for the Line Planning Problem T2 - ATMOS 2013 - 13th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems Y1 - 2013 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2013.68 VL - 33 SP - 68 EP - 79 PB - Schloss Dagstuhl--Leibniz-Zentrum für Informatik ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Friedow, Isabel A1 - Karbstein, Marika T1 - Optimierung des Linienplans 2010 in Potsdam JF - Der Nahverkehr Y1 - 2012 VL - 30 IS - 4 SP - 34 EP - 39 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika T1 - A Configuration Model for the Line Planning Problem N2 - We propose a novel extended formulation for the line planning problem in public transport. It is based on a new concept of frequency configurations that account for all possible options to provide a required transportation capacity on an infrastructure edge. We show that this model yields a strong LP relaxation. It implies, in particular, general classes of facet defining inequalities for the standard model. T3 - ZIB-Report - 13-40 KW - combinatorial optimization KW - polyhedral combinatorics KW - line planning Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-41903 SN - 1438-0064 ER - TY - JOUR A1 - Karbstein, Marika T1 - Ohne Umsteigen ans Ziel JF - OR News N2 - Die Anforderungen an das Liniennetz eines Verkehrsunternehmens sind vielfältig: kurze Fahrzeiten, viele Direktverbindungen und geringe Kosten. Mathematische Optimierungsmethoden können die Planung von Liniennetzen unterstützen und beste Kompromisse bzgl. aller Anforderungen berechnen. Y1 - 2014 VL - 52 SP - 12 EP - 14 ER - TY - GEN A1 - Sagnol, Guillaume A1 - Borndörfer, Ralf A1 - Grima, Mickaël A1 - Seeling, Matthes A1 - Spies, Claudia T1 - Robust Allocation of Operating Rooms with Lognormal case Durations N2 - The problem of allocating operating rooms (OR) to surgical cases is a challenging task, involving both combinatorial aspects and uncertainty handling. In this article, we formulate this problem as a job shop scheduling problem, in which the job durations follow a lognormal distribution. We propose to use a cutting-plane approach to solve a robust version of this optimization problem. To this end, we develop an algorithm based on fixed-point iterations to solve the subproblems that identify worst-case scenarios and generate cut inequalities. The procedure is illustrated with numerical experiments based on real data from a major hospital in Berlin. T3 - ZIB-Report - 16-16 KW - robust optimization KW - lognormal duration KW - Hilbert's projective metric Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-58497 UR - http://www.pms2016.com/congreso/ficha.en.html SN - 1438-0064 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Fügenschuh, Armin A1 - Klug, Torsten A1 - Schang, Thilo A1 - Schlechte, Thomas A1 - Schülldorf, Hanno T1 - The Freight Train Routing Problem for Congested Railway Networks with Mixed Traffic JF - Transportation Science N2 - We consider the following freight train routing problem (FTRP). Given is a transportation network with fixed routes for passenger trains and a set of freight trains (requests), each defined by an origin and destination station pair. The objective is to calculate a feasible route for each freight train such that the sum of all expected delays and all running times is minimal. Previous research concentrated on microscopic train routings for junctions or inside major stations. Only recently approaches were developed to tackle larger corridors or even networks. We investigate the routing problem from a strategic perspective, calculating the routes in a macroscopic transportation network of Deutsche Bahn AG. In this context, macroscopic refers to an aggregation of complex and large real-world structures into fewer network elements. Moreover, the departure and arrival times of freight trains are approximated. The problem has a strategic character since it asks only for a coarse routing through the network without the precise timings. We provide a mixed-integer nonlinear programming (MINLP) formulation for the FTRP, which is a multicommodity flow model on a time-expanded graph with additional routing constraints. The model’s nonlinearities originate from an algebraic approximation of the delays of the trains on the arcs of the network by capacity restraint functions. The MINLP is reduced to a mixed-integer linear model (MILP) by piecewise linear approximation. The latter is solved by a state-of-the art MILP solver for various real-world test instances. Y1 - 2016 U6 - https://doi.org/10.1287/trsc.2015.0656 VL - 50 IS - 2 SP - 408 EP - 423 ER - TY - CHAP A1 - Karbstein, Marika T1 - Integrated Line Planning and Passenger Routing: Connectivity and Transfers T2 - Operations Research Proceedings 2014 N2 - The integrated line planning and passenger routing problem is an important planning problem in service design of public transport. A major challenge is the treatment of transfers. A main property of a line system is its connectivity. In this paper we show that analysing the connecvitiy aspect of a line plan gives a new idea to handle the transfer aspect of the line planning problem. Y1 - 2016 U6 - https://doi.org/10.1007/978-3-319-28697-6_37 SP - 263 EP - 269 ER - TY - CHAP A1 - Beckenbach, Isabel A1 - Borndörfer, Ralf T1 - An Approximation Result for Matchings in Partitioned Hypergraphs T2 - Operations Research Proceedings 2014 N2 - We investigate the matching and perfect matching polytopes of hypergraphs having a special structure, which we call partitioned hypergraphs. We show that the integrality gap of the standard LP-relaxation is at most $2\sqrt{d}$ for partitioned hypergraphs with parts of size $\leq d$. Furthermore, we show that this bound cannot be improved to $\mathcal{O}(d^{0.5-\epsilon})$. Y1 - 2016 U6 - https://doi.org/10.1007/978-3-319-28697-6_5 SP - 31 EP - 36 PB - Springer International Publishing ER - TY - JOUR A1 - Hoppmann, Heide T1 - Linienplanung und Minimale Konfigurationen JF - OR News Y1 - 2015 VL - 55 SP - 22 EP - 23 ER - TY - CHAP A1 - Liebchen, Christian A1 - Swarat, Elmar ED - Fischetti, Matteo ED - Widmayer, Peter T1 - The Second Chvatal Closure Can Yield Better Railway Timetables T2 - ATMOS 2008 - 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0030-drops-15802 UR - http://drops.dagstuhl.de/opus/volltexte/2008/1580 PB - Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany CY - Dagstuhl, Germany ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Erol, Berkan A1 - Graffagnino, Thomas A1 - Schlechte, Thomas A1 - Swarat, Elmar T1 - Optimizing the Simplon railway corridor JF - Annals of Operations Research Y1 - 2012 UR - http://dx.doi.org/10.1007/s10479-012-1260-9 U6 - https://doi.org/10.1007/s10479-012-1260-9 VL - 218 IS - 1 SP - 93 EP - 106 PB - Springer US ET - Annals of Operations Research ER - TY - CHAP A1 - Schlechte, Thomas A1 - Tanner, Andreas T1 - Railway capacity auctions with dual prices T2 - Selected Proceedings of the 12th World Conference on Transport Research Y1 - 2010 UR - http://opus.kobv.de/zib/volltexte/2010/1233/ ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Schlechte, Thomas ED - Liebchen, Christian ED - Ahuja, Ravindra ED - Mesa, Juan T1 - Models for Railway Track Allocation T2 - ATMOS 2007 - 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems Y1 - 2007 VL - 07001 PB - Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Schlechte, Thomas ED - Ehrgott, Matthias ED - Naujoks, Boris ED - Stewart, Theo ED - Wallenius, Jyrki T1 - Balancing Efficiency and Robustness T2 - MCDM for Sustainable Energy and Transportation Systems Y1 - 2008 UR - http://opus.kobv.de/zib/volltexte/2008/1105/ PB - Lecture Notes in Economics and Mathematical Systems ER - TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Löbel, Andreas T1 - Der Schnellste Weg zum Ziel N2 - Wir geben eine Einführung in die Mathematik von und mit Wegen. Nicht auf dem kürzesten, aber auf einem hoffentlich kurzweiligen Weg! T3 - ZIB-Report - SC-99-32 KW - Kürzeste Wege KW - Kombinatorische Optimierung KW - Operations Research Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4209 ER - TY - GEN A1 - Schwartz, Stephan A1 - Borndörfer, Ralf A1 - Bartz, Gerald T1 - The Graph Segmentation Problem N2 - 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. T3 - ZIB-Report - 16-53 KW - toll billing KW - graph segmentation KW - combinatorial optimization Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-60750 SN - 1438-0064 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika A1 - Löbel, Fabian T1 - The Modulo Network Simplex with Integrated Passenger Routing T2 - Operations Research Proceedings 2016 N2 - Periodic timetabling is an important strategic planning problem in public transport. The task is to determine periodic arrival and departure times of the lines in a given network, minimizing the travel time of the passengers. We extend the modulo network simplex method, a well-established heuristic for the periodic timetabling problem, by integrating a passenger (re)routing step into the pivot operations. Computations on real-world networks show that we can indeed find timetables with much shorter total travel time, when we take the passengers' travel paths into consideration. Y1 - 2016 ER - TY - THES A1 - Wenzel, Ron T1 - On the In-Flight Rest Assignment Problem N2 - The airplane has changed the world in a tremendous way. Efficient scheduling of airmen and aircrafts is of considerable importance for cost-effectiveness of compa- nies. Attentiveness of flight crew members is vital as fatigue can lead to severe accidents. Therefore, duty times of flight crews are strictly limited. Long distance flights may be difficult to schedule with only one set of crew members. Furthermore, pertu- bations of the schedules may entail exchanging the entire crew, which confounds multiday schedules. A new EU regulation introduced in-flight rest: a schedule may extend pilots’ duty times if they rest for a certain time in designated crew compart- ments provided aboard airplanes. Of course they have to be replaced in that period of time. This thesis examines the in-flight rest assignment problem, which is the decision problem whether a given schedule allows for all crew members to take their compul- sory rest. The problem can be seen as multimachine scheduling problem. Efficient algorithms for special cases were developed and an alternative approach for entire hard cases is discussed. Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-59328 ER - TY - GEN A1 - Sagnol, Guillaume A1 - Balzer, Felix A1 - Borndörfer, Ralf A1 - Spies, Claudia A1 - von Dincklage, Falk T1 - Makespan and Tardiness in Activity Networks with Lognormal Activity Durations N2 - We propose an algorithm to approximate the distribution of the completion time (makespan) and the tardiness costs of a project, when durations are lognormally distributed. This problem arises naturally for the optimization of surgery scheduling, where it is very common to assume lognormal procedure times. We present an analogous of Clark's formulas to compute the moments of the maximum of a set of lognormal variables. Then, we use moment matching formulas to approximate the earliest starting time of each activity of the project by a shifted lognormal variable. This approach can be seen as a lognormal variant of a state-of-the-art method used for the statistical static timing analysis (SSTA) of digital circuits. We carried out numerical experiments with instances based on real data from the application to surgery scheduling. We obtained very promising results, especially for the approximation of the mean overtime in operating rooms, for which our algorithm yields results of a similar quality to Monte-Carlo simulations requiring an amount of computing time several orders of magnitude larger. T3 - ZIB-Report - 16-23 KW - scheduling KW - activity network KW - lognormal distribution Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-59290 SN - 1438-0064 ER - TY - GEN A1 - Sagnol, Guillaume A1 - Hege, Hans-Christian A1 - Weiser, Martin T1 - Using sparse kernels to design computer experiments with tunable precision N2 - Statistical methods to design computer experiments usually rely on a Gaussian process (GP) surrogate model, and typically aim at selecting design points (combinations of algorithmic and model parameters) that minimize the average prediction variance, or maximize the prediction accuracy for the hyperparameters of the GP surrogate. In many applications, experiments have a tunable precision, in the sense that one software parameter controls the tradeoff between accuracy and computing time (e.g., mesh size in FEM simulations or number of Monte-Carlo samples). We formulate the problem of allocating a budget of computing time over a finite set of candidate points for the goals mentioned above. This is a continuous optimization problem, which is moreover convex whenever the tradeoff function accuracy vs. computing time is concave. On the other hand, using non-concave weight functions can help to identify sparse designs. In addition, using sparse kernel approximations drastically reduce the cost per iteration of the multiplicative weights updates that can be used to solve this problem. T3 - ZIB-Report - 16-33 KW - Optimal design of computer experiments KW - Sparse kernels KW - Gaussian Process Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-59605 SN - 1438-0064 ER - TY - GEN A1 - Beckenbach, Isabel A1 - Scheidweiler, Robert T1 - Perfect f-Matchings and f-Factors in Hypergraphs - A Combinatorial Approach N2 - We prove characterizations of the existence of perfect f-matchings in uniform mengerian and perfect hypergraphs. Moreover, we investigate the f-factor problem in balanced hypergraphs. For uniform balanced hypergraphs we prove two existence theorems with purely combinatorial arguments, whereas for non-uniform balanced hypergraphs we show that the f-factor problem is NP-hard. T3 - ZIB-Report - 16-22 KW - perfect f-matchings in hypergraphs KW - f-factors in hypergraphs KW - mengerian hypergraph KW - balanced hypergraph KW - perfect hypergraph KW - Hall's Theorem Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-59071 SN - 1438-0064 ER - TY - JOUR A1 - Sagnol, Guillaume A1 - Harman, Radoslav T1 - Computing exact D-optimal designs by mixed integer second-order cone programming JF - The Annals of Statistics N2 - Let the design of an experiment be represented by an $s-$dimensional vector $w$ of weights with nonnegative components. Let the quality of $w$ for the estimation of the parameters of the statistical model be measured by the criterion of $D-$optimality, defined as the $m$th root of the determinant of the information matrix $M(w)=\sum_{i=1}^s w_i A_i A_i^T$, where $A_i$,$i=1,\ldots,s$ are known matrices with $m$ rows. In this paper, we show that the criterion of $D-$optimality is second-order cone representable. As a result, the method of second-order cone programming can be used to compute an approximate $D-$optimal design with any system of linear constraints on the vector of weights. More importantly, the proposed characterization allows us to compute an exact $D-$optimal design, which is possible thanks to high-quality branch-and-cut solvers specialized to solve mixed integer second-order cone programming problems. Our results extend to the case of the criterion of $D_K-$optimality, which measures the quality of $w$ for the estimation of a linear parameter subsystem defined by a full-rank coefficient matrix $K$. We prove that some other widely used criteria are also second-order cone representable, for instance, the criteria of $A-$, $A_K$-, $G-$ and $I-$optimality. We present several numerical examples demonstrating the efficiency and general applicability of the proposed method. We show that in many cases the mixed integer second-order cone programming approach allows us to find a provably optimal exact design, while the standard heuristics systematically miss the optimum. Y1 - 2015 U6 - https://doi.org/10.1214/15-AOS1339 VL - 43 IS - 5 SP - 2198 EP - 2224 ER - TY - CHAP A1 - Duarte, Belmiro P.M. A1 - Sagnol, Guillaume A1 - Oliveira, Nuno M.C. T1 - A Robust Minimax Semidefinite Programming Formulation for Optimal Design of Experiments for Model Parametrization T2 - 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering N2 - Model-based optimal design of experiments (M-bODE) is a crucial step in model parametrization since it encloses a framework that maximizes the amount of information extracted from a battery of lab experiments. We address the design of M-bODE for dynamic models considering a continuous representation of the design. We use Semidefinite Programming (SDP) to derive robust minmax formulations for nonlinear models, and extend the formulations to other criteria. The approaches are demonstrated for a CSTR where a two-step reaction occurs. Y1 - 2015 U6 - https://doi.org/10.1016/B978-0-444-63578-5.50146-8 VL - 37 SP - 905 EP - 910 ER - TY - GEN A1 - Schenker, Sebastian A1 - Borndörfer, Ralf A1 - Skutella, Martin T1 - A novel partitioning of the set of non-dominated points N2 - We consider a novel partitioning of the set of non-dominated points for general multi-objective integer programs with $k$ objectives. The set of non-dominated points is partitioned into a set of non-dominated points whose efficient solutions are also efficient for some restricted subproblem with one less objective; the second partition comprises the non-dominated points whose efficient solutions are inefficient for any of the restricted subproblems. We show that the first partition has the nice property that it yields finite rectangular boxes in which the points of the second partition are located. T3 - ZIB-Report - 16-55 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61286 SN - 1438-0064 ER - TY - CHAP A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Schade, Stanley T1 - Regularity patterns for rolling stock rotation optimization T2 - 8th International Conference on Applied Operational Research, Proceedings N2 - The operation of railways gives rise to many fundamental optimization problems. One of these problems is to cover a given set of timetabled trips by a set of rolling stock rotations. This is well known as the Rolling Stock Rotation Problem (RSRP). Most approaches in the literature focus primarily on modeling and minimizing the operational costs. However, an essential aspect for the industrial application is mostly neglected. As the RSRP follows timetabling and line planning, where periodicity is a highly desired property, it is also desired to carry over periodic structures to rolling stock rotations and following operations. We call this complex requirement regularity. Regularity turns out to be of essential interest, especially in the industrial scenarios that we tackle in cooperation with DB Fernverkehr AG. Moreover, regularity in the context of the RSRP has not been investigated thoroughly in the literature so far. We introduce three regularity patterns to tackle this requirement, namely regular trips, regular turns, and regular handouts. We present a two-stage approach in order to optimize all three regularity patterns. At first, we integrate regularity patterns into an integer programming approach for the minimization of the operational cost of rolling stock rotations. Afterwards regular handouts are computed. These handouts present the rotations of the first stage in the most regular way. Our computational results (i.e., rolling stock rotations evaluated by planners of DB Fernverkehr AG) show that the three regularity patterns and our concept are a valuable and, moreover, an essential contribution to rolling stock rotation optimization. Y1 - 2016 VL - 8 SP - 28 EP - 32 ER - TY - GEN A1 - Duarte, Belmiro P.M. A1 - Sagnol, Guillaume A1 - Oliveira, Nuno M.C. T1 - A robust minimax Semidefinite Programming formulation for optimal design of experiments for model parametrization N2 - Model-based optimal design of experiments (M-bODE) is a crucial step in model parametrization since it encloses a framework that maximizes the amount of information extracted from a battery of lab experiments. We address the design of M-bODE for dynamic models considering a continuous representation of the design. We use Semidefinite Programming (SDP) to derive robust minmax formulations for nonlinear models, and extend the formulations to other criteria. The approaches are demonstrated for a CSTR where a two-step reaction occurs. T3 - ZIB-Report - 15-03 KW - Optimal design of experiments KW - Semidefinite Programming KW - Robust minmax designs Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-54626 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc T1 - Models for Fare Planning in Public Transport N2 - The optimization of fare systems in public transit allows to pursue objectives such as the maximization of demand, revenue, profit, or social welfare. We propose a non-linear optimization approach to fare planning that is based on a detailed discrete choice model of user behavior. The approach allows to analyze different fare structures, optimization objectives, and operational scenarios involving, e.g., subsidies. We use the resulting models to compute optimized fare systems for the city of Potsdam, Germany. T3 - ZIB-Report - 08-16 KW - Preisplanung KW - Nachfragefunktion KW - Optimierung KW - Nahverkehr Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10708 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc T1 - Angebotsplanung im öffentlichen Nahverkehr T1 - Service Design in Public Transport N2 - Die Angebotsplanung im öffentlichen Nahverkehr umfasst die Aufgaben der Netz-, Linien-,Fahr- und Preisplanung. Wir stellen zwei mathematische Optimierungsmodelle zur Linien- und Preisplanung vor. Wir zeigen anhand von Berechnungen für die Verkehrsbetriebe in Potsdam(ViP), dass sich damit komplexe Zusammenhänge quantitativ analysieren lassen. Auf diese Weise untersuchen wir die Auswirkungen von Freiheitsgraden auf die Konstruktion von Linien und die Wahl von Reisewegen der Passagiere, Abhängigkeiten zwischen Kosten und Reisezeiten sowie den Einfluss verschiedener Preissysteme auf Nachfrage und Kostendeckung. T3 - ZIB-Report - 08-04 KW - Preisplanung KW - Linienplanung KW - Optimierung Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10555 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc T1 - Fare Planning for Public Transport N2 - In this paper we introduce the fare planning problem for public transport which consists in designing a system of fares maximizing revenue. We propose a new simple general model for this problem. It i s based on a demand function and constraints for the different fares. The constraints define the structure of the fare system, e.g., distance dependent fares or zone fares. We discuss a simple example with a quadratic demand function and distance dependent fares. Then we introduce a more realistic discrete choice model in which passengers choose between different alternatives depending on the numb er of trips per month. We demonstrate the examples by computational experiments. T3 - ZIB-Report - 05-20 KW - fare planning KW - demand function KW - discrete choice model Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8541 ER - TY - GEN A1 - Beckenbach, Isabel A1 - Peis, Britta A1 - Schaudt, Oliver A1 - Scheidweiler, Robert T1 - A Combinatorial Proof of a König-type Theorem for Unimodular Hypergraphs N2 - We state purely combinatorial proofs for König- and Hall-type theorems for a wide class of combinatorial optimization problems. Our methods rely on relaxations of the matching and vertex cover problem and, moreover, on the strong coloring properties admitted by bipartite graphs and their generalizations. T3 - ZIB-Report - 17-27 KW - Packing KW - Covering KW - Total Unimodularity KW - König's Theorem KW - Factors Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64017 SN - 1438-0064 ER - TY - GEN A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schade, Stanley A1 - Schlechte, Thomas T1 - A Propagation Approach to Acyclic Rolling Stock Rotation Optimization N2 - The rolling stock, i.e., railway vehicles, are one of the key ingredients of a running railway system. As it is well known, the offer of a railway company to their customers, i.e., the railway timetable, changes from time to time. Typical reasons for that are different timetables associated with different seasons, maintenance periods or holidays. Therefore, the regular lifetime of a timetable is split into (more or less) irregular periods where parts of the timetable are changed. In order to operate a railway timetable most railway companies set up sequences that define the operation of timetabled trips by a single physical railway vehicle called (rolling stock) rotations. Not surprisingly, the individual parts of a timetable also affect the rotations. More precisely, each of the parts brings up an acyclic rolling stock rotation problem with start and end conditions associated with the beginning and ending of the corresponding period. In this paper, we propose a propagation approach to deal with large planning horizons that are composed of many timetables with shorter individual lifetimes. The approach is based on an integer linear programming formulation that propagates rolling stock rotations through the irregular parts of the timetable while taking a large variety of operational requirements into account. This approach is implemented within the rolling stock rotation optimization framework ROTOR used by DB Fernverkehr AG, one of the leading railway operators in Europe. Computational results for real world scenarios are presented to evaluate the approach. T3 - ZIB-Report - 17-24 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63930 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Buwaya, Julia A1 - Sagnol, Guillaume A1 - Swarat, Elmar T1 - Optimizing Toll Enforcement in Transportation Networks: a Game-Theoretic Approach N2 - We present a game-theoretic approach to optimize the strategies of toll enforcement on a motorway network. In contrast to previous approaches, we consider a network with an arbitrary topology, and we handle the fact that users may choose their Origin-Destination path; in particular they may take a detour to avoid sections with a high control rate. We show that a Nash equilibrium can be computed with an LP (although the game is not zero-sum), and we give a MIP for the computation of a Stackelberg equilibrium. Experimental results based on an application to the enforcement of a truck toll on German motorways are presented. T3 - ZIB-Report - 12-47 KW - Stackelberg Equilibrium KW - Game Theory KW - Mixed Integer Programming Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17401 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Sagnol, Guillaume A1 - Swarat, Elmar T1 - An IP Approach to Toll Enforcement Optimization on German Motorways N2 - This paper proposes the first model for toll enforcement optimization on German motorways. The enforcement is done by mobile control teams and our goal is to produce a schedule achieving network-wide control, proportional to spatial and time-dependent traffic distributions. Our model consists of two parts. The first plans control tours using a vehicle routing approach with profits and some side constraints. The second plans feasible rosters for the control teams. Both problems can be modeled as Multi-Commodity Flow Problems. Adding additional coupling constraints produces a large-scale integrated integer programming formulation. We show that this model can be solved to optimality for real world instances associated with a control area in East Germany. T3 - ZIB-Report - 11-42 KW - Toll Enforcement KW - Vehicle Routing Problem KW - Duty Roster Planning KW - Integer Programming Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14299 SN - 1438-0064 ER - TY - GEN A1 - Sagnol, Guillaume A1 - Borndörfer, Ralf A1 - Schlechte, Thomas A1 - Swarat, Elmar T1 - The Price of Spite in Spot-checking games N2 - We introduce the class of spot-checking games (SC games). These games model problems where the goal is to distribute fare inspectors over a toll network. Although SC games are not zero-sum, we show that a Nash equilibrium can be computed by linear programming. The computation of a strong Stackelberg equilibrium is more relevant for this problem, but we show that this is NP-hard. However, we give some bounds on the \emph{price of spite}, which measures how the payoff of the inspector degrades when committing to a Nash equilibrium. Finally, we demonstrate the quality of these bounds for a real-world application, namely the enforcement of a truck toll on German motorways. T3 - ZIB-Report - 14-38 Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-52775 SN - 1438-0064 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Sagnol, Guillaume A1 - Schwartz, Stephan T1 - An Extended Network Interdiction Problem for Optimal Toll Control T2 - INOC 2015 – 7th International Network Optimization Conference N2 - We study an extension of the shortest path network interdiction problem and present a novel real-world application in this area. We consider the problem of determining optimal locations for toll control stations on the arcs of a transportation network. We handle the fact that drivers can avoid control stations on parallel secondary roads. The problem is formulated as a mixed integer program and solved using Benders decomposition. We present experimental results for the application of our models to German motorways. Y1 - 2016 U6 - https://doi.org/10.1016/j.endm.2016.03.040 VL - 52 SP - 301 EP - 308 ER - TY - GEN A1 - Schade, Stanley A1 - Schlechte, Thomas A1 - Witzig, Jakob T1 - Structure-based Decomposition for Pattern-Detection for Railway Timetables N2 - We consider the problem of pattern detection in large scale railway timetables. This problem arises in rolling stock optimization planning in order to identify invariant sections of the timetable for which a cyclic rotation plan is adequate. We propose a dual reduction technique which leads to an decomposition and enumeration method. Computational results for real world instances demonstrate that the method is able to produce optimal solutions as fast as standard MIP solvers. T3 - ZIB-Report - 17-40 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64525 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika A1 - Löbel, Fabian T1 - The Modulo Network Simplex with Integrated Passenger Routing N2 - Periodic timetabling is an important strategic planning problem in public transport. The task is to determine periodic arrival and departure times of the lines in a given network, minimizing the travel time of the passengers. We extend the modulo network simplex method, a well-established heuristic for the periodic timetabling problem, by integrating a passenger (re)routing step into the pivot operations. Computations on real-world networks show that we can indeed find timetables with much shorter total travel time, when we take the passengers' travel paths into consideration. T3 - ZIB-Report - 16-43 KW - periodic timetabling, modulo network simplex, passenger routing Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-60319 SN - 1438-0064 ER - TY - CHAP A1 - Schade, Stanley A1 - Strehler, Martin ED - Goerigk, Marc ED - Werneck, Renato T1 - The Maximum Flow Problem for Oriented Flows T2 - 16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016) N2 - In several applications of network flows, additional constraints have to be considered. In this paper, we study flows, where the flow particles have an orientation. For example, cargo containers with doors only on one side and train coaches with 1st and 2nd class compartments have such an orientation. If the end position has a mandatory orientation, not every path from source to sink is feasible for routing or additional transposition maneuvers have to be made. As a result, a source-sink path may visit a certain vertex several times. We describe structural properties of optimal solutions, determine the computational complexity, and present an approach for approximating such flows. Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0030-drops-65318 UR - http://drops.dagstuhl.de/opus/volltexte/2016/6531 SN - 978-3-95977-021-7 SN - 2190-6807 N1 - Keywords: network flow with orientation, graph expansion, approximation, container logistics, train routing VL - 54 SP - 1 EP - 13 PB - Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik CY - Dagstuhl, Germany ER - TY - GEN A1 - Borndörfer, Ralf A1 - Klug, Torsten A1 - Lamorgese, Leonardo A1 - Mannino, Carlo A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - Recent Success Stories on Optimization of Railway Systems N2 - Planning and operating railway transportation systems is an extremely hard task due to the combinatorial complexity of the underlying discrete optimization problems, the technical intricacies, and the immense size of the problem instances. Because of that, however, mathematical models and optimization techniques can result in large gains for both railway cus- tomers and operators, e.g., in terms of cost reductions or service quality improvements. In the last years a large and growing group of researchers in the OR community have devoted their attention to this domain devel- oping mathematical models and optimization approaches to tackle many of the relevant problems in the railway planning process. However, there is still a gap to bridge between theory and practice, with a few notable exceptions. In this paper we address three success stories, namely, long-term freight train routing (part I), mid-term rolling stock rotation planning (part II), and real-time train dispatching (part III). In each case, we describe real-life, successful implementations. We will dis- cuss the individual problem setting, survey the optimization literature, and focus on particular aspects addressed by the mathematical models. We demonstrate on concrete applications how mathematical optimization can support railway planning and operations. This gives proof that math- ematical optimization can support the planning of rolling stock resources. Thus, mathematical models and optimization can lead to a greater effi- ciency of railway operations and will serve as a powerful and innovative tool to meet recent challenges of the railway industry. T3 - ZIB-Report - 14-47 KW - railway planning KW - railway operations KW - capacity optimization Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-53726 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Karbstein, Marika T1 - Metric Inequalities for Routings on Direct Connections with Application in Line Planning N2 - We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We derive a feasibility condition for path capacities supporting such direct connection flows similar to the feasibility condition for arc capacities in ordinary multi-commodity flows. The concept allows to solve large-scale real-world line planning problems in public transport including a novel passenger routing model that favors direct connections over connections with transfers. T3 - ZIB-Report - 15-07 KW - combinatorial optimization KW - integer programming KW - line planning KW - transfers KW - direct connection KW - metric inequalities Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-53507 SN - 1438-0064 ER - TY - GEN A1 - Harman, Radoslav A1 - Sagnol, Guillaume T1 - Computing D-optimal experimental designs for estimating treatment contrasts under the presence of a nuisance time trend N2 - We prove a mathematical programming characterisation of approximate partial D-optimality under general linear constraints. We use this characterisation with a branch-and-bound method to compute a list of all exact D-optimal designs for estimating a pair of treatment contrasts in the presence of a nuisance time trend up to the size of 24 consecutive trials. T3 - ZIB-Report - 15-02 KW - optimal design of experiments KW - nuisance trend KW - branch and bound Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-53640 SN - 1438-0064 ER - TY - CHAP A1 - Sagnol, Guillaume A1 - Harman, Radoslav ED - Steland, Ansgar ED - Rafajłowicz, Ewaryst ED - Szajowski, Krzysztof T1 - Optimal Designs for Steady-state Kalman filters T2 - Stochastic Models, Statistics and Their Applications N2 - We consider a stationary discrete-time linear process that can be observed by a finite number of sensors. The experimental design for the observations consists of an allocation of available resources to these sensors. We formalize the problem of selecting a design that maximizes the information matrix of the steady-state of the Kalman filter, with respect to a standard optimality criterion, such as $D-$ or $A-$optimality. This problem generalizes the optimal experimental design problem for a linear regression model with a finite design space and uncorrelated errors. Finally, we show that under natural assumptions, a steady-state optimal design can be computed by semidefinite programming. Y1 - 2015 U6 - https://doi.org/10.1007/978-3-319-13881-7_17 VL - 122 SP - 149 EP - 157 PB - Springer ER - TY - CHAP A1 - Harman, Radoslav A1 - Sagnol, Guillaume ED - Steland, Ansgar ED - Rafajłowicz, Ewaryst ED - Szajowski, Krzysztof T1 - Computing D-optimal experimental designs for estimating treatment contrasts under the presence of a nuisance time trend T2 - Stochastic Models, Statistics and Their Applications N2 - We prove a mathematical programming characterisation of approximate partial D-optimality under general linear constraints. We use this characterisation with a branch-and-bound method to compute a list of all exact D-optimal designs for estimating a pair of treatment contrasts in the presence of a nuisance time trend up to the size of 24 consecutive trials. Y1 - 2015 U6 - https://doi.org/10.1007/978-3-319-13881-7_10 VL - 122 SP - 83 EP - 91 PB - Springer ER - TY - GEN A1 - Borndörfer, Ralf A1 - Schlechte, Thomas A1 - Swarat, Elmar T1 - Railway Track Allocation - Simulation, Aggregation, and Optimization N2 - Today the railway timetabling process and the track allocation is one of the most challenging problems to solve by a railway company. Especially due to the deregulation of the transport market in the recent years several suppliers of railway traffic have entered the market in Europe. This leads to more potential conflicts between trains caused by an increasing demand of train paths. Planning and operating railway transportation systems is extremely hard due to the combinatorial complexity of the underlying discrete optimization problems, the technical intricacies, and the immense size of the problem instances. In order to make best use of the infrastructure and to ensure economic operation, efficient planning of the railway operation is indispensable. Mathematical optimization models and algorithms can help to automatize and tackle these challenges. Our contribution in this paper is to present a renewed planning process due to the liberalization in Europe and an associated concept for track allocation, that consists of three important parts, simulation, aggregation, and optimization. Furthermore, we present results of our general framework for real world data. T3 - ZIB-Report - 11-35 KW - railway models, railway capacity, track allocation framework Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14031 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Friedow, Isabel A1 - Karbstein, Marika T1 - Optimierung des Linienplans 2010 in Potsdam N2 - Im Zuge der Übernahme von 6 Linien der Havelbus Verkehrsgesellschaft mbH durch die ViP Verkehr in Potsdam GmbH ergab sich 2009 die Notwendigkeit der Entwicklung eines neuen Linien- und Taktplans für das Jahr 2010. Das Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB) entwickelt in einem Projekt des DFG-Forschungszentrums Matheon ein Verfahren zur mathematischen Linienoptimierung. Dieses Tool wurde bei der Optimierung des ViP Linienplans 2010 in einer projektbegleitenden Studie eingesetzt, um Alternativen bei verschiedenen Planungs- und Zielvorgaben auszuloten. In dem Artikel wird eine Auswertung der Ergebnisse mit dem Verkehrsanalysesystem Visum der PTV AG beschrieben. Die Auswertungen bestätigen, dass mit Hilfe von mathematischer Optimierung eine weitere Verkürzung der Reisezeit um 1%, eine als um 6% verkürzt empfundene Reisezeit, 10% weniger Fahrzeit im Fahrzeug und eine gleichzeitige Kostenreduktion um 5% möglich sind. T3 - ZIB-Report - 12-04 KW - Fallstudie KW - Linienplan KW - Optimierung Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14486 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Heismann, Olga T1 - Minimum Cost Hyperassignments with Applications to ICE/IC Rotation Planning N2 - Vehicle rotation planning is a fundamental problem in rail transport. It decides how the railcars, locomotives, and carriages are operated in order to implement the trips of the timetable. One important planning requirement is operational regularity, i.e., using the rolling stock in the same way on every day of operation. We propose to take regularity into account by modeling the vehicle rotation planning problem as a minimum cost hyperassignment problem (HAP). Hyperassignments are generalizations of assignments from directed graphs to directed hypergraphs. Finding a minimum cost hyperassignment is NP-hard. Most instances arising from regular vehicle rotation planning, however, can be solved well in practice. We show that, in particular, clique inequalities strengthen the canonical LP relaxation substantially. T3 - ZIB-Report - 11-46 KW - hyperassignments KW - vehicle rotation planning Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14564 UR - http://link.springer.com/chapter/10.1007%2F978-3-642-29210-1_10 SN - 1438-0064 ER -