@inproceedings{HeismannBorndoerfer2013, author = {Heismann, Olga and Bornd{\"o}rfer, Ralf}, title = {The Random Hypergraph Assignment Problem}, booktitle = {Proceedings of the 16th International Multiconference INFORMATION SOCIETY - IS 2013}, pages = {599 -- 602}, year = {2013}, abstract = {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.}, language = {en} } @inproceedings{Sagnol2012, author = {Sagnol, Guillaume}, title = {Network-related problems in optimal experimental design and second order cone programming}, volume = {51}, booktitle = {Proceedings of PROBASTAT'2011, Tatra Mountains Mathematical Publications}, doi = {10.2478/v10127-012-0016-x}, pages = {161 -- 171}, year = {2012}, abstract = {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.}, language = {en} } @article{Sagnol2013, author = {Sagnol, Guillaume}, title = {On the semidefinite representation of real functions applied to symmetric matrices}, volume = {439}, journal = {Linear Algebra and its Applications}, number = {10}, doi = {10.1016/j.laa.2013.08.021}, pages = {2829 -- 2843}, year = {2013}, abstract = {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.}, language = {en} } @inproceedings{HildenbrandtReineltHeismann2013, author = {Hildenbrandt, Achim and Reinelt, Gerhard and Heismann, Olga}, title = {Integer Programming Models for the Target Visitation Problem}, booktitle = {Proceedings of the 16th International Multiconference INFORMATION SOCIETY - IS 2013}, pages = {569 -- 572}, year = {2013}, abstract = {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.}, language = {en} } @inproceedings{HeismannBorndoerfer2012, author = {Heismann, Olga and Bornd{\"o}rfer, Ralf}, title = {Minimum Cost Hyperassignments with Applications to ICE/IC Rotation Planning}, booktitle = {Operations Research Proceedings 2011}, pages = {59 -- 64}, year = {2012}, abstract = {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.}, language = {en} } @article{LangenhanBorndoerferLoebeletal.2012, author = {Langenhan, Andreas and Bornd{\"o}rfer, Ralf and L{\"o}bel, Andreas and Schulz, Christof and Weider, Steffen}, title = {Duty Scheduling Templates}, journal = {Proceedings of Conference on Advanced Systems for Public Transport 2012 (CASPT12)}, editor = {Mu{\~n}oz, J. C. and Voß, S.}, year = {2012}, abstract = {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.}, language = {en} } @phdthesis{Karbstein2013, author = {Karbstein, Marika}, title = {Line Planning and Connectivity}, isbn = {978-3-8439-1062-0}, year = {2013}, abstract = {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.}, language = {en} } @article{HillerKlugTuchscherer2013, author = {Hiller, Benjamin and Klug, Torsten and Tuchscherer, Andreas}, title = {An Exact Reoptimization Algorithm for the Scheduling of Elevator Groups}, journal = {Flexible Services and Manufacturing Journal}, doi = {10.1007/s10696-013-9175-6}, pages = {1 -- 24}, year = {2013}, language = {en} } @inproceedings{Schlechte2012, author = {Schlechte, Thomas}, title = {Railway Track Allocation}, booktitle = {Operations Research Proceedings}, doi = {10.1007/978-3-319-00795-314}, pages = {15 -- 20}, year = {2012}, language = {en} } @article{BorndoerferKarbsteinPfetsch2013, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika and Pfetsch, Marc}, title = {The Steiner connectivity problem}, volume = {142}, journal = {Mathematical Programming A}, number = {1}, doi = {10.1007/s10107-012-0564-5}, pages = {133 -- 167}, year = {2013}, language = {en} } @misc{BorndoerferGroetschelKlostermeieretal.1993, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Klostermeier, Fridolin and K{\"u}ttner, Christian}, title = {Telebus-Disposition: Ein Konzept zur Serviceverbesserung bei gleichzeitiger Kostensenkung.[nur hausintern]}, number = {TR-93-03}, year = {1993}, abstract = {"`Telebus"' ist der soziale Behindertenfahrdienst im Land Berlin. Das Telebus-Forschungsprojekt des Konrad-Zuse-Zentrums f{\"u}r 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 M{\"o}glichkeiten zur Verbesserung des Service und zur Reduzierung der Kosten skizziert. \originalTeX}, language = {de} } @article{BorndoerferReutherSchlechteetal.2012, author = {Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas and Weider, Steffen}, title = {Vehicle Rotation Planning for Intercity Railways}, journal = {Proceedings of Conference on Advanced Systems for Public Transport 2012 (CASPT12)}, editor = {Mu{\~n}oz, J. C. and Voß, S.}, year = {2012}, abstract = {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.}, language = {en} } @article{BorndoerferLoebelReutheretal.2013, author = {Bornd{\"o}rfer, Ralf and L{\"o}bel, Andreas and Reuther, Markus and Schlechte, Thomas and Weider, Steffen}, title = {Rapid Branching}, volume = {5}, journal = {Public Transport}, number = {1}, editor = {Mu{\~n}oz, J. C. and Voß, S.}, publisher = {Springer Berlin Heidelberg}, pages = {3 -- 23}, year = {2013}, abstract = {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.}, language = {en} } @inproceedings{ScheumannFuegenschuhSchenkeretal.2012, author = {Scheumann, Ren{\´e} and F{\"u}genschuh, Armin and Schenker, Sebastian and Vierhaus, Ingmar and Bornd{\"o}rfer, Ralf and Finkbeiner, Matthias}, title = {Global Manufacturing: How to Use Mathematical Optimisation Methods to Transform to Sustainable Value Creation}, booktitle = {Proceedings of the 10th Global Conference on Sustainable Manufacturing}, editor = {Seliger, G{\"u}nther}, isbn = {978-605-63463-1-6}, pages = {538 -- 545}, year = {2012}, language = {en} } @article{Sagnol2013, author = {Sagnol, Guillaume}, title = {Approximation of a maximum-submodular-coverage problem involving spectral functions, with application to experimental designs}, volume = {161}, journal = {Discrete Applied Mathematics}, number = {1-2}, doi = {10.1016/j.dam.2012.07.016}, pages = {258 -- 276}, year = {2013}, abstract = {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\$.}, language = {en} } @article{Sagnol2011, author = {Sagnol, Guillaume}, title = {A class of Semidefinite Programs with rank-one solutions}, volume = {435}, journal = {Linear Algebra and its Applications}, number = {6}, doi = {10.1016/j.laa.2011.03.027}, pages = {1446 -- 1463}, year = {2011}, abstract = {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.}, language = {en} } @article{BorndoerferSchlechteSwarat2012, author = {Bornd{\"o}rfer, Ralf and Schlechte, Thomas and Swarat, Elmar}, title = {Railway Track Allocation -- Simulation, Aggregation, and Optimization}, volume = {2}, journal = {Proc. 1st International Workshop on High-speed and Intercity Railways (IWHIR 2011)}, number = {148}, doi = {10.1007/978-3-642-27963-8}, pages = {53 -- 70}, year = {2012}, abstract = {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.}, language = {en} } @article{BorndoerferReutherSchlechteetal.2011, author = {Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas and Weider, Steffen}, title = {A Hypergraph Model for Railway Vehicle Rotation Planning}, volume = {OpenAccess Series in Informatics (OASIcs)}, journal = {11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems}, number = {20}, doi = {10.4230/OASIcs.ATMOS.2011.146}, pages = {146 -- 155}, year = {2011}, abstract = {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.}, language = {en} } @article{Schlechte2011, author = {Schlechte, Thomas}, title = {Railway Track Allocation - Simulation and Optimization}, volume = {4}, journal = {Proceedings of 4th International Seminar on Railway Operations Modelling and Analysis (IAROR)}, year = {2011}, abstract = {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.}, language = {en} } @inproceedings{BorndoerferNeumann2011, author = {Bornd{\"o}rfer, Ralf and Neumann, Marika}, title = {Linienoptimierung - reif f{\"u}r die Praxis?}, booktitle = {Heureka '11 : Optimierung in Verkehr und Transport}, year = {2011}, abstract = {Wir stellen in dieser Arbeit ein mathematisches Optimierungsmodell zur Bestimmung eines optimalen Linienplans vor, das sowohl die Fahrzeiten und die Anzahl der Umstiege ber{\"u}cksichtigt 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 f{\"u}r Potsdam entwickelt. Unsere Berechnungen zeigen, dass die mathematische Optimierung in nichts einer "Handplanung" des Liniennetzes nachsteht. Im Gegenteil, mit Hilfe des Optimierungsprogramms ist es m{\"o}glich, durch Ver{\"a}nderung der Parameter mehrere verschiedene Szenarien zu berechnen, miteinander zu vergleichen und Aussagen {\"u}ber minimale Kosten und Fahrzeiten zu machen.}, language = {de} } @inproceedings{BorndoerferHoppmannKarbstein2013, author = {Bornd{\"o}rfer, Ralf and Hoppmann, Heide and Karbstein, Marika}, title = {A Configuration Model for the Line Planning Problem}, volume = {33}, booktitle = {ATMOS 2013 - 13th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems}, editor = {Frigioni, Daniele and Stiller, Sebastian}, publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik}, doi = {10.4230/OASIcs.ATMOS.2013.68}, pages = {68 -- 79}, year = {2013}, language = {en} } @article{BorndoerferFriedowKarbstein2012, author = {Bornd{\"o}rfer, Ralf and Friedow, Isabel and Karbstein, Marika}, title = {Optimierung des Linienplans 2010 in Potsdam}, volume = {30}, journal = {Der Nahverkehr}, number = {4}, pages = {34 -- 39}, year = {2012}, language = {de} } @misc{BorndoerferHoppmannKarbstein2013, author = {Bornd{\"o}rfer, Ralf and Hoppmann, Heide and Karbstein, Marika}, title = {A Configuration Model for the Line Planning Problem}, issn = {1438-0064}, doi = {10.4230/OASIcs.ATMOS.2013.68}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-41903}, year = {2013}, abstract = {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.}, language = {en} } @article{Karbstein2014, author = {Karbstein, Marika}, title = {Ohne Umsteigen ans Ziel}, volume = {52}, journal = {OR News}, pages = {12 -- 14}, year = {2014}, abstract = {Die Anforderungen an das Liniennetz eines Verkehrsunternehmens sind vielf{\"a}ltig: kurze Fahrzeiten, viele Direktverbindungen und geringe Kosten. Mathematische Optimierungsmethoden k{\"o}nnen die Planung von Liniennetzen unterst{\"u}tzen und beste Kompromisse bzgl. aller Anforderungen berechnen.}, language = {de} } @misc{SagnolBorndoerferGrimaetal.2016, author = {Sagnol, Guillaume and Bornd{\"o}rfer, Ralf and Grima, Micka{\"e}l and Seeling, Matthes and Spies, Claudia}, title = {Robust Allocation of Operating Rooms with Lognormal case Durations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-58497}, year = {2016}, abstract = {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.}, language = {en} } @article{BorndoerferFuegenschuhKlugetal.2016, author = {Bornd{\"o}rfer, Ralf and F{\"u}genschuh, Armin and Klug, Torsten and Schang, Thilo and Schlechte, Thomas and Sch{\"u}lldorf, Hanno}, title = {The Freight Train Routing Problem for Congested Railway Networks with Mixed Traffic}, volume = {50}, journal = {Transportation Science}, number = {2}, doi = {10.1287/trsc.2015.0656}, pages = {408 -- 423}, year = {2016}, abstract = {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.}, language = {en} } @inproceedings{Karbstein2016, author = {Karbstein, Marika}, title = {Integrated Line Planning and Passenger Routing: Connectivity and Transfers}, booktitle = {Operations Research Proceedings 2014}, doi = {10.1007/978-3-319-28697-6_37}, pages = {263 -- 269}, year = {2016}, abstract = {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.}, language = {en} } @inproceedings{BeckenbachBorndoerfer2016, author = {Beckenbach, Isabel and Bornd{\"o}rfer, Ralf}, title = {An Approximation Result for Matchings in Partitioned Hypergraphs}, booktitle = {Operations Research Proceedings 2014}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-319-28697-6_5}, pages = {31 -- 36}, year = {2016}, abstract = {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})\$.}, language = {en} } @article{Hoppmann2015, author = {Hoppmann, Heide}, title = {Linienplanung und Minimale Konfigurationen}, volume = {55}, journal = {OR News}, pages = {22 -- 23}, year = {2015}, language = {de} } @inproceedings{LiebchenSwarat2008, author = {Liebchen, Christian and Swarat, Elmar}, title = {The Second Chvatal Closure Can Yield Better Railway Timetables}, booktitle = {ATMOS 2008 - 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems}, editor = {Fischetti, Matteo and Widmayer, Peter}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany}, address = {Dagstuhl, Germany}, doi = {10.4230/OASIcs.ATMOS.2008.1580}, url = {http://nbn-resolving.de/urn:nbn:de:0030-drops-15802}, year = {2008}, language = {en} } @article{BorndoerferErolGraffagninoetal.2012, author = {Bornd{\"o}rfer, Ralf and Erol, Berkan and Graffagnino, Thomas and Schlechte, Thomas and Swarat, Elmar}, title = {Optimizing the Simplon railway corridor}, volume = {218}, journal = {Annals of Operations Research}, number = {1}, edition = {Annals of Operations Research}, publisher = {Springer US}, doi = {10.1007/s10479-012-1260-9}, pages = {93 -- 106}, year = {2012}, language = {en} } @inproceedings{SchlechteTanner2010, author = {Schlechte, Thomas and Tanner, Andreas}, title = {Railway capacity auctions with dual prices}, booktitle = {Selected Proceedings of the 12th World Conference on Transport Research}, year = {2010}, language = {en} } @inproceedings{BorndoerferSchlechte2007, author = {Bornd{\"o}rfer, Ralf and Schlechte, Thomas}, title = {Models for Railway Track Allocation}, volume = {07001}, booktitle = {ATMOS 2007 - 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems}, editor = {Liebchen, Christian and Ahuja, Ravindra and Mesa, Juan}, publisher = {Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany}, year = {2007}, language = {en} } @inproceedings{BorndoerferSchlechte2008, author = {Bornd{\"o}rfer, Ralf and Schlechte, Thomas}, title = {Balancing Efficiency and Robustness}, booktitle = {MCDM for Sustainable Energy and Transportation Systems}, editor = {Ehrgott, Matthias and Naujoks, Boris and Stewart, Theo and Wallenius, Jyrki}, publisher = {Lecture Notes in Economics and Mathematical Systems}, year = {2008}, language = {en} } @misc{BorndoerferGroetschelLoebel1999, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and L{\"o}bel, Andreas}, title = {Der Schnellste Weg zum Ziel}, doi = {10.1007/978-3-322-96366-6_5}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4209}, number = {SC-99-32}, year = {1999}, abstract = {Wir geben eine Einf{\"u}hrung in die Mathematik von und mit Wegen. Nicht auf dem k{\"u}rzesten, aber auf einem hoffentlich kurzweiligen Weg!}, language = {de} } @misc{SchwartzBorndoerferBartz2016, author = {Schwartz, Stephan and Bornd{\"o}rfer, Ralf and Bartz, Gerald}, title = {The Graph Segmentation Problem}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60750}, year = {2016}, abstract = {We investigate a graph theoretical problem arising in the automatic billing of a network toll. Given a network and a family of user paths, we study the graph segmentation problem (GSP) to cover parts of the user paths by a set of disjoint segments. The GSP is shown to be NP-hard but for special cases it can be solved in polynomial time. We also show that the marginal utility of a segment is bounded. Computational results for real-world instances show that in practice the problem is more amenable than the theoretic bounds suggest.}, language = {en} } @inproceedings{BorndoerferHoppmannKarbsteinetal.2016, author = {Bornd{\"o}rfer, Ralf and Hoppmann, Heide and Karbstein, Marika and L{\"o}bel, Fabian}, title = {The Modulo Network Simplex with Integrated Passenger Routing}, booktitle = {Operations Research Proceedings 2016}, year = {2016}, abstract = {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.}, language = {en} } @misc{Wenzel2016, type = {Master Thesis}, author = {Wenzel, Ron}, title = {On the In-Flight Rest Assignment Problem}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59328}, pages = {76}, year = {2016}, abstract = {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.}, language = {en} } @misc{SagnolBalzerBorndoerferetal.2016, author = {Sagnol, Guillaume and Balzer, Felix and Bornd{\"o}rfer, Ralf and Spies, Claudia and von Dincklage, Falk}, title = {Makespan and Tardiness in Activity Networks with Lognormal Activity Durations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59290}, year = {2016}, abstract = {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.}, language = {en} } @misc{SagnolHegeWeiser2016, author = {Sagnol, Guillaume and Hege, Hans-Christian and Weiser, Martin}, title = {Using sparse kernels to design computer experiments with tunable precision}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59605}, year = {2016}, abstract = {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.}, language = {en} } @misc{BeckenbachScheidweiler2016, author = {Beckenbach, Isabel and Scheidweiler, Robert}, title = {Perfect f-Matchings and f-Factors in Hypergraphs - A Combinatorial Approach}, issn = {1438-0064}, doi = {10.1016/j.disc.2017.05.005}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59071}, year = {2016}, abstract = {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.}, language = {en} } @article{SagnolHarman2015, author = {Sagnol, Guillaume and Harman, Radoslav}, title = {Computing exact D-optimal designs by mixed integer second-order cone programming}, volume = {43}, journal = {The Annals of Statistics}, number = {5}, doi = {10.1214/15-AOS1339}, pages = {2198 -- 2224}, year = {2015}, abstract = {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.}, language = {en} } @inproceedings{DuarteSagnolOliveira2015, author = {Duarte, Belmiro P.M. and Sagnol, Guillaume and Oliveira, Nuno M.C.}, title = {A Robust Minimax Semidefinite Programming Formulation for Optimal Design of Experiments for Model Parametrization}, volume = {37}, booktitle = {12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering}, doi = {10.1016/B978-0-444-63578-5.50146-8}, pages = {905 -- 910}, year = {2015}, abstract = {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.}, language = {en} } @misc{SchenkerBorndoerferSkutella2016, author = {Schenker, Sebastian and Bornd{\"o}rfer, Ralf and Skutella, Martin}, title = {A novel partitioning of the set of non-dominated points}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61286}, year = {2016}, abstract = {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.}, language = {en} } @inproceedings{GrimmBorndoerferReutheretal.2016, author = {Grimm, Boris and Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas and Schade, Stanley}, title = {Regularity patterns for rolling stock rotation optimization}, volume = {8}, booktitle = {8th International Conference on Applied Operational Research, Proceedings}, pages = {28 -- 32}, year = {2016}, abstract = {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.}, language = {en} } @misc{DuarteSagnolOliveira2015, author = {Duarte, Belmiro P.M. and Sagnol, Guillaume and Oliveira, Nuno M.C.}, title = {A robust minimax Semidefinite Programming formulation for optimal design of experiments for model parametrization}, issn = {1438-0064}, doi = {10.1016/B978-0-444-63578-5.50146-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54626}, year = {2015}, abstract = {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.}, language = {en} } @misc{BorndoerferNeumannPfetsch2008, author = {Bornd{\"o}rfer, Ralf and Neumann, Marika and Pfetsch, Marc}, title = {Models for Fare Planning in Public Transport}, issn = {1438-0064}, doi = {10.1016/j.dam.2012.02.027}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10708}, number = {08-16}, year = {2008}, abstract = {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.}, language = {en} } @misc{BorndoerferNeumannPfetsch2008, author = {Bornd{\"o}rfer, Ralf and Neumann, Marika and Pfetsch, Marc}, title = {Angebotsplanung im {\"o}ffentlichen Nahverkehr}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10555}, number = {08-04}, year = {2008}, abstract = {Die Angebotsplanung im {\"o}ffentlichen 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 f{\"u}r die Verkehrsbetriebe in Potsdam(ViP), dass sich damit komplexe Zusammenh{\"a}nge quantitativ analysieren lassen. Auf diese Weise untersuchen wir die Auswirkungen von Freiheitsgraden auf die Konstruktion von Linien und die Wahl von Reisewegen der Passagiere, Abh{\"a}ngigkeiten zwischen Kosten und Reisezeiten sowie den Einfluss verschiedener Preissysteme auf Nachfrage und Kostendeckung.}, language = {de} } @misc{BorndoerferNeumannPfetsch2005, author = {Bornd{\"o}rfer, Ralf and Neumann, Marika and Pfetsch, Marc}, title = {Fare Planning for Public Transport}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8541}, number = {05-20}, year = {2005}, abstract = {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.}, language = {en} } @misc{BeckenbachPeisSchaudtetal.2017, author = {Beckenbach, Isabel and Peis, Britta and Schaudt, Oliver and Scheidweiler, Robert}, title = {A Combinatorial Proof of a K{\"o}nig-type Theorem for Unimodular Hypergraphs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64017}, year = {2017}, abstract = {We state purely combinatorial proofs for K{\"o}nig- 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.}, language = {en} } @misc{GrimmBorndoerferReutheretal.2017, author = {Grimm, Boris and Bornd{\"o}rfer, Ralf and Reuther, Markus and Schade, Stanley and Schlechte, Thomas}, title = {A Propagation Approach to Acyclic Rolling Stock Rotation Optimization}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-63930}, year = {2017}, abstract = {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.}, language = {en} }