@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} }