@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} } @article{BorndoerferSagnolSchlechteetal.2016, author = {Bornd{\"o}rfer, Ralf and Sagnol, Guillaume and Schlechte, Thomas and Swarat, Elmar}, title = {Optimal duty rostering for toll enforcement inspectors}, volume = {252(2)}, journal = {Annals of Operations Research}, edition = {252}, publisher = {Springer US}, doi = {10.1007/s10479-016-2152-1}, pages = {383 -- 406}, year = {2016}, abstract = {We present the problem of planning mobile tours of inspectors on German motorways to enforce the payment of the toll for heavy good trucks. This is a special type of vehicle routing problem with the objective to conduct as good inspections as possible on the complete network. In addition, we developed a personalized crew rostering model, to schedule the crews of the tours. The planning of daily tours and the rostering are combined in a novel integrated approach and formulated as a complex and large scale Integer Program. The main focus of this paper extends our previous publications on how different requirements for the rostering can be modeled in detail. The second focus is on a bi-criteria analysis of the planning problem to find the balance between the control quality and the roster acceptance. Finally, computational results on real-world instances show the practicability of our method and how different input parameters influence the problem complexity.}, language = {en} } @article{BeckenbachScheidweiler2017, author = {Beckenbach, Isabel and Scheidweiler, Robert}, title = {Perfect f-Matchings and f-Factors in Hypergraphs - A Combinatorial Approach}, volume = {340}, journal = {Discrete Mathematics}, number = {10}, doi = {10.1016/j.disc.2017.05.005}, pages = {2499 -- 2506}, year = {2017}, 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 = {de} } @article{BorndoerferHoppmannKarbstein2016, author = {Bornd{\"o}rfer, Ralf and Hoppmann, Heide and Karbstein, Marika}, title = {Passenger routing for periodic timetable optimization}, journal = {Public Transport}, publisher = {Springer-Verlag Berlin Heidelberg}, doi = {10.1007/s12469-016-0132-0}, year = {2016}, abstract = {The task of periodic timetabling is to determine trip arrival and departure times in a public transport system such that travel and transfer times are minimized. This paper investigates periodic timetabling models with integrated passenger routing. We show that different routing models can have a huge influence on the quality of the entire system: Whatever metric is applied, the performance ratios of timetables w.r.t. different routing models can be arbitrarily large. Computations on a real-world instance for the city of Wuppertal substantiate the theoretical findings. These results indicate the existence of untapped optimization potentials that can be used to improve the efficiency of public transport systems by integrating passenger routing.}, language = {en} } @article{BorndoerferKarbstein2015, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika}, title = {Metric inequalities for routings on direct connections with application to line planning}, volume = {18}, journal = {Discrete Optimization}, pages = {56 -- 73}, year = {2015}, abstract = {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 well-known feasibility condition for arc capacities in ordinary multi-commodity flows. The condition can be expressed in terms of a class of metric inequalities for routings on direct connections. We illustrate the concept on the example of the line planning problem in public transport and present an application to large-scale real-world problems.}, language = {en} } @article{BorndoerferBuwayaSagnoletal.2015, author = {Bornd{\"o}rfer, Ralf and Buwaya, Julia and Sagnol, Guillaume and Swarat, Elmar}, title = {Network spot-checking games: Theory and application to toll enforcing in transportation networks}, volume = {65}, journal = {Networks}, publisher = {Wiley Periodicals, Inc.}, doi = {10.1002/net.21596}, pages = {312 -- 328}, year = {2015}, abstract = {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. In an SC game, the pure strategies of network users correspond to paths in a graph, and the pure strategies of the inspectors are subset of arcs to be controlled. 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 (SSE) is more relevant for this problem and we give a mixed integer programming (MIP) formulation for this problem. We show that the computation of such an equilibrium is NP-hard. More generally, we prove that it is NP-hard to compute a SSE in a polymatrix game, even if the game is pairwise zero-sum. Then, we give some bounds on the price of spite, which measures how the payoff of the inspector degrades when committing to a Nash equilibrium. Finally, we report computational experiments on instances constructed from real data, for an application to the enforcement of a truck toll in Germany. These numerical results show the efficiency of the proposed methods, as well as the quality of the bounds derived in this article.}, language = {en} } @article{BorndoerferReutherSchlechteetal.2016, author = {Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas and Waas, Kerstin and Weider, Steffen}, title = {Integrated Optimization of Rolling Stock Rotations for Intercity Railways}, volume = {50}, journal = {Transportation Science}, number = {3}, doi = {10.1287/trsc.2015.0633}, pages = {863 -- 877}, year = {2016}, abstract = {This paper proposes a highly integrated solution approach for rolling stock planning problems in the context of long distance passenger traffic between cities. The main contributions are a generic hypergraph-based mixed-integer programming model for the considered rolling stock rotation problem and an integrated algorithm for its solution. The newly developed algorithm is able to handle a large spectrum of industrial railway requirements, such as vehicle composition, maintenance constraints, infrastructure capacities, and regularity aspects. We show that our approach has the power to produce rolling stock rotations that can be implemented in practice. In this way, the rolling stock rotations at the largest German long distance operator Deutsche Bahn Fernverkehr AG could be optimized by an automated system utilizing advanced mathematical programming techniques.}, language = {en} } @article{BorndoerferGrimmReutheretal.2017, author = {Bornd{\"o}rfer, Ralf and Grimm, Boris and Reuther, Markus and Schlechte, Thomas}, title = {Template-based Re-optimization of Rolling Stock Rotations}, journal = {Public Transport}, publisher = {Springer}, doi = {10.1007/s12469-017-0152-4}, pages = {1 -- 19}, year = {2017}, abstract = {Rolling stock, i.e., the set of railway vehicles, is among the most expensive and limited assets of a railway company and must be used efficiently. We consider in this paper the re-optimization problem to recover from unforeseen disruptions. We propose a template concept that allows to recover cost minimal rolling stock rotations from reference rotations under a large variety of operational requirements. To this end, connection templates as well as rotation templates are introduced and their application within a rolling stock rotation planning model is discussed. We present an implementation within the rolling stock rotation optimization framework rotor and computational results for scenarios provided by DB Fernverkehr AG, one of the leading railway operators in Europe.}, language = {en} } @article{BorndoerferKarbstein2015, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika}, title = {Neue Planungsinstrumente nutzen: Das Verkehrsangebot verbessern und Kosten sparen}, volume = {68}, journal = {Verkehr und Technik}, number = {7}, pages = {239 -- 243}, year = {2015}, abstract = {Wir illustrieren anhand des Liniennetzes der Stadt Potsdam das Potenzial mathematischer Methoden der Angebotsplanung. Wir zeigen, dass das "bestm{\"o}gliche" Verkehrsangebot stark von planerischen Vorgaben beeinflusst wird, mit denen man die Erreichung unterschiedlicher und teilweise gegenl{\"a}ufiger Ziele steuern kann. Die Komplexit{\"a}t des Systems f{\"u}hrt zum Auftreten von R{\"u}ckkoppelungseffekten, die man nicht mit Hilfe von Daumenregeln beherrschen kann. Vielmehr ist der Einsatz moderner Planungsverfahren in einer interdisziplin{\"a}ren Zusammenarbeit von politischen Entscheidungstr{\"a}gern, Verkehrsingenieuren und Mathematikern notwendig, um die aktuellen Herausforderungen in der Verkehrsplanung zu meistern. Der Artikel dokumentiert einen Beitrag zum 7. {\"O}PNV Innovationskongress des Ministeriums f{\"u}r Verkehr und Infrastruktur des Landes Baden-W{\"u}rttemberg, der vom 9.-11. M{\"a}rz 2015 in Freiburg stattfand.}, language = {de} }