90B06 Transportation, logistics
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Institute
Umsteigen ohne Warten
(2017)
Wir stellen einen mathematischen Optimierungsansatz zur Berechnung von periodischen Taktfahrplänen vor, bei dem die Umsteigezeiten unter
Berücksichtigung des Passagierverhaltens minimiert werden. Wir untersuchen damit den Einfluss wichtiger Systemparameter und Verhaltensmuster auf die Beförderungsqualität.
SAP's decision support systems for optimized supply network planning rely on mixed-integer programming as the core engine to compute optimal or near-optimal solutions. The modeling flexibility and the optimality guarantees provided by mixed-integer programming greatly aid the design of a robust and future-proof decision support system for a large and diverse customer base. In this paper we describe our coordinated efforts to ensure that the performance of the underlying solution algorithms matches the complexity of the large supply chain problems and tight time limits encountered in practice.
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.
The task of periodic timetabling is to schedule the trips in a public transport system by determining arrival and departure times at every station such that travel and transfer times are minimized. To date, the optimization literature generally assumes that passengers do not respond to changes in the timetable, i.e., the passenger routes are fixed. This is unrealistic and ignores potentially valuable degrees of freedom. We investigate in this paper periodic timetabling models with integrated passenger routing. We show that different routing models have a huge influence on the quality of the entire system: Whatever metric is applied, the performance ratios of timetables w.r.t. to 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.
Wir illustrieren anhand des Liniennetzes der Stadt Potsdam das Potenzial mathematischer Methoden der Angebotsplanung. Wir zeigen,
dass das "bestmögliche" Verkehrsangebot stark von planerischen Vorgaben beeinflusst wird, mit denen man die Erreichung unterschiedlicher und teilweise gegenläufiger Ziele steuern kann. Die Komplexität des Systems führt zum Auftreten von Rückkoppelungseffekten, die man nicht mit Hilfe von Daumenregeln beherrschen kann. Vielmehr ist der Einsatz moderner Planungsverfahren in einer interdisziplinären Zusammenarbeit von politischen Entscheidungsträgern, Verkehrsingenieuren und Mathematikern notwendig, um die aktuellen Herausforderungen in der Verkehrsplanung zu meistern. Der Artikel dokumentiert einen Beitrag zum 7. ÖPNV Innovationskongress des Ministeriums für Verkehr und Infrastruktur des Landes Baden-Württemberg, der vom 9.-11. März 2015 in Freiburg stattfand.
The task of timetabling is to schedule the trips in a public transport system by determining periodic arrival and departure times at every station. The goal is to provide a service that is both attractive for passengers and can be operated economically. To date, timetable optimization is generally done with respect to fixed passenger routes, i.e., it is assumed that passengers do not respond to changes in the timetable. This is unrealistic and ignores potentially valuable degrees of freedom. We investigate in this paper periodic timetabling models with integrated passenger routing. We propose several models that differ in the allowed passenger paths and the objectives. We compare these models theoretically and report on computations on real-world instances for the city of Wuppertal.
In this thesis we present a novel extended formulation for the line planning problem that is based on what we call "configurations" of lines and frequencies. Configurations are combinatorial building blocks of primal solutions; they rule out the "capacity numerics" and make the problem purely combinatorial. The concept of configurations can also be adapted to other capacitated network design problems.
The configuration model is strong in the sense that it implies several facet-defining inequalities for the standard model: set cover, symmetric band, multicover, and MIR inequalities. These theoretical findings can be confirmed in computations, however, the enormous number of configurations can blow up the formulation for large instances. We propose a mixed model that enriches the standard model by a judiciously chosen subset of configurations that provide a good compromise between model strength and size. Computational results for large-scale line planning problems are presented.
Mathematik im Verkehr
(2014)
Nach einem kurzen Abriss über die Bedeutung des Verkehrssektors als eine wichtige Schlüsseltechnologie im gesamten Verlauf der Menschheitsgeschichte skizzieren wir die Rolle der Mathematik für Verkehr und Transport. Wir spekulieren dann über zukünftige Entwicklungen, insbesondere im Bereich des öffentlichen Personenverkehrs, und begründen, dass die in diesem Bereich anstehenden Herausforderungen nur mit dem Einsatz mathematischer Methoden angemessen bewältigt werden können. Die demographischen Prozesse, die in verschiedenen Teilen der Welt unterschiedlich verlaufen, wie z.B. Überalterung in Europa oder dynamische Trends zu Megastädten in Entwicklungsländern, sich ändernde Lebens- und Produktionsverhältnisse, stark wachsender Bedarf nach Mobilität und enormes Anwachsen der Komplexität der Verkehrsplanung und -durchführung, machen einen verstärkten Zugriff auf mathematische Modellierung, Simulation und Optimierung notwendig. Diese Entwicklung stellt sowohl große Herausforderungen an die Mathematik, wo vielfach noch keine geeigneten Methoden vorhanden sind, als auch an die Praktiker im Bereich von Verkehr und Transport, die sich mit neuen Planungs- und Steuerungstechnologien befassen und diese effizient einsetzen müssen. Hier wird intensive Kooperation zwischen vielen beteiligten Akteuren gefragt sein.
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.
In this paper we present the problem of computing optimal tours of toll inspectors on German motorways. This problem is a special type of vehicle routing problem and builds up an integrated model, consisting of a tour
planning and a duty rostering part. The tours should guarantee a network-wide control whose intensity is proportional to given spatial and time dependent traffic distributions. We model this using a space-time network
and formulate the associated optimization problem by an integer program (IP). Since sequential approaches fail, we integrated the assignment of crews to the tours in our model. In this process all duties of a crew member must fit in a feasible roster. It is modeled as a Multi-Commodity Flow Problem in a directed acyclic graph, where specific paths correspond to
feasible rosters for one month. We present computational results in a
case-study on a German subnetwork which documents the practicability of our approach.