Catálogo de publicaciones - libros

At an airport, a large number of activities required for serving an aircraft while on the ground have to be scheduled. These activities include, for example, passenger and flight crew transportation, check-in and boarding services, various technical services, loading and unloading of cargo and baggage, or catering and cleaning services. With the steady increase of civil air traffic and the corresponding growth of airports over the past decades, the complexity of the task has increased significantly.

Seit dem inzwischen schon legendär gewordenen Ausspruch von Henry Ford „Any customer can have a car painted any colour that he wants so long as it is black.“ hat ein fundamentaler Wandel bezüglich der Anforderungen an Produktionssysteme stattgefunden. So bietet heute etwa Daimler-Chrysler seine Mercedes C-Klasse aufgrund einer Vielzahl an vom Kunden individuell auswählbarer Optionen in 2^27 theoretisch möglichen Varianten an [10]. Nichtsdestoweniger kann trotz dieser enormen Variantenvielfalt mittels Universalmaschinen mit automatisiertem Werkzeugwechsel und flexibel ausgebildeter Werker die effiziente Produktionsform der Fließfertigung aufrechterhalten werden. Eine solche Organisationsform der Fließfertigung, die eine Vielzahl an Varianten eines einheitlichen Grundmodells in wahlfreier Fertigungsfolge (Losgröße Eins) produzieren, bezeichnet man als Variantenfließfertigung. Man findet sie nicht nur bei der Endmontage von Autos und verwandten Produkten wie Bussen und sonstigen Nutzfahrzeugen, sondern auch in weiten Teilen der Elektroindustrie. Als Tribut an die gestiegene Variantenvielfalt muss jedoch eine größere Komplexität der Produktionsplanung in Kauf genommen werden. War es in den traditionellen Ein-Produkt-Fließsystemen mehr oder minder ausreichend eine einmalige Fließbandabstimmung bei der Installation des Fließsystems vorzunehmen, so treten bei einer Variantenfließfertigung gänzlich neue Planungsprobleme auf, deren hierarchisches Zusammenspiel in Abbildung 1 dargestellt ist [5].

Traffic peaks are peaks in cost. This in particular holds for rural counties, where the organization of public mass transportation is focused on the demand of pupils. About half to two third of pupils in rural areas take a bus to get to school. Most of them are integrated in the public bus system, a minority is transfered by special purpose school buses. In all cases the respective county in which the pupils live is responsible for the transfer, meaning that the county administration pays the fees. Since tax money is a scarce resource, the administration has great interest in reducing these payments.

Quantitative Ansätze zum Bestandsmanagement im Rahmen der Kreislauflogistik fokussieren hauptsächlich auf Losgrößen- und Sicherheitsbestände. Aufgrund der dabei genutzten statischen Modellannahmen sind sie kaum in der Lage, die häufig in der Praxis vorzufindenden hohen Bestände insbesondere an Altprodukten zu erklären. Eine explizite Berücksichtigung dynamischer Einflüsse, wie sie beispielsweise Saisonalitäten, Produktlebenszyklen oder auch die Kostendynamik darstellen, führt zu neuen Motiven für die Lagerhaltung. Aufgabe der Dissertation [5] war es, solche Motivationen zu identifizieren. Dabei wurde auf eine zeitstetige Modellierung zurückgegriffen. Als Lösungsmethodik wurde Pontryagins Maximumprinzip genutzt, mit welchem generelle Struktureigenschaften optimaler Lösungen für ganze Problemklassen ermittelt werden können. Dieser Artikel gibt einen Überblick über wesentliche Resultate der Dissertation.

„The timetable is the essence of the service offered by any provider of public transport.“ (Jonothan Tyler, CASPT 2006)

We treat a simplified model of a Simulated Moving Bed (SMB) chromatographic separation process that contains time-dependent discrete decisions. SMB processes have been gaining increased attention lately, see [3], [4] for further references. The related optimization problems are challenging from a mathematical point of view, as they combine periodic nonlinear optimal control problems in partial differential equations (PDE) with time-dependent discrete decisions. For this problem class of mixed-integer optimal control problems (MIOCP) a novel numerical method, developed in [5], is applied.

Game theory in general and the concept of Nash equilibrium in particular have lately come under increased scrutiny by theoretical computer scientists. Computing a mixed Nash equilibrium is a case in point. For many years, one of the most important open problems was the complexity of computing a mixed Nash equilibrium in games with only two players. Only recently was it solved by a sequence of significant papers (Goldberg and Papadimitriou (2006), Daskalakis et.al. (2006), Chen and Deng (2005), Daskalakis and Papadimitriou (2005), and Chen and Deng (2006)).

The optimization of traffic flow in congested urban road networks faces a well-known dilemma: Optimizing system performance is unfair with respect to the individual drivers’ travel times; and a fair user equilibrium may result in bad system performance. As a remedy, computing a system optimum with fairness conditions, realized by length constraints on the routes actually used by drivers, has been suggested in [5]. This poses interesting mathematical challenges, namely the nonlinearity of the objective function and the necessity to deal with path constraints in large networks. While the authors present results suggesting that solutions to this constrained system optimum problem (CSO) are indeed equally good and fair, they rely on a standard Frank-Wolfe/Partan-algorithm to obtain them. In this paper, we present a Lagrangian relaxation of the CSO problem for which the Lagrangian dual function can be evaluated by a decomposition into constrained shortest path problems which we solve exactly employing state-of-the-art acceleration techniques. The Lagrangian dual problem is then solved by a special cutting plane method. Finally, we obtain test results which suggest that this approach outperforms previously described solution schemes for the CSO problem.

In this paper we investigate the fare planning model for public transport, which consists in designing a system of fares maximizing the revenue. We discuss a discrete choice model in which passengers choose between different travel alternatives to express the demand as a function of fares. Furthermore, we give a computational example for the city of Potsdam and discuss some theoretical aspects.

We will briefly survey the state of the art of the Robust Optimization (RO) methodology for solving convex conic optimization problems, both static and dynamic (multi-stage) emphasizing issues of computational tractability, and probabilistic guarantees satisfied by the optimal robust solution. We then introduce a recent extension of the methodology in which the solution is required to exhibit a controlled deterioration in the performance for uncertain data outside the nominal uncertainty set. Finally we discuss uncertainly affected linear control systems and introduce a novel reparameterization scheme that converts the, otherwise nonconvex, control problem into a convex programming one.