We introduce, discuss, and solve a hard practical optimization problem which we call the ship traffic control problem (STCP). Since we plan bi-directional traffic, STCP relates to, and in fact generalizes train timetabling on single-track networks. The objective of finding quickest routes motivates the integration of recent algorithmic ideas from dynamic collision-free routing of automated guided vehicles. We offer a unified view of routing and scheduling which blends simultaneous (global) and sequential (local) solution approaches to allot scarce network resources to a fleet of vehicles in a collision-free manner. This leads us to construct a fast online heuristic. The STCP originates from the Kiel Canal which is the basis for the trade between the countries of the baltic area and the rest of the world. As traffic is projected to significantly increase, the canal is planned to be enlarged in a billion Euro project. Our work forms the mathematical and algorithmic basis for a tool to evaluate the different enlargement options. In view of computational experiments on real traffic data expert planners approved that our combinatorial algorithm is well-suited for this decision support. With the help of instance-dependent lower bounds we assess the quality of our solutions which significantly improves upon manual plans. We are confident that our ideas can be extended to other application areas like train timetabling and collision-free routing, also in more general networks.

We study the fundamental problem of scheduling bidirectional traffic along a path composed of multiple segments. The main feature of the problem is that jobs traveling in the same direction can be scheduled in quick succession on a segment, while jobs in opposing directions cannot cross a segment at the same time. We show that this tradeoff makes the problem significantly harder than the related flow shop problem, by proving that it is NP-hard even for identical jobs. We complement this result with a PTAS for a single segment and non-identical jobs. If we allow some pairs of jobs traveling in different directions to cross a segment concurrently, the problem becomes APX-hard even on a single segment and with identical jobs. We give polynomial algorithms for the setting with restricted compatibilities between jobs on a single and any constant number of segments, respectively. * This research was carried out in the framework of Matheon supported by Einstein Foundation Berlin.

Die vorliegende Dissertation liefert theoretische und praktische Erkenntnisse im Zusammenhang mit der Planung von bidirektionalem Verkehr entlang einer Strecke mit Engpassstellen. Auf diesen du ¨rfen sich entgegengesetzte Fahrzeuge nicht begegnen. Eingleisige Streckenabschnitte im Schienenverkehr stellen beispielsweise solche Engpässe dar. Konkret setzt sich die Arbeit mit der Verkehrsflussoptimierung des Schiffsverkehrs auf dem Nord-Ostsee-Kanal (NOK) auseinander. Dieser verbindet Nord-und Ostsee und wird in beiden Richtungen befahren. Sind zwei entgegengesetzte Schiffe zu groß, ist ausschließlich eine Begegnung in den dafu ¨r vorgesehenen Weichen erlaubt. Die Arbeit legt Ihren Fokus auf zwei charakteristische Eigenschaften dieser Verkehrsflussoptimierung. Der erste Fokus liegt auf der bidirektionalen Komponente: Schiffe in gleicher Richtung können einen Abschnitt mit kurzem Zeitabstand hintereinander befahren, während Schiffe in entgegengesetzter Richtung lange warten mu ¨ssen, bis der Abschnitt wieder verlassen wurde. Zweitens melden sich Schiffe zur Durchfahrt recht kurzfristig an, d. h. der Plan muss online angepasst werden. Um ein Verständnis fu ¨r den bidirektionalen Charakter zu erlangen, wird das kompakte Modell des Bidirektionalen Scheduling entwickelt, welches verwandt zu klassischem Scheduling auf Maschinen ist. Im Offline-Fall werden Eigenschaften identifiziert, welche die Komplexität des bidirektionalen Scheduling im Vergleich zu klassischem Maschinen Scheduling erhöhen. Mittels Kompetetivitätsanalyse werden daraufhin Einsichten

No abstract

We propose a new approach to competitive analysis in online scheduling by introducing the novel concept of competitive-ratio approximation schemes. Such a scheme algorithmically constructs an online algorithm with a competitive ratio arbitrarily close to the best possible competitive ratio for any online algorithm. We study the problem of scheduling jobs online to minimize the weighted sum of completion times on parallel, related, and unrelated machines, and we derive both deterministic and randomized algorithms that are almost best possible among all online algorithms of the respective settings. We also generalize our techniques to arbitrary monomial cost functions and apply them to the makespan objective. Our method relies on an abstract characterization of online algorithms combined with various simplifications and transformations. We also contribute algorithmic means to compute the actual value of the best possible competitive ratio up to an arbitrary accuracy. This strongly contrasts with nearly all previous manually obtained competitiveness results, and, most importantly, it reduces the search for the optimal competitive ratio to a question that a computer can answer. We believe that our concept can also be applied to many other problems and yields a new perspective on online algorithms in general.