TUHH Open Research (TORE)https://tore.tuhh.deTORE captures, stores, indexes, preserves, and distributes digital research material.Thu, 23 Mar 2023 02:26:36 GMT2023-03-23T02:26:36Z5051Fleet based schedule optimisation for product tanker considering shipʼs stabilityhttp://hdl.handle.net/11420/3789Title: Fleet based schedule optimisation for product tanker considering shipʼs stability
Authors: Rizvanolli, Anisa; Haupt, Alexander; Müller, Peter Marvin; Dornemann, Jorin
Abstract: Purpose: Scheduling a fleet of product tankers in a cost effective and robust way to satisfy orders is a complex task. A variety of constraints and preferences complicate this attempt. Manual solutions as common in tramp shipping are not sufficient to deliver optimal and robust schedules. Methodology: For this, we present a mixed integer linear programming formulation of the scheduling problem. Additionally intact stability calculations for each ship of the fleet are implemented in a separate program that checks the feasibility of MILP solutions and creates new cuts for the integer program. Findings: Usually the checking of the stability criteria is done before an order will be accepted and the schedule of the ship is planed accordingly. This requires the selection of a ship a priori. Checking the admissibility of a voyage gives access to a wider variety of possible combinations. Originality: To our knowledge fleet scheduling under consideration of intact stability requirements has received little attention in the literature. Previous works make very simple assumptions on the capacity of the ships and do not include in their linear pro- grams any stability models.
Thu, 26 Sep 2019 00:00:00 GMThttp://hdl.handle.net/11420/37892019-09-26T00:00:00ZEnumeration of s-omino towers and row-convex k-omino towershttp://hdl.handle.net/11420/9335Title: Enumeration of s-omino towers and row-convex k-omino towers
Authors: Haupt, Alexander
Abstract: We first enumerate a generalization of domino towers that was proposed by Brown, which we call S-omino towers. We establish equations that the generating function must satisfy, and then apply the Lagrange inversion formula to find a closed formula for the number of towers. We also show a connection to generalized Dyck paths and describe an explicit bijection. Finally, we consider the set of row-convex k-omino towers, introduced by Brown, and calculate an exact generating function.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/11420/93352021-01-01T00:00:00ZCombinatorial proof of Selberg's integral formulahttp://hdl.handle.net/11420/10264Title: Combinatorial proof of Selberg's integral formula
Authors: Haupt, Alexander
Abstract: In this paper we present a combinatorial proof of Selberg's integral formula. We prove a theorem about the number of topological orderings of a certain related directed graph bijectively. Selberg's integral formula then follows by induction. This solves a problem posed by R. Stanley in 2009. Our proof is based on Anderson's analytic proof of the formula. As part of the proof we show a further generalisation of the generalised Vandermonde determinant.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/11420/102642022-01-01T00:00:00ZNew combinatorial proofs for enumeration problems and random anchored structureshttp://hdl.handle.net/11420/11138Title: New combinatorial proofs for enumeration problems and random anchored structures
Authors: Haupt, Alexander
Abstract: Wir finden einen kombinatorischen Beweis der Selbergschen Integralformel, welches eine Frage von Stanley beantwortet. Dann zählen wir S-omino-Türme bijektiv ab. Auch berechnen wir die erzeugende Funktion von reihenkonvexen k-omino-Türmen. Anschließend zählen wir Rundwege auf einem Schachbrett, die ein Turm ablaufen kann, bijektiv ab. Zuletzt beschäftigen wir uns mit einer probabilistischen Version eines kombinatorischen Problems von Freedman.; This thesis is divided into four parts. We present a combinatorial proof of Selberg's integral formula, which answers a question posed by Stanley. In the second part we enumerate S-omino towers bijectively. We also calculate the generating function of row-convex k-omino towers. In the third part we enumerate walks a rook can move along on a chess board. Finally, we study a new probabilistic version of a combinatorial problem posed by Freedman.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/11420/111382021-01-01T00:00:00ZFast strategies in waiter-client gameshttp://hdl.handle.net/11420/7720Title: Fast strategies in waiter-client games
Authors: Clemens, Dennis; Gupta, Pranshu; Hamann, Fabian; Haupt, Alexander; Mikalački, Mirjana; Mogge, Yannick
Abstract: Waiter-Client games are played on some hypergraph (X,��), where �� denotes the family of winning sets. For some bias b, during each round of such a game Waiter offers to Client b+1 elements of X, of which Client claims one for himself while the rest go to Waiter. Proceeding like this Waiter wins the game if she forces Client to claim all the elements of any winning set from ��. In this paper we study fast strategies for several Waiter-Client games played on the edge set of the complete graph, i.e. X=E(Kn), in which the winning sets are perfect matchings, Hamilton cycles, pancyclic graphs, fixed spanning trees or factors of a given graph.
Fri, 18 Sep 2020 00:00:00 GMThttp://hdl.handle.net/11420/77202020-09-18T00:00:00Z