@misc{RambauSantos, author = {Rambau, J{\"o}rg and Santos, Francisco}, title = {The Generalized Baues Problem for Cyclic Polytopes I.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3579}, number = {SC-98-14}, abstract = {The Generalized Baues Problem asks whether for a given point configuration the order complex of all its proper polyhedral subdivisions, partially ordered by refinement, is homotopy equivalent to a sphere. In this paper, an affirmative answer is given for the vertex sets of cyclic polytopes in all dimensions. This yields the first non-trivial class of point configurations with neither a bound on the dimension, the codimension, nor the number of vertice for which this is known to be true. Moreover, it is shown that all triangulations of cyclic polytopes are lifting triangulations. This contrasts the fact that in general there are many non-regular triangulations of cyclic polytopes. Beyond this, we find triangulations of \$C(11,5)\$ with flip deficiency. This proves---among other things---that there are triangulations of cyclic polytopes that are non-regular for every choice of points on the moment curve.}, language = {en} } @misc{AscheuerGroetschelKaminetal., author = {Ascheuer, Norbert and Gr{\"o}tschel, Martin and Kamin, Nicola and Rambau, J{\"o}rg}, title = {Combinatorial Online Optimization in Practice}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3508}, number = {SC-98-07}, abstract = {This paper gives a short introduction into combinatorial online optimization. It explains a few evaluation concepts of online algorithms, such as competitiveness, and discusses limitations in their application to real--world problems. The main focus, however, is a survey of combinatorial online problems coming up in practice, in particular, in large scale material flow and flexible manufacturing systems.}, language = {en} } @misc{KrumkeRambauWeider, author = {Krumke, Sven and Rambau, J{\"o}rg and Weider, Steffen}, title = {An Approximation Algorithm for the Non-Preemptive Capacitated Dial-a-Ride Problem}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6217}, number = {00-53}, abstract = {In the Capacitated Dial-a-Ride Problem (CDARP) we are given a transportation network and a finite set of transportation jobs. Each job specifies the source and target location which are both part of the network. A server which can carry at most \$C\$~objects at a time can move on the transportation network in order to process the transportation requests. The problem CDARP consists of finding a shortest transportation for the jobs starting and ending at a designated start location. In this paper we are concerned with the restriction of CDARP to graphs which are simple paths. This setting arises for instance when modelling applications in elevator transportation systems. It is known that even for this restricted class of graphs CDARP is NP-hard to solve. We provide a polynomial time approximation algorithm that finds a transportion of length at most thrice the length of the optimal transportation.}, language = {en} } @misc{KrumkeRambau, author = {Krumke, Sven and Rambau, J{\"o}rg}, title = {Online Optimierung}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6238}, number = {00-55}, abstract = {Wie soll man einen Aufzug steuern, wenn man keine Informationen {\"u}ber zuk{\"u}nftige Fahrauftr{\"a}ge besitzt? Soll man eine Bahncard kaufen, wenn die n{\"a}chsten Bahnreisen noch unbekannt sind? In der klassischen kombinatorischen Optimierung geht man davon aus, daß die Daten jeder Probleminstanz vollst{\"a}ndig gegeben sind. In vielen F{\"a}llen modelliert diese \emph{Offline-Optimierung} jedoch die Situationen aus Anwendungen nur ungen{\"u}gend. Zahlreiche Problemstellungen in der Praxis sind in nat{\"u}rlicher Weise \emph{online}: Sie erfordern Entscheidungen, die unmittelbar und ohne Wissen zuk{\"u}nftiger Ereignisse getroffen werden m{\"u}ssen. Als ein Standardmittel zur Beurteilung von Online-Algorithmen hat sich die \emph{kompetitive Analyse} durchgesetzt. Dabei vergleicht man den Zielfunktionswert einer vom Online-Algorithmus generierten L{\"o}sung mit dem Wert einer optimalen Offline-L{\"o}sung. Mit Hilfe der kompetitiven Analyse werden im Skript Algorithmen zum Caching, Netzwerk-Routing, Scheduling und zu Transportaufgaben untersucht. Auch die Schw{\"a}chen der kompetitiven Analyse werden aufgezeigt und alternative Analysekonzepte vorgestellt. Neben der theoretischen Seite werden auch die Anwendungen der Online-Optimierung in der Praxis, vor allem bei Problemen der innerbetrieblichen Logistik, beleuchtet. Bei der Steuerung automatischer Transportsysteme tritt eine F{\"u}lle von Online-Problemen auf. Hierbei werden an die Algorithmen oftmals weitere Anforderungen gestellt. So m{\"u}ssen Entscheidungen unter strikten Zeitbeschr{\"a}nkungen gef{\"a}llt werden (Echtzeit-Anforderungen). Dieses Skript ist aus dem Online-Teil der Vorlesung -Ausgew{\"a}hlte Kapitel aus der ganzzahligen Optimierung- (Wintersemester~1999/2000) und der Vorlesung -Online Optimierung- (Sommersemester~2000) an der Technischen Universit{\"a}t Berlin entstanden.}, language = {de} } @misc{AscheuerKrumkeRambau, author = {Ascheuer, Norbert and Krumke, Sven and Rambau, J{\"o}rg}, title = {The Online Transportation Problem: Competitive Scheduling of Elevators}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3779}, number = {SC-98-34}, abstract = {In this paper we consider the following online transportation problem (\textsc{Oltp}): Objects are to be transported between the vertices of a given graph. Transportation requests arrive online, specifying the objects to be transported and the corresponding source and target vertex. These requests are to be handled by a server which commences its work at a designated origin vertex and which picks up and drops objects at their starts and destinations. After the end of its service the server returns to its start. The goal of \textsc{Oltp} is to come up with a transportation schedule for the server which finishes as early as possible. We first show a lower bound of~\$5/3\$ for the competitive ratio of any deterministic algorithm. We then analyze two simple and natural strategies which we call \textsf{REPLAN} and \textsf{IGNORE}. \textsf{REPLAN} completely discards its schedule and recomputes a new one when a new request arrives. \textsf{IGNORE} always runs a (locally optimal) schedule for a set of known requests and ignores all new requests until this schedule is completed. We show that both strategies, \textsf{REPLAN} and \textsf{IGNORE}, are \$5/2\$-competitive. We also present a somewhat less natural strategy \textsf{SLEEP}, which in contrast to the other two strategies may leave the server idle from time to time although unserved requests are known. We also establish a competitive ratio of~\$5/2\$ for the algorithm \textsf{SLEEP}. Our results are extended to the case of ``open schedules'' where the server is not required to return to its start position at the end of its service.}, language = {en} } @misc{KrumkeRambau, author = {Krumke, Sven and Rambau, J{\"o}rg}, title = {Probieren geht {\"u}ber Studieren? Entscheidungshilfen f{\"u}r kombinatorische Online-Optimierungsprobleme in der innerbetrieblichen Logistik}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6723}, number = {02-05}, abstract = {Die Automatisierung von innerbetrieblicher Logistik erfordert -- {\"u}ber die physikalische Steuerung von Ger{\"a}ten hinaus -- auch eine effiziente Organisation der Transporte: ein Aufgabenfeld der kombinatorischen Optimierung. Dieser Artikel illustriert anhand von konkreten Aufgabenstellungen die Online-Problematik (unvollst{\"a}ndiges Wissen) sowie die Echtzeit-Problematik (beschr{\"a}nkte Rechenzeit), auf die man in der innerbetrieblichen Logistik trifft. Der Text gibt einen {\"U}berblick {\"u}ber allgemeine Konstruktionsprinzipien f{\"u}r Online-Algorithmen und Bewertungsmethoden, die bei der Entscheidung helfen, welche Algorithmen f{\"u}r eine vorliegende Problemstellung geeignet sind.}, language = {de} } @misc{HeinzKaibelPeinhardtetal., author = {Heinz, Stefan and Kaibel, Volker and Peinhardt, Matthias and Rambau, J{\"o}rg and Tuchscherer, Andreas}, title = {LP-Based Local Approximation for Markov Decision Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9131}, number = {06-20}, abstract = {The standard computational methods for computing the optimal value functions of Markov Decision Problems (MDP) require the exploration of the entire state space. This is practically infeasible for applications with huge numbers of states as they arise, e.\,g., from modeling the decisions in online optimization problems by MDPs. Exploiting column generation techniques, we propose and apply an LP-based method to determine an \$\varepsilon\$-approximation of the optimal value function at a given state by inspecting only states in a small neighborhood. In the context of online optimization problems, we use these methods in order to evaluate the quality of concrete policies with respect to given initial states. Moreover, the tools can also be used to obtain evidence of the impact of single decisions. This way, they can be utilized in the design of policies.}, language = {en} } @misc{HauptmeierKrumkeRambau, author = {Hauptmeier, Dietrich and Krumke, Sven and Rambau, J{\"o}rg}, title = {The Online Dial-a-Ride Problem under Reasonable Load}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3961}, number = {SC-99-08}, abstract = {In this paper, we analyze algorithms for the online dial-a-ride problem with request sets that fulfill a certain worst-case restriction: roughly speaking, a set of requests for the online dial-a-ride problem is reasonable if the requests that come up in a sufficiently large time period can be served in a time period of at most the same length. This new notion is a stability criterion implying that the system is not overloaded. The new concept is used to analyze the online dial-a-ride problem for the minimization of the maximal resp.\ average flow time. Under reasonable load it is possible to distinguish the performance of two particular algorithms for this problem, which seems to be impossible by means of classical competitive analysis.}, language = {en} } @misc{GroetschelHauptmeierKrumkeetal., author = {Gr{\"o}tschel, Martin and Hauptmeier, Dietrich and Krumke, Sven and Rambau, J{\"o}rg}, title = {Simulation Studies for the Online-Dial-a-Ride Problem}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3976}, number = {SC-99-09}, abstract = {In a large distribution center of Herlitz AG, Berlin, we invesigated the elevator subsystem of the fully automated pallet transportation system. Each elevator may carry one pallet and has to serve eight levels. The goal is to minimize the average resp.\ the maximum flow time. The variants of this elevator control problem have been subject of recent theoretical research and are known as online-dial-a-ride problems. In this paper we investigate several online algorithms for several versions of online-dial-a-ride problems by means of a simulation program, developed on the basis of the simulation library AMSEL. We draw statistics from samples of randomly generated data providing for different load situations. Moreover, we provide preliminary studies with real production data for a system of five elevators connected by a conveyor circuit, as can be found at the Herlitz plant. We show which algorithms are best under certain load situations and which lead to break downs under particular circumstances.}, language = {en} }