TY - GEN A1 - Ascheuer, Norbert A1 - Grötschel, Martin A1 - Kamin, Nicola A1 - Rambau, Jörg T1 - Combinatorial Online Optimization in Practice N2 - 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. T3 - ZIB-Report - SC-98-07 KW - Online optimization KW - combinatorial optimization KW - real-world problems Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3508 ER - TY - GEN A1 - Ascheuer, Norbert A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg T1 - Combinatorial Online Optimization N2 - In ``classical'' optimization, all data of a problem instance are considered given. The standard theory and the usual algorithmic techniques apply to such cases only. Online optimization is different. Many decisions have to be made before all data are available. In addition, decisions once made cannot be changed. How should one act ``best'' in such an environment? In this paper we survey online problems coming up in combinatorial optimization. We first outline theoretical concepts, such as competitiveness against various adversaries, to analyze online problems and algorithms. The focus, however, lies on real-world applications. We report, in particular, on theoretical investigations and our practical experience with problems arising in transportation and the automatic handling of material. T3 - ZIB-Report - SC-98-24 KW - Online Optimization KW - competitiveness KW - combinatorial optimization KW - real-world problems Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3674 ER - TY - GEN A1 - Ascheuer, Norbert A1 - Krumke, Sven A1 - Rambau, Jörg T1 - The Online Transportation Problem: Competitive Scheduling of Elevators N2 - 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. T3 - ZIB-Report - SC-98-34 KW - online optimization KW - competitive analysis KW - elevator Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3779 ER - TY - GEN A1 - Athanasiadis, Christos A. A1 - Rambau, Jörg A1 - Santos, Francisco T1 - The Generalized Baues Problem for Cyclic Polytopes II N2 - Given an affine surjection of polytopes $\pi: P \to Q$, the Generalized Baues Problem asks whether the poset of all proper polyhedral subdivisions of $Q$ which are induced by the map $\pi$ has the homotopy type of a sphere. We extend earlier work of the last two authors on subdivisions of cyclic polytopes to give an affirmative answer to the problem for the natural surjections between cyclic polytopes $\pi: C(n,d') \to C(n,d)$ for all $1 \leq d < d' < n$. T3 - ZIB-Report - SC-98-43 KW - Generalized Baues Problem KW - Polyhedral Subdivisions KW - Induced Subdivisions KW - Poset KW - Spherical KW - Cyclic Polytopes KW - Bistellar Operations Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3862 ER - TY - GEN A1 - Friese, Philipp A1 - Rambau, Jörg T1 - Online-Optimization of Multi-Elevator Transport Systems with Reoptimization Algorithms based on Set-Partitioning Models N2 - We develop and experimentally compare policies for the control of a system of $k$ elevators with capacity one in a transport environment with $\ell$ floors, an idealized version of a pallet elevator system in a large distribution center of the Herlitz PBS AG in Falkensee. Each elevator in the idealized system has an individual waiting queue of infinite capacity. On each floor, requests arrive over time in global waiting queues of infinite capacity. The goal is to find a policy that, without any knowledge about future requests, assigns an elevator to each req uest and a schedule to each elevator so that certain expected cost functions (e.g., the average or the maximal flow times) are minimized. We show that a reoptimization policy for minimizing average sq uared waiting times can be implemented to run in real-time ($1\,s$) using dynamic column generation. Moreover, in discrete event simulations with Poisson input it outperforms other commonly used polic ies like multi-server variants of greedy and nearest neighbor. T3 - ZIB-Report - 05-03 KW - elevator group control KW - policy KW - reoptimization KW - online KW - real-time KW - simulation Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8373 ER - TY - GEN A1 - Grötschel, Martin A1 - Hauptmeier, Dietrich A1 - Krumke, Sven A1 - Rambau, Jörg T1 - Simulation Studies for the Online-Dial-a-Ride Problem N2 - 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. T3 - ZIB-Report - SC-99-09 KW - online optimization KW - competitive analysis KW - elevator KW - simulation studies Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3976 ER - TY - GEN A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg T1 - Online Optimization of Complex Transportation Systems N2 - This paper discusses online optimization of real-world transportation systems. We concentrate on transportation problems arising in production and manufacturing processes, in particular in company internal logistics. We describe basic techniques to design online optimization algorithms for such systems, but our main focus is decision support for the planner: which online algorithm is the most appropriate one in a particular setting? We show by means of several examples that traditional methods for the evaluation of online algorithms often do not suffice to judge the strengths and weaknesses of online algorithms. We present modifications of well-known evaluation techniques and some new methods, and we argue that the selection of an online algorithm to be employed in practice should be based on a sound combination of several theoretical and practical evaluation criteria, including simulation. T3 - ZIB-Report - 01-17 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6438 ER - TY - GEN A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg T1 - Wo bleibt der Aufzug? N2 - Dieser Artikel gibt eine allgemeinverständliche Einführung in die spezielle Problematik kombinatorischer Online-Problem am Beispiel der Fahrstuhlsteuerung. T3 - ZIB-Report - SC-99-29 KW - Aufzugsteuerung KW - Online-Optimierung KW - Echtzeit-Optimierung KW - kompetitive Analyse Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4175 ER - TY - GEN A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg A1 - Torres, Luis Miguel T1 - Making the Yellow Angels Fly: Online Dispatching Of Service Vehicles in Real Time N2 - Combinatorial online optimization is an area with lots of applications and potential for significant progress, both in theory and practice. In this short note we sketch the ADACproblem, a typical large-scale online optimization problem, discuss some theoretical and pratical issues coming up, and explain, very briefly, how we approach this problem mathematically. Online problems are a battlefield of heuristics with many strong claims about their solution quality. We indicate that a stronger problem orientation and the use of a little more mathematics may yield. T3 - ZIB-Report - 02-18 KW - vehicle dispatching KW - soft time windows KW - real-time KW - column generation KW - pricing KW - branch and bound KW - real world data KW - ADAC Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6858 ER - TY - GEN A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg A1 - Winter, Thomas A1 - Zimmermann, Uwe T1 - Combinatorial Online Optimization in Real Time N2 - Optimization is the task of finding an optimum solution to a given problem. When the decision variables are discrete we speak of a combinatorial optimization problem. Such a problem is online when decisions have to be made before all data of the problem are known. And we speak of a real-time online problem when online decisions have to be computed within very tight time bounds. This paper surveys the are of combinatorial online and real-time optimization, it discusses, in particular, the concepts with which online and real-time algorithms can be analyzed. T3 - ZIB-Report - 01-16 KW - Online Optimization KW - Realtime Optimization KW - Competitive Analysis KW - Heuristics KW - Survey Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6424 ER - TY - GEN A1 - Hauptmeier, Dietrich A1 - Krumke, Sven A1 - Rambau, Jörg T1 - The Online Dial-a-Ride Problem under Reasonable Load N2 - 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. T3 - ZIB-Report - SC-99-08 KW - online optimization KW - competitive analysis KW - elevator Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3961 ER - TY - GEN A1 - Hauptmeier, Dietrich A1 - Krumke, Sven A1 - Rambau, Jörg A1 - Wirth., Hans-Christoph T1 - Euler is Standing in Line N2 - In this paper we study algorithms for ``Dial-a-Ride'' transportation problems. In the basic version of the problem we are given transportation jobs between the vertices of a graph and the goal is to find a shortest transportation that serves all the jobs. This problem is known to be NP-hard even on trees. We consider the extension when precedence relations between the jobs with the same source are given. Our results include a polynomial time algorithm on paths and an approximation algorithm on general graphs with a performance of~$9/4$. For trees we improve the performance to~$5/3$. T3 - ZIB-Report - SC-99-06 KW - NP-completeness KW - polynomial-time approximation algorithms KW - stacker-crane problem KW - vehicle routing KW - elevator system KW - Eulerian Cycle Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3947 ER - TY - GEN A1 - Heinz, Stefan A1 - Kaibel, Volker A1 - Peinhardt, Matthias A1 - Rambau, Jörg A1 - Tuchscherer, Andreas T1 - LP-Based Local Approximation for Markov Decision Problems N2 - 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. T3 - ZIB-Report - 06-20 KW - Markov decision problem KW - linear programming KW - column generation Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9131 ER - TY - GEN A1 - Heinz, Stefan A1 - Krumke, Sven A1 - Megow, Nicole A1 - Rambau, Jörg A1 - Tuchscherer, Andreas A1 - Vredeveld, Tjark T1 - The Online Target Date Assignment Problem N2 - Many online problems encountered in real-life involve a two-stage decision process: upon arrival of a new request, an irrevocable first-stage decision (the assignment of a specific resource to the request) must be made immediately, while in a second stage process, certain ``subinstances'' (that is, the instances of all requests assigned to a particular resource) can be solved to optimality (offline) later. We introduce the novel concept of an \emph{Online Target Date Assignment Problem} (\textsc{OnlineTDAP}) as a general framework for online problems with this nature. Requests for the \textsc{OnlineTDAP} become known at certain dates. An online algorithm has to assign a target date to each request, specifying on which date the request should be processed (e.\,g., an appointment with a customer for a washing machine repair). The cost at a target date is given by the \emph{downstream cost}, the optimal cost of processing all requests at that date w.\,r.\,t.\ some fixed downstream offline optimization problem (e.\,g., the cost of an optimal dispatch for service technicians). We provide general competitive algorithms for the \textsc{OnlineTDAP} independently of the particular downstream problem, when the overall objective is to minimize either the sum or the maximum of all downstream costs. As the first basic examples, we analyze the competitive ratios of our algorithms for the par ticular academic downstream problems of bin-packing, nonpreemptive scheduling on identical parallel machines, and routing a traveling salesman. T3 - ZIB-Report - 05-61 KW - Online Algorithms KW - Online Target Date Assignment Problem Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8945 ER - TY - GEN A1 - Hiller, Benjamin A1 - Krumke, Sven A1 - Rambau, Jörg T1 - Reoptimization Gaps versus Model Errors in Online-Dispatching of Service Units for ADAC N2 - Under high load, the automated dispatching of service vehicles for the German Automobile Association (ADAC) must reoptimize a dispatch for 100--150 vehicles and 400 requests in about ten seconds to near optimality. In the presence of service contractors, this can be achieved by the column generation algorithm ZIBDIP. In metropolitan areas, however, service contractors cannot be dispatched automatically because they may decline. The problem: a model without contractors yields larger optimality gaps within ten seconds. One way-out are simplified reoptimization models. These compute a short-term dispatch containing only some of the requests: unknown future requests will influence future service anyway. The simpler the models the better the gaps, but also the larger the model error. What is more significant: reoptimization gap or reoptimization model error? We answer this question in simulations on real-world ADAC data: only the new model ZIBDIP{\footnotesize dummy} can keep up with ZIBDIP. T3 - ZIB-Report - 04-17 KW - vehicle dispatching KW - soft time windows KW - online KW - real-time KW - ADAC KW - optimality gap KW - high load Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7928 ER - TY - GEN A1 - Huber, Birkett A1 - Rambau, Jörg A1 - Santos, Francisco T1 - The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings N2 - In 1994, Sturmfels gave a polyhedral version of the Cayley Trick of elimination theory: he established an order-preserving bijection between the posets of \emph{coherent} mixed subdivisions of a Minkowski sum $\mathcal{A}_1+\cdots+\mathcal{A}_r$ of point configurations and of \emph{coherent} polyhedral subdivisions of the associated Cayley embedding $\mathcal{C}(\mathcal{A}_1,\dots,\mathcal{A}_r)$. In this paper we extend this correspondence in a natural way to cover also \emph{non-coherent} subdivisions. As an application, we show that the Cayley Trick combined with results of Santos on subdivisions of Lawrence polytopes provides a new independent proof of the Bohne-Dress Theorem on zonotopal tilings. This application uses a combinatorial characterization of lifting subdivisions, also originally proved by Santos. T3 - ZIB-Report - SC-98-44 KW - Polyhedral subdivision KW - fiber polytope KW - mixed subdivision KW - lifting subdivision KW - Minkowski sum KW - Cayley Trick KW - Bohne-Dress Theorem Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3874 ER - TY - GEN A1 - Hülsermann, Ralf A1 - Jäger, Monika A1 - Krumke, Sven A1 - Poensgen, Diana A1 - Rambau, Jörg A1 - Tuchscherer, Andreas T1 - Dynamic Routing Algorithms in Transparent Optical Networks An Experimental Study Based on Real Data N2 - Today's telecommunication networks are configured statically. Whenever a connection is established, the customer has permanent access to it. However, it is observed that usually the connection is not used continuously. At this point, dynamic provisioning could increase the utilization of network resources. WDM based Optical Transport Networks (OTNs) will shortly allow for fast dynamic network reconfiguration. This enables optical broadband leased line services on demand. Since service requests competing for network resources may lead to service blocking, it is vital to use appropriate strategies for routing and wavelength assignment in transparent optical networks. We simulate the service blocking probabilities of various dynamic algorithms for this problem using a well-founded traffic model for two realistic networks. One of the algorithms using shortest path routings performs best on all instances. Surprisingly, the tie-breaking rule between equally short paths in different wavelengths decides between success or failure. T3 - ZIB-Report - 02-35 KW - Dynamic Network Configuration KW - Routing and Wavelength Allocation KW - Transparent Optical Networks KW - Blocking Probability KW - Simulation Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7025 ER - TY - GEN A1 - Krumke, Sven A1 - Lipmann, Maarten A1 - Paepe, Willem de A1 - Poensgen, Diana A1 - Rambau, Jörg A1 - Stougie, Leen A1 - Woeginger, Gerhard T1 - How to Cut a Cake Almost Fairly N2 - In the cake cutting problem, $n\ge2$ players want to cut a cake into $n$ pieces so that every player gets a ``fair'' share of the cake by his own measure. We describe a protocol with $n-1$~cuts in which each player can enforce to get a share of at least~$1/(2n-2)$. Moreover we show that no protocol with $n-1$~cuts can guarantee a better fraction. T3 - ZIB-Report - 02-23 KW - Fair division KW - cake cutting Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6905 ER - TY - GEN A1 - Krumke, Sven A1 - Paepe, Willem de A1 - Rambau, Jörg A1 - Stougie, Leen T1 - Online Bin-Coloring N2 - We introduce a new problem that was motivated by a (more complicated) problem arising in a robotized assembly enviroment. The bin coloring problem is to pack unit size colored items into bins, such that the maximum number of different colors per bin is minimized. Each bin has size~$B\in\mathbb{N}$. The packing process is subject to the constraint that at any moment in time at most $q\in\mathbb{N}$ bins may be partially filled. Moreover, bins may only be closed if they are filled completely. An online algorithm must pack each item must be packed without knowledge of any future items. We investigate the existence of competitive online algorithms for the online uniform binpacking problem. We show upper bounds for the bin coloring problem. We prove an upper bound of $3q$ - 1 and a lower bound of $2q$ for the competitive ratio of a natural greedy-type algorithm, and show that surprisingly a trivial algorithm which uses only one open bin has a strictly better competitive ratio of $2q$ - 1. Morever, we show that any deterministic algorithm has a competitive ratio $\Omega (q)$ and that randomization does not improve this lower bound even when the adversary is oblivious. T3 - ZIB-Report - 01-07 KW - Online Optimization KW - randomized algorithms KW - lower bounds KW - competitive analysis Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6338 ER - TY - GEN A1 - Krumke, Sven A1 - Rambau, Jörg T1 - Online Optimierung N2 - Wie soll man einen Aufzug steuern, wenn man keine Informationen über zukünftige Fahraufträge besitzt? Soll man eine Bahncard kaufen, wenn die nächsten Bahnreisen noch unbekannt sind? In der klassischen kombinatorischen Optimierung geht man davon aus, daß die Daten jeder Probleminstanz vollständig gegeben sind. In vielen Fällen modelliert diese \emph{Offline-Optimierung} jedoch die Situationen aus Anwendungen nur ungenügend. Zahlreiche Problemstellungen in der Praxis sind in natürlicher Weise \emph{online}: Sie erfordern Entscheidungen, die unmittelbar und ohne Wissen zukünftiger Ereignisse getroffen werden müssen. 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 Lösung mit dem Wert einer optimalen Offline-Lösung. Mit Hilfe der kompetitiven Analyse werden im Skript Algorithmen zum Caching, Netzwerk-Routing, Scheduling und zu Transportaufgaben untersucht. Auch die Schwächen 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 Fülle von Online-Problemen auf. Hierbei werden an die Algorithmen oftmals weitere Anforderungen gestellt. So müssen Entscheidungen unter strikten Zeitbeschränkungen gefällt werden (Echtzeit-Anforderungen). Dieses Skript ist aus dem Online-Teil der Vorlesung -Ausgewählte Kapitel aus der ganzzahligen Optimierung- (Wintersemester~1999/2000) und der Vorlesung -Online Optimierung- (Sommersemester~2000) an der Technischen Universität Berlin entstanden. T3 - ZIB-Report - 00-55 KW - Kompetitive Analyse KW - Online Optimierung KW - Online Algorithmen Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6238 ER -