TY - GEN A1 - Hiller, Benjamin A1 - Krumke, Sven A1 - Saliba, Sleman A1 - Tuchscherer, Andreas T1 - Randomized Online Algorithms for Dynamic Multi-Period Routing Problems N2 - The Dynamic Multi-Period Routing Problem DMPRP introduced by Angelelli et al. gives a model for a two-stage online-offline routing problem. At the beginning of each time period a set of customers becomes known. The customers need to be served either in the current time period or in the following. Postponed customers have to be served in the next time period. The decision whether to postpone a customer has to be done online. At the end of each time period, an optimal tour for the customers assigned to this period has to be computed and this computation can be done offline. The objective of the problem is to minimize the distance traveled over all planning periods assuming optimal routes for the customers selected in each period. We provide the first randomized online algorithms for the DMPRP which beat the known lower bounds for deterministic algorithms. For the special case of two planning periods we provide lower bounds on the competitive ratio of any randomized online algorithm against the oblivious adversary. We identify a randomized algorithm that achieves the optimal competitive ratio of $\frac{1+\sqrt{2}}{2}$ for two time periods on the real line. For three time periods, we give a randomized algorithm that is strictly better than any deterministic algorithm. T3 - ZIB-Report - 09-03 KW - Online-Optimierung KW - Randomisierte Algorithmen KW - Zweistufiges Problem KW - Traveling-Salesman-Problem KW - online optimization KW - randomized algorithm KW - two-stage problem KW - traveling salesman problem Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11132 SN - 1438-0064 ER - TY - GEN A1 - Achterberg, Tobias A1 - Koch, Thorsten A1 - Tuchscherer, Andreas T1 - On the Effects of Minor Changes in Model Formulations N2 - Starting with the description of the Traveling Salesmen Problem formulation as given by van Vyve and Wolsey in the article Approximate extended formulations'', we investigate the effects of small variations onto the performance of contemporary mixed integer programming solvers. We will show that even minor changes in the formulation of the model can result in performance difference of more than a factor of 1000. As the results show it is not obvious which changes will result in performance improvements and which not. T3 - ZIB-Report - 08-29 Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10808 SN - 1438-0064 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 - Abdel-Hamid, Atef Abdel-Aziz A1 - Borndörfer, Ralf T1 - On the Complexity of Storage Assignment Problems. N2 - {\def\NP{\hbox{$\cal N\kern-.1667em\cal P$}} The {\sl storage assignment problem} asks for the cost minimal assignment of containers with different sizes to storage locations with different capacities. Such problems arise, for instance, in the optimal control of automatic storage devices in flexible manufacturing systems. This problem is known to be $\NP$-hard in the strong sense. We show that the storage assignment problem is $\NP$-hard for {\sl bounded sizes and capacities}, even if the sizes have values $1$ and~$2$ and the capacities value~$2$ only, a case we encountered in practice. Moreover, we prove that no polynomial time $\epsilon$-approximation algorithm exists. This means that almost all storage assignment problems arising in practice are indeed hard.} T3 - ZIB-Report - SC-94-14 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1430 ER - TY - GEN A1 - Grötschel, Martin A1 - Hiller, Benjamin A1 - Tuchscherer, Andreas T1 - Combinatorial Online Optimization: Elevators & Yellow Angels N2 - In \emph{classical optimization} it is assumed that full information about the problem to be solved is given. This, in particular, includes that all data are at hand. The real world may not be so nice'' to optimizers. Some problem constraints may not be known, the data may be corrupted, or some data may not be available at the moments when decisions have to be made. The last issue is the subject of \emph{online optimization} which will be addressed here. We explain some theory that has been developed to cope with such situations and provide examples from practice where unavailable information is not the result of bad data handling but an inevitable phenomenon. T3 - ZIB-Report - 07-36 KW - Online-Optimierung KW - Aufzugssteuerung KW - Dispatching von Fahrzeugen KW - online optimization KW - elevator control KW - vehicle dispatching Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10360 SN - 1438-0064 ER - TY - GEN A1 - Hiller, Benjamin A1 - Vredeveld, Tjark T1 - Stochastic dominance analysis of Online Bin Coloring algorithms N2 - This paper proposes a new method for probabilistic analysis of online algorithms. It is based on the notion of stochastic dominance. We develop the method for the online bin coloring problem introduced by Krumke et al (2008). Using methods for the stochastic comparison of Markov chains we establish the result that the performance of the online algorithm GreedyFit is stochastically better than the performance of the algorithm OneBin for any number of items processed. This result gives a more realistic picture than competitive analysis and explains the behavior observed in simulations. T3 - ZIB-Report - 12-42 KW - online algorithms, stochastic dominance, algorithm analysis, Markov chains Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16502 SN - 1438-0064 ER - TY - JOUR A1 - Grötschel, Martin A1 - Hinrichs, Hinrich A1 - Schröer, Klaus A1 - Tuchscherer, Andreas T1 - Ein gemischt-ganzzahliges lineares Optimierungsmodell für ein Laserschweißproblem im Karosseriebau JF - Zeitschrift für wirtschaftlichen Fabrikbetrieb (ZWF) Karosseriebau Y1 - 2006 UR - http://opus.kobv.de/zib/volltexte/2006/915/ VL - 101 IS - 5 SP - 260 EP - 264 ER - TY - CHAP A1 - Hiller, Benjamin A1 - Krumke, Sven A1 - Saliba, Sleman A1 - Tuchscherer, Andreas T1 - Randomized Online Algorithms for Dynamic Multi-Period Routing Problems T2 - Proceedings of MAPSP Y1 - 2009 SP - 71 EP - 73 ER - TY - CHAP A1 - Heinz, Stefan A1 - Krumke, Sven A1 - Megow, Nicole A1 - Rambau, Jörg A1 - Tuchscherer, Andreas A1 - Vredeveld, Tjark ED - Erlebach, Thomas ED - Persiano, Giuseppe T1 - The Online Target Date Assignment Problem T2 - Proc. 3rd Workshop on Approximation and Online Algorithms Y1 - 2006 UR - http://opus.kobv.de/zib/volltexte/2005/894/ VL - 3879 SP - 230 EP - 243 PB - Springer ER - TY - JOUR A1 - Heinz, Stefan A1 - Kaibel, Volker A1 - Peinhardt, Matthias A1 - Rambau, Jörg A1 - Tuchscherer, Andreas T1 - LP-Based Local Approximation for Markov Decision Problems Y1 - 2006 IS - 343 PB - Matheon ER - TY - CHAP A1 - Hiller, Benjamin A1 - Vredeveld, Tjark T1 - Stochastic dominance analysis of online bin coloring algorithms T2 - 9th Workshop on Models and Algorithms for Planning and Scheduling Problems Y1 - 2009 ER - TY - THES A1 - Borndörfer, Ralf T1 - Mengenpartitionen und ihre Anwendung auf ein Maschinenbelegungsproblem Y1 - 1991 ER - TY - GEN A1 - Hiller, Benjamin A1 - Tuchscherer, Andreas T1 - Real-Time Destination-Call Elevator Group Control on Embedded Microcontrollers N2 - Algorithmic control of elevator systems has been studied for a long time. More recently, a new paradigm for elevator control has emerged. In destination call systems, the passenger specifies not only the direction of his ride, but the destination floor. Such a destination call system is very interesting from an optimization point of view, since more information is available earlier, which should allow improved planning. However, the real-world destination call system envisioned by our industry partner requires that each destination call (i.e. passenger) is assigned to a serving elevator immediately. This early assignment restricts the potential gained from the destination information. Another aspect is that there is no way to specify the destination floor in the cabin. Therefore, the elevator has to stop on every destination floor of an assigned call, although the passenger may not have boarded the cabin, e.g. due to insufficient capacity. In this paper we introduce a new destination call control algorithm suited to this setting. Since the control algorithm for an entire elevator group has to run on embedded microprocessors, computing resources are very scarce. Since exact optimization is not feasible on such hardware, the algorithm is an insertion heuristic using a non-trivial data structure to maintain a set of tours. To assess the performance of our algorithm, we compare it to similar and more powerful algorithms by simulation. We also compare to algorithms for a conventional system and with a more idealized destination call system. This gives an indication of the relative potentials of these systems. In particular, we assess how the above real-world restrictions influence performance. The algorithm introduced has been implemented by our industry partner for real-world use. T3 - ZIB-Report - 07-26 KW - Aufzugsgruppensteuerung KW - Zielrufsteuerung KW - Echzeitoptimierung KW - Online-Optimierung KW - elevator group control KW - destination call system KW - real time optimation KW - online optimization Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10108 SN - 1438-0064 ER - TY - GEN A1 - Hiller, Benjamin A1 - Klug, Torsten A1 - Tuchscherer, Andreas T1 - Improving the performance of elevator systems using exact reoptimization algorithms N2 - This extended abstract is about algorithms for controlling elevator systems employing destination hall calls, i.e. the passenger provides his destination floor when calling an elevator. We present the first exact algorithm for controlling a group of elevators and report on simulation results indicating that destination hall call systems outperform conventional systems. T3 - ZIB-Report - 09-05 KW - Aufzugssteuerung KW - Onlineoptimierung KW - Exakte Reoptimierung KW - elevator control KW - online optimization KW - exact reoptimation Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11155 SN - 1438-0064 ER - TY - GEN A1 - Grötschel, Martin A1 - Hinrichs, Hinrich A1 - Schröer, Klaus A1 - Tuchscherer, Andreas T1 - Ein gemischt-ganzzahliges lineares Optimierungsmodell für ein Laserschweißproblem im Karosseriebau N2 - Wir beschäftigen uns mit dem Problem der Betriebsplanung von Laserschweißrobotern im Karosseriebau. Gegeben ist eine Menge von Schweißnähten, die innerhalb einer Fertigungszelle an einem Karosserieteil gefertigt werden müssen. Die Schweißnähte werden durch mehrere parallel betriebene Roboter bearbeitet. Die Aufgabe besteht darin, für jeden Roboter eine Reihenfolge und eine zeitliche Koordinierung seiner Bewegungen zu finden, so dass alle Schweißnähte innerhalb der Taktzeit der Fertigungszelle bearbeitet werden und so wenig Laserquellen wie möglich eingesetzt werden. Dabei müssen einige Nebenbedingungen berücksichtigt werden. Für dieses spezielle Schweißproblem haben wir eine Formulierung als gemischt-ganzzahliges lineares Programm entwickelt, welches sich für die untersuchten praktischen Fälle sehr schnell lösen lässt. T3 - ZIB-Report - 06-21 KW - Laserschweißen KW - Gemischt-ganzzahlige Optimierung Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9141 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 -