@misc{GroetschelKrumkeRambauetal., author = {Gr{\"o}tschel, Martin and Krumke, Sven and Rambau, J{\"o}rg and Torres, Luis Miguel}, title = {Making the Yellow Angels Fly: Online Dispatching Of Service Vehicles in Real Time}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6858}, number = {02-18}, abstract = {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.}, language = {en} } @misc{GroetschelKrumkeRambauetal., author = {Gr{\"o}tschel, Martin and Krumke, Sven and Rambau, J{\"o}rg and Winter, Thomas and Zimmermann, Uwe}, title = {Combinatorial Online Optimization in Real Time}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6424}, number = {01-16}, abstract = {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.}, language = {en} } @misc{KrumkeRambauTorres, author = {Krumke, Sven and Rambau, J{\"o}rg and Torres, Luis Miguel}, title = {Real-Time Dispatching of Guided and Unguided Automobile Service Units with Soft Time Windows}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6484}, number = {01-22}, abstract = {Given a set of service requests (events), a set of guided servers (units), and a set of unguided service contractors (conts), the vehicle dispatching problem {\sl vdp} is the task to find an assignment of events to units and conts as well as tours for all units starting at their current positions and ending at their home positions (dispatch) such that the total cost of the dispatch is minimized. The cost of a dispatch is the sum of unit costs, cont costs, and event costs. Unit costs consist of driving costs, service costs and overtime costs; cont costs consist of a fixed cost per service; event costs consist of late costs linear in the late time, which occur whenever the service of the event starts later than its deadline. The program \textsf{ZIBDIP} based on dynamic column generation and set partitioning yields solutions on heavy-load real-world instances (215 events, 95 units) in less than a minute that are no worse than 1\\% from optimum on state-of-the-art personal computers.}, language = {en} } @misc{KrumkePaepeRambauetal., author = {Krumke, Sven and Paepe, Willem de and Rambau, J{\"o}rg and Stougie, Leen}, title = {Online Bin-Coloring}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6338}, number = {01-07}, abstract = {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.}, language = {en} } @misc{FrieseRambau, author = {Friese, Philipp and Rambau, J{\"o}rg}, title = {Online-Optimization of Multi-Elevator Transport Systems with Reoptimization Algorithms based on Set-Partitioning Models}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8373}, number = {05-03}, abstract = {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.}, language = {en} } @misc{HelmbergRoehl, author = {Helmberg, Christoph and R{\"o}hl, Stefan}, title = {A Case Study of Joint Online Truck Scheduling and Inventory Management for Multiple Warehouses}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8454}, number = {05-11}, abstract = {For a real world problem --- transporting pallets between warehouses in order to guarantee sufficient supply for known and additional stochastic demand --- we propose a solution approach via convex relaxation of an integer programming formulation, suitable for online optimization. The essential new element linking routing and inventory management is a convex piecewise linear cost function that is based on minimizing the expected number of pallets that still need transportation. For speed, the convex relaxation is solved approximately by a bundle approach yielding an online schedule in 5 to 12 minutes for up to 3 warehouses and 40000 articles; in contrast, computation times of state of the art LP-solvers are prohibitive for online application. In extensive numerical experiments on a real world data stream, the approximate solutions exhibit negligible loss in quality; in long term simulations the proposed method reduces the average number of pallets needing transportation due to short term demand to less than half the number observed in the data stream.}, language = {en} } @misc{BorndoerferGroetschelPfetsch, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Pfetsch, Marc}, title = {A Column-Generation Approach to Line Planning in Public Transport}, doi = {/10.1287/trsc.1060.0161}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8522}, number = {05-18}, abstract = {The line planning problem is one of the fundamental problems in strategic planning of public and rail transport. It consists in finding lines and corresponding frequencies in a transport network such that a given travel demand can be satisfied. There are (at least) two objectives. The transport company wishes to minimize operating costs, the passengers want to minimize travel times. We propose a n ew multi-commodity flow model for line planning. Its main features, in comparison to existing models, are that the passenger paths can be freely routed and that the lines are generated dynamically. We discuss properties of this model and investigate its complexity. Results with data for the city of Potsdam, Germany, are reported.}, language = {en} } @misc{KrumkeRambauTorres, author = {Krumke, Sven and Rambau, J{\"o}rg and Torres, Luis Miguel}, title = {Online-Dispatching of Automobile Service Units}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7117}, number = {02-44}, abstract = {We present an online algorithm for a real-world vehicle dispatching problem at ADAC, the German Automobile Association.}, language = {en} } @misc{HillerKrumkeRambau, author = {Hiller, Benjamin and Krumke, Sven and Rambau, J{\"o}rg}, title = {Reoptimization Gaps versus Model Errors in Online-Dispatching of Service Units for ADAC}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7928}, number = {04-17}, abstract = {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.}, language = {en} } @misc{BorndoerferGroetschelPfetsch, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Pfetsch, Marc}, title = {Models for Line Planning in Public Transport}, doi = {10.1007/978-3-540-73312-6_18}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7854}, number = {04-10}, abstract = {The \emph{line planning problem} is one of the fundamental problems in strategic planning of public and rail transport. It consists of finding lines and corresponding frequencies in a public transport network such that a given travel demand can be satisfied. There are (at least) two objectives. The transport company wishes to minimize its operating cost; the passengers request short travel times. We propose two new multi-commodity flow models for line planning. Their main features, in comparison to existing models, are that the passenger paths can be freely routed and that the lines are generated dynamically.}, language = {en} }