TY - GEN A1 - Burgschweiger, Jens A1 - Gnädig, Bernd A1 - Steinbach, Marc T1 - Nonlinear Programming Techniques for Operative Planning in Large Drinking Water Networks N2 - Mathematical decision support for operative planning in water supply systems is highly desirable but leads to very difficult optimization problems. We propose a nonlinear programming approach that yields practically satisfactory operating schedules in acceptable computing time even for large networks. Based on a carefully designed model supporting gradient-based optimization algorithms, this approach employs a special initialization strategy for convergence acceleration, special minimum up and down time constraints together with pump aggregation to handle switching decisions, and several network reduction techniques for further speed-up. Results for selected application scenarios at Berliner Wasserbetriebe demonstrate the success of the approach. T3 - ZIB-Report - 05-31 KW - Water supply KW - large-scale nonlinear programming KW - convergence enhancement KW - discrete decisions KW - network reduction Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8657 ER - TY - GEN A1 - Burgschweiger, Jens A1 - Gnädig, Bernd A1 - Steinbach, Marc T1 - Optimierte Tagesplanung im Berliner Trinkwassernetz N2 - Der Artikel beschreibt ein mathematisches Optimierungssystem zur Betriebsplanung in großen Wassernetzen, das bei den Berliner Wasserbetrieben eingesetzt wird. Für das Berliner Versorgungsnetz werden Optimierungsergebnisse vorgestellt. T3 - ZIB-Report - 05-32 KW - Trinkwasserversorgung KW - kostenminimale Betriebsplanung KW - nichtlineare Optimierung KW - diskrete Entscheidungen Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8668 ER - TY - THES A1 - Koch, Thorsten T1 - Rapid Mathematical Programming N2 - The thesis deals with the implementation and application of out-of-the-box tools in linear and mixed integer programming. It documents the lessons learned and conclusions drawn from five years of implementing, maintaining, extending, and using several computer codes to solve real-life industrial problems. By means of several examples it is demonstrated how to apply algebraic modeling languages to rapidly devise mathematical models of real-world problems. It is shown that today's MIP solvers are capable of solving the resulting mixed integer programs, leading to an approach that delivers results very quickly. Even though, problems are tackled that not long ago required the implementation of specialized branch-and-cut algorithms. In the first part of the thesis the modeling language Zimpl is introduced. Chapter 2 contains a complete description of the language. In the subsequent chapter details of the implementation are described. Both theoretical and practical considerations are discussed. Aspects of software engineering, error prevention, and detection are addressed. In the second part several real-world projects are examined that employed the methodology and the tools developed in the first part. Chapter 4 presents three projects from the telecommunication industry dealing with facility location problems. Chapter 5 characterizes questions that arise in UMTS planning. Problems, models, and solutions are discussed. Special emphasis is put on the dependency of the precision of the input data and the results. Possible reasons for unexpected and undesirable solutions are explained. Finally, the Steiner tree packing problem in graphs, a well-known hard combinatorial problem, is revisited. A formerly known, but not yet used model is applied to combine switchbox wire routing and via minimization. All instances known from the literature are solved by this approach, as are some newly generated bigger problem instances. T3 - ZIB-Report - 04-58 KW - Modelling Languages KW - Mixed Integer Programming KW - Steiner Tree Packing in Graphs KW - Location Planning in Telecommunications KW - UMTS Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8346 ER - TY - GEN A1 - Helmberg, Christoph A1 - Röhl, Stefan T1 - A Case Study of Joint Online Truck Scheduling and Inventory Management for Multiple Warehouses N2 - 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. T3 - ZIB-Report - 05-11 KW - convex relaxation KW - integer programming KW - stochastic demand KW - network models KW - large scale problems KW - bundle method KW - logistics KW - vehicle routing Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8454 ER - TY - GEN A1 - Koster, Arie M.C.A. T1 - Wavelength Assignment in Multi-Fiber WDM Networks by Generalized Edge Coloring N2 - In this paper, we study wavelength assignment problems in multi-fiber WDM networks. We focus on the special case that all lightpaths have at most two links. This in particular holds in case the network topology is a star. As the links incident to a specific node in a meshed topology form a star subnetwork, results for stars are also of interest for general meshed topologies. We show that wavelength assignment with at most two links per lightpath can be modeled as a generalized edge coloring problem. By this relation, we show that for a network with an even number of fibers at all links and at most two links per lightpath, all lightpaths can be assigned a wavelength without conversion. Moreover, we derive a lower bound on the number of lightpaths to be converted for networks with arbitrary numbers of fibers at the links. A comparison with linear programming lower bounds reveals that the bounds coincide for problems with at most two links per lightpath. For meshed topologies, the cumulative lower bound over all star subnetworks equals the best known solution value for all realistic wavelength assignment instances available, by this proving optimality. T3 - ZIB-Report - 05-13 KW - wavelength assignment KW - optical networks KW - graph theory KW - combinatorial optimization KW - integer programming Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8478 ER -