TY - CHAP A1 - Grötschel, Martin A1 - Wakabayashi, Yoshiko ED - Cottle, Richard ED - Kelmanson, Milton ED - Korte, Bernhard T1 - Constructions of hypotraceable digraphs T2 - Mathematical Programming. Proceedings of the International Congress on Mathematical Programming, Rio de Janeiro, Brazil, 6-8 April 1981 Y1 - 1984 SP - 147 EP - 175 PB - North-Holland ER - TY - JOUR A1 - Barahona, Francisco A1 - Grötschel, Martin A1 - Mahjoub, Ali T1 - Facets of the Bipartite Subgraph Polytope JF - Mathematics of Operations Research Y1 - 1985 VL - 10 SP - 340 EP - 358 ER - TY - JOUR A1 - Grötschel, Martin A1 - Holland, Olaf T1 - Solving matching problems with linear programming JF - Mathematical Programming Y1 - 1985 VL - 33 IS - 3 SP - 243 EP - 259 ER - TY - CHAP A1 - Grötschel, Martin A1 - Jünger, Michael A1 - Reinelt, Gerhard ED - Rival, Ivan T1 - Acyclic subdigraphs and linear orderings T2 - Graphs and Order. The Role of Graphs in the Theory of Ordered Sets and its Applications, Proceedings of NATO ASI, Ser. C 147, Banff/Canada 1984 Y1 - 1985 SP - 217 EP - 264 PB - D. Reidel Publishing Company ER - TY - JOUR A1 - Grötschel, Martin A1 - Jünger, Michael A1 - Reinelt, Gerhard T1 - On the acyclic subgraph polytope JF - Mathematical Programming Y1 - 1985 VL - 33 IS - 1 SP - 28 EP - 42 PB - North-Holland ER - TY - JOUR A1 - Grötschel, Martin A1 - Jünger, Michael A1 - Reinelt, Gerhard T1 - Facets of the linear ordering polytope JF - Mathematical Programming Y1 - 1985 VL - 33 IS - 1 SP - 43 EP - 60 PB - North-Holland ER - TY - CHAP A1 - Grötschel, Martin A1 - Padberg, Manfred ED - Lawler, Eugene ED - Lenstra, Jan ED - Kan, Alexander ED - Shmoys, David T1 - Polyhedral theory T2 - The Traveling Salesman Problem. A Guided Tour of Combinatorial Optimization Y1 - 1985 SP - 251 EP - 306 PB - Wiley ER - TY - CHAP A1 - Padberg, Manfred A1 - Grötschel, Martin ED - Lawler, Eugene ED - Lenstra, Jan ED - Kan, Alexander ED - Shmoys, David T1 - Polyhedral computations T2 - The Traveling Salesman Problem. A Guided Tour of Combinatorial Optimization Y1 - 1985 SP - 307 EP - 360 PB - Wiley ER - TY - RPRT A1 - Barahona, Francisco A1 - Grötschel, Martin T1 - The Travelling Salesman Problem for Graphs not Contractible to K_5 - e Y1 - 1985 IS - 77 PB - Mathematisches Institut, Universität Augsburg ER - TY - JOUR A1 - Barahona, Francisco A1 - Grötschel, Martin T1 - On the Cycle Polytope of a Binary Matroid JF - Journal of Combinatorial Theory, Series B Y1 - 1986 VL - 40 SP - 40 EP - 62 ER - TY - CHAP A1 - Grötschel, Martin ED - Kerber, Adalbert T1 - Polyedrische Kombinatorik und Schnittebenenverfahren, Tagungsbericht 2. Sommerschule Diskrete Strukturen, Bayreuth 1985 T2 - Diskrete Strukturen, algebraische Methoden und Anwendungen Y1 - 1986 VL - 21 SP - 69 EP - 100 PB - Institut für Mathematik, Universität Bayreuth ER - TY - CHAP A1 - Grötschel, Martin ED - Krelle, Wilhelm T1 - Fortschritte in der polyedrischen Kombinatorik T2 - Ökonomische Prognose-, Entscheidungs- und Gleichgewichtsmodelle, Abschlußberichte des SFB 21 Y1 - 1986 SP - 341 EP - 367 PB - Verlag Chemie CY - Weinheim ER - TY - JOUR A1 - Grötschel, Martin A1 - Lovász, Lászlo A1 - Schrijver, Alexander T1 - Relaxations of Vertex Packing JF - Journal of Combinatorial Theory, Series B Y1 - 1986 VL - 40 SP - 330 EP - 343 ER - TY - JOUR A1 - Grötschel, Martin A1 - Pulleyblank, William T1 - Clique tree inequalities and the symmetric travelling salesman problem JF - Mathematics of Operations Research Y1 - 1986 VL - 11 IS - 4 SP - 537 EP - 569 ER - TY - JOUR A1 - Grötschel, Martin A1 - Holland, Olaf T1 - A Cutting Plane Algorithm for Minimum Perfect 2-Matchings JF - Computing Y1 - 1987 VL - 39 SP - 327 EP - 344 ER - TY - JOUR A1 - Grötschel, Martin A1 - Thomassen, Carsten A1 - Wakabayashi, Yoshiko T1 - Hypotraceable digraphs JF - Journal of Graph Theory Y1 - 1980 VL - 4 SP - 377 EP - 381 ER - TY - JOUR A1 - Grötschel, Martin A1 - Wakabayashi, Yoshiko T1 - Hypohamiltonian digraphs JF - Methods of Operations Research Y1 - 1980 VL - 36 SP - 99 EP - 119 ER - TY - BOOK A1 - Bachem, Achim A1 - Butz, Lothar A1 - Grötschel, Martin A1 - (Bearb.), Rainer A1 - Leitung), Bernhard T1 - Input-Output-Analyse bei unternehmensgrößenspezifischen Fragestellungen Y1 - 1981 PB - Institut für Mittelstandsforschung CY - Bonn ER - TY - JOUR A1 - Bachem, Achim A1 - Grötschel, Martin T1 - Homogenization of polyhedra JF - Methods of Operations Research Y1 - 1981 VL - 40 SP - 215 EP - 219 ER - TY - CHAP A1 - Bachem, Achim A1 - Grötschel, Martin ED - König, Heinz ED - Korte, Bernhard ED - Ritter, Klaus T1 - Characterizations of adjacency of faces of polyhedra T2 - Mathematical Programming at Oberwolfach Y1 - 1981 VL - 14 SP - 1 EP - 22 PB - North-Holland ER - TY - JOUR A1 - Grötschel, Martin A1 - Lovász, Lászlo A1 - Schrijver, Alexander T1 - The ellipsoid method and its consequences in combinatorial optimization JF - Combinatorica Y1 - 1981 VL - 1 IS - 2 SP - 169 EP - 197 ER - TY - JOUR A1 - Grötschel, Martin A1 - Lovász, Lászlo A1 - Schrijver, Alexander T1 - The ellipsoid method and its consequences in combinatorial optimization JF - IIASA Collab. Proceedings Ser. CP-81-S1 Y1 - 1981 SP - 511 EP - 546 ER - TY - JOUR A1 - Grötschel, Martin A1 - Pulleyblank, William T1 - Weakly bipartite graphs and the max-cut problem JF - Operations Research Letters Y1 - 1981 VL - 1 IS - 1 SP - 23 EP - 27 ER - TY - JOUR A1 - Grötschel, Martin A1 - Wakabayashi, Yoshiko T1 - On the structure of the monotone asymmetric travelling salesman polytope I JF - Discrete Mathematics Y1 - 1981 VL - 34 SP - 43 EP - 59 ER - TY - JOUR A1 - Grötschel, Martin A1 - Wakabayashi, Yoshiko T1 - On the structure of the monotone asymmetric travelling salesman polytope II JF - Mathematical Programming Study Y1 - 1981 VL - 14 SP - 77 EP - 97 ER - TY - CHAP A1 - Bachem, Achim A1 - Grötschel, Martin ED - Korte, Bernhard T1 - New aspects of polyhedral theory T2 - Modern Applied Mathematics Y1 - 1982 SP - 51 EP - 106 PB - North-Holland ER - TY - CHAP A1 - Grötschel, Martin ED - Korte, Bernhard T1 - Approaches to Hard Combinatorial Optimization Problems T2 - Modern Applied Mathematics, Optimization and Operations Research, Lect. Summer Sch., Bonn 1979 Y1 - 1982 SP - 437 EP - 515 PB - North-Holland ER - TY - CHAP A1 - Grötschel, Martin ED - der Universität Bonn, Der T1 - Kombinatorische Optimierung T2 - Forschungsbericht 1978-1980 der Rheinischen Friedrich-Wilhelms-Universität Y1 - 1982 SP - 45 EP - 54 PB - Bouvier CY - Bonn ER - TY - CHAP A1 - Grötschel, Martin ED - Bollobás, Béla T1 - On Intersections of Longest Cycles T2 - Graph Theory and Combinatorics Y1 - 1984 SP - 171 EP - 189 PB - Academic Press ER - TY - CHAP A1 - Grötschel, Martin ED - Jäger, Willi ED - Moser, J. ED - Remmert, R. T1 - Developments in combinatorial optimization T2 - Perspectives in Mathematics (Anniversary of Oberwolfach 1984) Y1 - 1984 SP - 249 EP - 294 PB - Birkhäuser CY - Basel ER - TY - CHAP A1 - Grötschel, Martin ED - O’Heigeartaigh, Michael ED - Lenstra, Jan ED - Kan, Alexander T1 - Polyhedral Combinatorics T2 - COMBINATORIAL OPTIMIZATION Y1 - 1984 SP - 1 EP - 10 PB - Wiley ER - TY - RPRT A1 - Grötschel, Martin T1 - Polyedrische Kombinatorik und Schnittebenenverfahren Y1 - 1984 IS - 231 PB - Forschungszentrum Graz, Österreich ER - TY - JOUR A1 - Grötschel, Martin A1 - Jünger, Michael A1 - Reinelt, Gerhard T1 - A Cutting Plane Algorithm for the Linear Ordering Problem JF - Operations Research Y1 - 1984 VL - 32 IS - 6 SP - 1195 EP - 1220 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Pfetsch, Marc T1 - A Column-Generation Approach to Line Planning in Public Transport JF - Transportation Science (INFORMS) Y1 - 2007 U6 - https://doi.org/10.1287/trsc.1060.0161 VL - 41 IS - 1 SP - 123 EP - 132 ER - TY - GEN A1 - Grötschel, Martin A1 - Löbel, Andreas A1 - Völker, Manfred T1 - Optimierung des Fahrzeugumlaufs im Öffentlichen Nahverkehr N2 - This paper addresses the problem of scheduling vehicles in a public mass transportation system. We show how this problem can be modelled as a special multicommodity flow problem and outline the solution methodology we have developed. Based on polyhedral investigations, we have designed and implemented a branch&cut algorithm and various heuristics with which real vehicle scheduling problems of truely large scale can be solved to optimality. We describe some implementation issues and report computational results. T3 - ZIB-Report - SC-96-08 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2195 ER - TY - GEN A1 - Ascheuer, Norbert A1 - Fischetti, Matteo A1 - Grötschel, Martin T1 - A polyhedral study of the asymmetric travelling salesman problem with time windows N2 - The asymmetric travelling salesman problem with time windows (ATSP-TW) is a basic model for scheduling and routing applications. In this paper we present a formulation of the problem involving only 0/1-variables associated with the arcs of the underlying digraph. This has the advantage of avoiding additional variables as well as the associated (typically very ineffective) linking constraints. In the formulation, time window restrictions are modelled by means of ``infeasible path elimination'' constraints. We present the basic form of these constraints along with some possible strengthenings. Several other classes of valid inequalities derived from related asymmetric travelling salesman problems are also described, along with a lifting theorem. We also study the ATSP-TW polytope, $P_{TW}$, defined as the convex hull of the integer solutions of our model. We show that determining the dimension of $P_{TW}$ is strongly {\em NP}--complete problem, even if only one time window is present. In this latter case, we provide a minimal equation system for $P_{TW}$. Computational experiments on the new formulation are reported in a companion paper [1997] where we show that it outperforms alternative formulations on some classes of problem instances. T3 - ZIB-Report - SC-97-11 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2807 ER - TY - GEN A1 - Alevras, Dimitris A1 - Grötschel, Martin A1 - Wessäly, Roland T1 - Cost-Efficient Network Synthesis from Leased Lines N2 - Given a communication demand between each pair of nodes of a network we consider the problem of deciding what capacity to install on each edge of the network in order to minimize the building cost of the network and to satisfy the demand between each pair of nodes. The feasible capacities that can be leased from a network provider are of a particular kind in our case. There are a few so-called basic capacities having the property that every basic capacity is an integral multiple of every smaller basic capacity. An edge can be equipped with a capacity only if it is an integer combination of the basic capacities. We treat, in addition, several restrictions on the routings of the demands (length restriction, diversification) and failures of single nodes or single edges. We formulate the problem as a mixed integer linear programming problem and develop a cutting plane algorithm as well as several heuristics to solve it. We report on computational results for real world data. T3 - ZIB-Report - SC-97-22 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2912 ER - TY - GEN A1 - Alevras, Dimitris A1 - Grötschel, Martin A1 - Wessäly, Roland T1 - Capacity and Survivability Models for Telecommunication Networks N2 - Designing low-cost networks that survive certain failure situations is one of the prime tasks in the telecommunication industry. In this paper we survey the development of models for network survivability used in practice in the last ten years. We show how algorithms integrating polyhedral combinatorics, linear programming, and various heuristic ideas can help solve real-world network dimensioning instances to optimality or within reasonable quality guarantees in acceptable running times. The most general problem type we address is the following. Let a communication demand between each pair of nodes of a telecommunication network be given. We consider the problem of choosing, among a discrete set of possible capacities, which capacity to install on each of the possible edges of the network in order to (i) satisfy all demands, (ii) minimize the building cost of the network. \noindent In addition to determining the network topology and the edge capacities we have to provide, for each demand, a routing such that (iii) no path can carry more than a given percentage of the demand, (iv) no path in the routing exceeds a given length. \noindent We also have to make sure that (v) for every single node or edge failure, a certain percentage of the demand is reroutable. \noindent Moreover, for all failure situations feasible routings must be computed. The model described above has been developed in cooperation with a German mobile phone provider. We present a mixed-integer programming formulation of this model and computational results with data from practice. T3 - ZIB-Report - SC-97-24 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2931 ER - TY - GEN A1 - Dalitz, Wolfgang A1 - Grötschel, Martin A1 - Lügger, Joachim T1 - Information Services for Mathematics in the Internet (Math-Net) N2 - The present paper gives a brief description of the Math-Net project which is carried out by nine mathematical institutions in Germany, supported by Deutsches Forschungsnetz (DFN) and Deutsche Telekom. The project aims at setting up the technical and organizational infrastructure for efficient, inexpensive and user-driven information services for mathematics. With the aid of active (structured retrieval mechanisms) and passive (profile services) components, electronic mathematical information in Germany will be made available to the scientist at his workplace. The emphasis is put on information about publications, software and data collections, teaching and research activities, but also on organizational and bibliographical information. Decentral organization structures, distributed search systems as well as the use of meta-information (metadata) in accordance with the Dublin Core (hopefully) guarantee a longterm, high-quality repository of data. The well-known mathematical software and data collection netlib\/ will be used as an example to illustrate how such a collection can be adapted to Math-Net. An integration of netlib into HyperWave offers additional perspectives and functionalities. T3 - ZIB-Report - SC-97-25 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2949 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Herzog, Werner A1 - Klostermeier, Fridolin A1 - Konsek, Wilhelm A1 - Küttner, Christian T1 - Kürzen muß nicht Kahlschlag heißen - das Beispiel Telebus-Behindertenfahrdienst Berlin N2 - Müssen Etatkürzungen bei staatlichen Dienstleistungseinrichtungen notwendig zu Leistungseinschränkungen oder Gebührenerhöhungen führen? Wir zeigen am Beispiel des Berliner Behindertenfahrdienstes {\em Telebus}, da\ss{} Sparzwang auch als Chance zur Verbesserung der eigenen Verwaltungs- und Arbeitsabläufe genutzt werden kann. Durch stärkere Dienstleistungsorientierung, Vereinfachung der Arbeitsabläufe und durch den Einsatz von moderner EDV und von mathematischen Optimierungsmethoden zur Fahrzeugeinsatzplanung werden bei Telebus heute staatliche Leistungen trotz geringeren Etats besser erbracht als vorher. T3 - ZIB-Report - SC-96-41 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2510 ER - TY - GEN A1 - Alevras, Dimitris A1 - Grötschel, Martin A1 - Jonas, Peter A1 - Paul, Ulrich A1 - Wessäly, Roland T1 - Survivable Mobile Phone Architectures: Models and Solution Methods N2 - In the highly competitive area of telecommunications, cost, quality, and network management are among the most important aspects to be considered when designing a network. We study the problem of dimensioning a telecommunication network that is still operating in case of a failure of a network component. Given a demand between each pair of nodes of a telecommunication network and a finite set of possible capacities for each edge of the network, we consider the problem of deciding what capacity to install on each edge of the network in order to minimize the building cost of the network and to satisfy the demand between each pair of nodes, even if a network component fails. The routing of the demands must satisfy the following additional restrictions: (a) there is a maximum number of nodes allowed in each path between any pair of nodes (path length restriction), and (b) there is a maximum percentage of the demand between each pair of nodes that can be routed through any network component (diversification restriction). Moreover, the chosen capacities must be such that, for every single node or single edge failure, a certain percentage of the demand between any pair of nodes is reroutable (i.e. it ``survives'' the particular failure). We formulate the problem as a mixed integer linear programming problem and present a cutting plane algorithm as well as several heuristics for its solution. Furthermore, we discuss several ways to implement survivability into a telecommunication network. T3 - ZIB-Report - SC-96-48 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2582 ER - TY - GEN A1 - Alevras, Dimitris A1 - Grötschel, Martin A1 - Wessäly, Roland T1 - A Network Dimensioning Tool N2 - Designing low cost networks that survive certain failure situations belongs to one of the prime tasks in the telecommunications industry. In this paper we describe a mathematical model combining several aspects of survivability that are elsewhere treated in a hierarchical fashion. We present mathematical investigations of this integrated model, a cutting plane algorithm, as well as several heuristics for its solution. Moreover, we report computational results with real world data. The problem we address is the following. Suppose, between each pair of nodes in a region, a communication demand is given. We want to determine the topology of a telecommunication network connecting the given nodes and to dimension all potential physical links. For each link, the possible capacities are restricted to a given finite set. The capacities must be chosen such that the communication demands are satisfied, even if certain network components fail, and such that the network building costs are as small as possible. Moreover, for each pair of nodes and each failure situation, we want to determine the paths on which the demand between the nodes is routed. T3 - ZIB-Report - SC-96-49 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2591 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Klostermeier, Fridolin A1 - Küttner, Christian T1 - Telebus Berlin - Mobilität für Behinderte N2 - Steigendes Mobilitätsbedürfnis der Behinderten bei angespannter Haushaltslage --- diese Situation ergab vor drei Jahren beim Berliner Behindertenfahrdienst {\em Telebus\/} Handlungsbedarf. Gleichzeitig stie\ss{} die verwendete manuelle (Fahrzeug-)Tourenplanung mit damals etwa 1.000 Fahrtwünschen pro Tag an ihre Grenzen. Zur Lösung dieser Probleme war der effiziente Einsatz von Computern und von {\em mathematischen Optimierungsverfahren\/} erforderlich. Ergebnis des daraufhin gestarteten {\em Telebus-Projektes\/} ist die Entwicklung eines neuen, alle Arbeitsabläufe unterstützenden Computersystems, das seit über einem Jahr im Einsatz ist. Herzstück dieses Systems ist ein auf mathematischen Methoden der ganzzahligen Optimierung basierendes Verfahren zur Tourenplanung. Ziel dieses Artikels ist die Beschreibung dieses Verfahrens und seiner Verwendung bei der Behindertenbeförderung. Das Beispiel Telebus zeigt, da\ss{} der Einsatz mathematischer Optimierungstechniken neue Möglichkeiten für Kosteneinsparungen bei gleichzeitiger Serviceverbesserung auch in anderen Bereichen des ÖPNV eröffnet. T3 - ZIB-Report - SC-96-40 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2500 ER - TY - GEN A1 - Abdel-Hamid, Atef Abdel-Aziz A1 - Ascheuer, Norbert A1 - Grötschel, Martin A1 - Schorer, Herbert T1 - Simulation und Optimierung einer PC-Fertigung unter Echtzeitbedingungen N2 - Die Business Unit PC in Augsburg ist die zentrale Produktionsstätte der Siemens--Nixdorf Informationssysteme (SNI) AG für Personal Computer sowie für einige Periphärgeräte. Das Werk, entworfen nach modernen CIM/CAI--Konzepten (Computer Integrated Manufacturing/ Computer Aided Industry), wurde 1987 errichtet. Bald zeigte sich jedoch, daß es für ein zu geringes Produktionsvolumen ausgelegt war und einige Komponenten des Systems Engpässe im Produktionsbetrieb darstellen. Das Management suchte nach Möglichkeiten, den Produktionsfluß zu verbessern, ohne teure technische Änderungen am System vornehmen zu müssen. Eine Forschungsgruppe des Konrad--Zuse--Zentrums für Informationstechnik (die ehemals an der Universität Augsburg ansässig war) analysierte, unterstützt von einigen Studenten und Ingenieuren der SNI, den Produktionsfluß und lokalisierte Schwachstellen. Basierend auf diesen Erkenntnissen wurden mathematische Fragestellungen erarbeitet und auf mathematischen Optimierungsverfahren basierende Softwarepakete entwickelt, die jetzt teilweise bei SNI im Einsatz sind. Im folgenden werden einige dieser Fragestellungen, deren Modellierung und mathematische Behandlung beschrieben. Einige der Ansätze, die hier dargestellt werden sollen, sind teilweise schon in Grötschel [Grö92] angesprochen worden. T3 - ZIB-Report - SC-95-04 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1700 ER - TY - GEN A1 - Grötschel, Martin A1 - Padberg, Manfred T1 - Ulysses 2000: In Search of Optimal Solutions to Hard Combinatorial Problems. N2 - Combinatorial optimization problems pervade many areas of human problem solving especially in the fields of business, economics and engineering. Intensive mathematical research and vast increases in raw computing power have advanced the state of the art in exact and heuristic problem solving at a pace that is unprecedented in human history. We survey here in layman's terms some of the fundamental concepts and principles that have led this progress. (This article will appear -- possibly in modified form -- in a popular science magazine.) T3 - ZIB-Report - SC-93-34 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1296 ER - TY - GEN A1 - Grötschel, Martin A1 - Monma, Clyde A1 - Stoer, Mechthild T1 - Design of Survivable Networks T3 - ZIB-Report - SC-93-09 Y1 - 1993 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1054 ER - TY - GEN A1 - Grötschel, Martin A1 - Lovász, Lászlo T1 - Combinatorial Optimization. N2 - This paper will appear as Chapter 28 of the forthcoming "Handbook on Combinatorics" (editors: R. Graham, M. Grötschel, L. Lovasz) to be published in 1994, by North-Holland. T3 - ZIB-Report - SC-93-13 Y1 - 1993 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1098 ER - TY - GEN A1 - Godsil, C. D. A1 - Grötschel, Martin A1 - Welsh, D. J. A. T1 - Combinatorics in Statistical Physics T3 - ZIB-Report - SC-91-19 Y1 - 1992 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-694 ER - TY - GEN A1 - Grötschel, Martin T1 - Discrete Mathematics in Manufacturing. N2 - Manufacturing is a topic that provides rich opportunities for important mathematical contributions to real-world problems. The purpose of this paper is to show, by means of several examples, where and how mathematical problems of a discrete nature arise in manufacturing and to demonstrate the savings and improvements that can be achieved by employing the techniques of combinatorial optimization. The topics covered range from the design phase of a product (e. g.,routing, placement and via minimization in VLSI design), the control of CNC machines (e. g., drilling and plotting), to the management of assembly lines, storage systems and whole factories. We also point out difficulties in the modelling of complex situations and outline the algorithmic methods that are used for the solution of the mathematical problems arising in manufacturing. {\bf Key words:} discrete mathematics , combinatorial optimization, applications to manufacturing. T3 - ZIB-Report - SC-92-03 KW - discrete mathematics KW - combinatorial optimization KW - applications to manufacturing Y1 - 1992 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-738 ER - TY - GEN A1 - Grötschel, Martin A1 - Monma, Clyde A1 - Stoer, Mechthild T1 - A Polyhedral Approach to Network Connectivity Problems (Extended Abstract). N2 - We present a polyhedral approach for the general problem of designing a minimum-cost network with specified connectivity requir T3 - ZIB-Report - SC-92-22 Y1 - 1992 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-924 ER -