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  • 1995-1999  (27)
  • 1990-1994  (4)
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  • 21
    Publication Date: 2020-03-09
    Description: {\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.}
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 22
    Publication Date: 2020-03-09
    Description: The world has experienced two hundred years of unprecedented advances in vehicle technology, transport system development, and traffic network extension. Technical progress continues but seems to have reached some limits. Congestion, pollution, and increasing costs have created, in some parts of the world, a climate of hostility against transportation technology. Mobility, however, is still increasing. What can be done? There is no panacea. Interdisciplinary cooperation is necessary, and we are going to argue in this paper that {\em Mathematics\/} can contribute significantly to the solution of some of the problems. We propose to employ methods developed in the {\em Theory of Optimization\/} to make better use of resources and existing technology. One way of optimization is better planning. We will point out that {\em Discrete Mathematics\/} provides a suitable framework for planning decisions within transportation systems. The mathematical approach leads to a better understanding of problems. Precise and quantitative models, and advanced mathematical tools allow for provable and reproducible conclusions. Modern computing equipment is suited to put such methods into practice. At present, mathematical methods contribute, in particular, to the solution of various problems of {\em operational planning}. We report about encouraging {\em results\/} achieved so far.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 23
    Publication Date: 2020-08-05
    Description: Diese Dissertation befaßt sich mit ganzzahligen Programmen mit 0/1 Systemen: SetPacking-, Partitioning- und Covering-Probleme. Die drei Teile der Dissertation behandeln polyedrische, algorithmische und angewandte Aspekte derartiger Modelle.
    Keywords: ddc:000
    Language: English
    Type: doctoralthesis , doc-type:doctoralThesis
    Format: application/pdf
    Format: application/postscript
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  • 24
    Publication Date: 2020-03-09
    Description: 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.
    Keywords: ddc:000
    Language: German
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 25
    Publication Date: 2020-03-09
    Description: 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.
    Keywords: ddc:000
    Language: German
    Type: reportzib , doc-type:preprint
    Format: application/postscript
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  • 26
    Publication Date: 2020-08-05
    Description: In this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so-called {\em bordered block diagonal form}. More precisely, given some matrix $A$, we try to assign as many rows as possible to some number of blocks of limited size such that no two rows assigned to different blocks intersect in a common column. Bordered block diagonal form is desirable because it can guide and speed up the solution process for linear and integer programming problems. We show that various matrices from the LP- and MIP-libraries NETLIB and MITLIB can indeed be decomposed into this form by computing optimal decompositions or decompositions with proven quality. These computations are done with a branch-and-cut algorithm based on polyhedral investigations of the matrix decomposition problem. In practice, however, one would use heuristics to find a good decomposition. We present several heuristic ideas and test their performance. Finally, we investigate the usefulness of optimal matrix decompositions into bordered block diagonal form for integer programming by using such decompositions to guide the branching process in a branch-and-cut code for general mixed integer programs.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
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  • 27
    Publication Date: 2020-08-05
    Description: {\em Telebus\/} is Berlin's dial-a-ride system for handicapped people that cannot use the public transportation system. The service is provided by a fleet of about 100 mini-busses and includes aid to get in and out of the vehicle. Telebus has between 1,000 and 1,500 transportation requests per day. The problem arises to schedule these requests into the vehicles such that punctual service is provided while operation costs should be minimum. Additional constraints include pre-rented vehicles, fixed bus driver shift lengths, obligatory breaks, and different vehicle capacities. We use a {\em set partitioning\/} approach for the solution of the bus scheduling problem that consists of two steps. The first {\em clustering\/} step identifies segments of possible bus tours (``orders'') such that more than one person is transported at a time; the aim in this step is to reduce the size of the problem and to make use of larger vehicle capacities. The problem to select a set of orders such that the traveling distance of the vehicles within the orders is minimal is a set partitioning problem that we can solve to optimality. In the second step the selected orders are {\em chained\/} to yield possible bus tours respecting all side constraints. The problem to select a set of such bus tours such that each order is serviced once and the total traveling distance of the vehicles is minimum is again a set partitioning problem that we solve approximately. We have developed a computer system for the solution of the bus scheduling problem that includes a branch-and-cut algorithm for the solution of the set partitioning problems. A version of this system is in operation at Telebus since July 1995. Its use made it possible that Telebus can service today about 30\% more requests per day for the same amount of money than before.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
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  • 28
    Publication Date: 2020-08-05
    Description: In diesem Artikel geben wir einen Überblick über das Telebus-Projekt am Konrad-Zuse-Zentrum, Berlin, durch das der Behindertenfahrdienst in Berlin reorganisiert und optimiert wurde. Wir berichten kurz über die mathematischen Probleme und, etwas ausführlicher, über die nicht-mathematischen Schwierigkeiten, die bei der Durchführung dieses Projektes auftraten.
    Keywords: ddc:000
    Language: German
    Type: reportzib , doc-type:preprint
    Format: application/postscript
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  • 29
    Publication Date: 2020-03-09
    Description: We present a graph-theoretic model for the \emph{frequency assignment problem} in Cellular Phone Networks: Obeying several technical and legal restrictions, frequencies have to be assigned to transceivers so that interference is as small as possible. This optimization problem is NP-hard. Good approximation cannot be guaranteed, unless P = NP. We describe several assignment heuristics. These heuristics are simple and not too hard to implement. We give an assessment of the heuristics' efficiency and practical usefulness. For this purpose, typical instances of frequency assignment problems with up to 4240 transceivers and 75 frequencies of a German cellular phone network operator are used. The results are satisfying from a practitioner's point of view. The best performing heuristics were integrated into a network planning system used in practice.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
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  • 30
    Publication Date: 2020-08-05
    Description: This paper investigates {\em relations\/} among combinatorial optimization problems. To establish such relations we introduce a transformation technique \mbox{---{\em aggregation}---} that allows to relax an integer program by means of another integer program. We prove that various families of prominent inequalities for the acyclic subdigraph problem, the multiple knapsack problem, the max cut, graph, and the clique partitioning problem, the set covering problem, and the set packing problem can be derived and separated in polynomial time in this way. Our technique is algorithmic. It has been implemented and used in a set partitioning code.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
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