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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-5217
    Keywords: Generalized convexity ; duality ; root term ; optimal solution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We extend the duality theorems for a class of nondifferentiable problems with Mond-Weir type duals.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-5217
    Keywords: Combinatorial optimization ; scheduling ; permutation flow shop problem ; networks ; structural investigations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In der vorliegenden Arbeit wird die kombinatorische Struktur desn/m/P/C max Permutationsflußproblems untersucht. Zu jeder zulässigen Lösung, beschreibbar durch eine Permutation vonn Elementen, wird ein Netzplan eingeführt, der die Bearbeitungsreihenfolge der Operationen charakterisiert. Aufbauend auf einem eingeführten verallgemeinerten Abstand zwischen einer Permutation und einem Weg in einem Netzplan werden danach einige kombinatorische Eigenschaften bezüglich spezieller Nachbarschaftsstrukturen abgeleitet, die im Hinblick auf die Entwicklung von iterativen Heuristiken für das betrachtete Problem von Bedeutung sind. So werden u. a. für ausgewählte Nachbarschaftsstrukturen mittlere Mächtigkeiten reduzierter Nachbarschaften, bei denen jeder Nachbar eine notwendige Bedingung für eine Zielfunktionswertverbesserung erfüllt, hergeleitet.
    Notes: Abstract In this paper we investigate the combinatorial structure of then/m/P/C max permutation flow shop problem. To each solution (a permutation ofn elements) we introduce a network which represents the job and machine orders. Based on the introduced generalized distance between a permutation and a path of a network we derive combinatorial properties with respect to special neighbourhoods which are important for developing iterative heuristics for the considered problem. For several neighbourhood structures we calculate the mean cardinality of reduced neighbourhoods where each neighbour satisfies a necessary condition for an objective improvement.
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  • 3
    ISSN: 1432-5217
    Keywords: Key words: Job-shop problem ; scheduling ; NP-hard
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. It is shown that the two machine preemptive job-shop problem with mean flow-time or makespan objective function and three jobs is NP-hard. This contrasts the fact that the nonpreemptive versions of these problems are polynomially solvable if the number of jobs is arbitrary but fixed. It is also shown that the preemptive problems can be solved pseudopolynomially if both the number of machines and the number of jobs is fixed.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1432-5217
    Keywords: Key words: Combinatorial optimization ; complexity ; ℳ?-completeness ; scheduling ; assignment ; stack
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. In this note, we prove ??-completeness of the following problem: Given a set of trams of different types, which are stacked on sidings in their depot and an order in which trams of specified types are supposed to leave. Is there an assignment of trams to departure times without any shunting movements? In the particular case where the number of sidings is fixed, the problem is solvable in polynomial time. We derive a dynamic program and improve its performance by a state elimination scheme. We implemented three variants of the dynamic program and applied them to random data as well as to real-world data.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-5217
    Keywords: Quasi-inverse ; epi-inverse ; hypo-inverse ; nondecreasing functions ; quasiconvex functions ; convex functions ; duality ; rearrangement ; modulus of continuity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In dieser Arbeit wird systematisch die Umkehrung monoton nichtfallender Funktionenf: ℝ → ℝ ∪ {−∞, +∞} studiert. Die Ergebnisse bilden die Grundlage für eine neue Dualitätstheorie quasikonvexer Probleme [6]. Da jedoch die Fragestellung bei einer ganzen Anzahl weiterer Situationen auftritt, verdient sie eine gesonderte Behandlung. Anwendungen in der Topologie, Wahrscheinlichkeitstheorie, monotonen Umordnungen und in der konvexen Analysis werden aufgezeigt und skizziert.
    Notes: Abstract This work is devoted to a systematic study of the inversion of nondecreasing one variable extended real-valued functions. Its results are preparatory for a new duality theory for quasiconvex problem [6]. However the question arises in a variety of situations and as such deserves a separate treatment. Applications to topology, probability theory, monotone rearrangements, convex analysis are either pointed out or sketched.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-5217
    Keywords: vectorial control-approximation problem ; vectorial location problem ; duality ; efficiency
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In der Arbeit werden für eine Klasse von vektoriellen Steuer-Approximationsproblemen in reellen reflexiven Banachräumen vektorielle Dualprobleme konstruiert und Dualitätseigenschaften hergeleitet. Als Spezialfall ergeben sich entsprechende Aussagen für vektorielle Standortprobleme.
    Notes: Abstract The author formulates vectorial dual problems for a certain class of vectorial control-approximation problems in real reflexive Banach spaces. A number of propositions concerning duality are derived. Corresponding propositions are mentioned for the special case of the vectorial location problems.
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  • 7
    ISSN: 1432-5217
    Keywords: Markov decision processes ; countable state space ; Linear programming ; duality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We present an Linear Programming formulation of MDPs with countable state and action spaces and no unichain assumption. This is an extension of the Hordijk and Kallenberg (1979) formulation in finite state and action spaces. We provide sufficient conditions for both existence of optimal solutions to the primal LP program and absence of duality gap. Then, existence of a (possibly randomized) average optimal policy is also guaranteed. Existence of a stationary average optimal deterministic policy is also investigated.
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  • 8
    ISSN: 1432-5217
    Keywords: scheduling ; production ; resource constraints ; flexible manufacturing systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Abstract Some variations are presented for the preemptive scheduling problem on unrelated processors, one shows how nonrenewable resources with a time-varying supply may be taken into account in an extension of the two-phase method; phase 1 consists in solving an LP problem and phase 2 is the construction of the schedule; such a construction reduces to the determination of integral vectors in polyhedra defined by totally unimodular matrices. In special cases, this is simply a compatible flow problem.
    Notes: Zusammenfassung Es werden Variationen für Reihenfolgeprobleme mit Unterbrechungen betrachtet bei denen die Aufgaben mit unterschiedlicher Bearbeitungszeit auf den einzelnen Maschinen gelöst werden können. Insbesondere wird ein Problem mit nichterneuerbaren Resourcen und zeitabhängigen Nachfragen behandelt und es wird gezeigt, daß dieses Problem durch eine Erweiterung der 2-Phasenmethode gelöst werden kann. In Phase 1 wird ein LP gelöst, während in Phase 2 ein zugehöriger Schedule konstruiert wird. Diese Konstruktion erfolgt durch die Bestimmung ganzzahliger Vektoren, die Ecken eines Polyeders entsprechen, der durch eine vollständig unimodulare Matrix definiert wird. In Spezialfällen reduziert sich dies auf Flußprobleme.
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  • 9
    ISSN: 1432-5217
    Keywords: dynamic programming ; VLSI-layout ; scheduling ; reliability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We examine an algorithm for the compactification of an arrangement of rectangles in the plane as it is used for floorplans in the automated design of electronic circuits (also called sizing of floorplans). We reformulate this problem as a multistage decision problem and show that the algorithm is in fact the optimal solution obtained by the backward induction procedure of dynamic programing. The model allows generalisations to non-geometrical applications in scheduling and reliability.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-5217
    Keywords: Optimization theory ; mathematical programming ; duality ; half spaces ; minimum norm duality ; separating hyperplanes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This note shows that half spaces play a very special role in the development of duality. In addition to the minimum norm duality, the duality in linear programming, and Wolfe's and Johri's formulations in nonlinear programming can all be derived via half spaces by following an identical five step procedure.
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