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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
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-5217
    Keywords: Key words: Stochastic scheduling ; dynamic programming ; index policies ; monotone failure rates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. In this paper we apply a new framework for the study of monotonicity in queueing systems to stochastic scheduling models. This allows us a unified treatment of many different models, among which are multiple and single server models (with and without feedback), discrete and continuous time models, models with controlled and uncontrolled arrivals, etc.
    Type of Medium: Electronic Resource
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  • 3
    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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  • 4
    ISSN: 1432-5217
    Keywords: linear arrangement ; dynamic programming ; NP-completeness ; Linear Arrangement ; dynamische Programmierung ; NP-Vollständigkeit
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Wir analysieren die Komplexität von eingeschränkten Linear Arrangement Problemen, bei denen nur solche Permutationen der Knoten erlaubt sind, die durch die Ordnung eines die Knoten des Graphen strukturierenden, binären Baumes — des sogenannten P-tress — entstehen. Derartige Versionen von Linear Arrangement Problemen tauchen an mehreren Stellen in heutigen Schaltkreis Layout Systemen auf. Der P-tree resultiert dabei aus einem rekursiven Zerteiluungsprozeß des Graphen. Wir zeigen, daß das MINCUT LINEAR ARRANGEMENT und das OPTIMAL LINEAR ARRANGEMENT Problem in polynomieller Zeit lösbar sind, wenn der P-tree balanciert ist. Alle anderen betrachteten Versionen von Linear Arrangement Problemen sind NP-vollständig.
    Notes: Abstract We analyze the complexity of the restrictions of linear arrangement problems that are obtained if the legal permutations of the nodes are restricted to those that can be obtained by orderings of a binary tree structuring the nodes of the graph, the so-called p-tree. These versions of the linear arrangement problems occur in several places in current circuit layout systems. There the p-tree is the result of a recursive partitioning process of the graph. We show that the MINCUT LINEAR ARRANGEMENT problem and the OPTIMAL LINEAR ARRANGEMENT problem can be solved in polynomial time, if the p-tree is balanced. All other versions of the linear arrangement problems we analyzed are NP-complete.
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  • 5
    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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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-5217
    Keywords: Subset selection ; checking procedure ; dynamic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract An item having a known initial failure probability is to be controlled by some out of a finite set of possible checks. Every check costs a certain amount of money, and budget constraints must be met. A check is characterized by the probabilities of three events: (i) letting a workable item pass, (ii) overlooking a failure if one is present, (iii) introducing a failure into a workable item. We show how any subset of checks to be employed is ordered optimally, and how the optimal subsequence of checks depends on the initial failure probability and oil the budget constraint.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-5217
    Keywords: Optimal choice problem ; dynamic programming ; pseudopolynomial algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract An item has probabilityp 0 of not being workable. Before, going into use it has to be controlled by some deliberately chosen checksC i which costsc i ≥0,1≤i≤n. Total checking costs must be not larger thanc 0〉0. It may happen that a check breaks a workable item, and failures may be overlooked. The problem is to determine an optimal sequence of checks subject to the cost constraints, such that the probability is maximized that an item leaving the checks is workable. In [1] this problem is solved by W. Stadje, but numerically the solution method only is applicable to problems of modest size. In this paper a simple reformulation of the original problem is presented. This first allows a simpler derivation of some of the results in [1]. Further, a dynamic programming algorithm is presented, which is pseudopolynomial, if costsc i are integers. It then requiresO(n·c 0) time.
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  • 8
    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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  • 9
    ISSN: 1432-5217
    Keywords: Scheduling ; dynamic programming ; μc rule ; repairman assignment
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The scheduling of a single server in a finite source model is considered. TheN customers in the system have different failure and repair rates. Also the costs depend on the customers which are broken down. We give a condition under which the average costs are minimized by a simple list policy, and with a counterexample we show that in the general case no optimal list policy may exist. This motivates us to derive policies which are optimal under low and high traffic conditions. They are again list policies, which behave well numerically.
    Type of Medium: Electronic Resource
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  • 10
    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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