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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: 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.
    Type of Medium: Electronic Resource
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  • 3
    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.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1432-5217
    Keywords: Scheduling ; Time complexity ; GERT networks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper deals with single machine scheduling problems with stochastic precedence relations (so calledGERT networks). Until now most investigations on such problems, dealt with algorithms running in polynomial time. On the other hand, for scheduling problems with deterministic precedence relations exist a lot of results about time complexity. Therefore, the object of this paper is to consider time complexity of scheduling problems with stochastic precedence constraints and to describe the boundary between theNP-hard problems and those which can be solved in polynomial time.
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 1432-5217
    Keywords: Scheduling ; resource constraint ; flowshop
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper we address the problem of scheduling unit time jobs in a flowshop to minimize makespan under a discrete renewable resource constraint. We propose algorithms having complexityO(n) for special cases of two machine and three machine problems. For the three machineN P-hard problem we develop a branch and bound procedure and several upper and lower bounds. We test the efficiency of the procedure and report our computational experience.
    Type of Medium: Electronic Resource
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  • 6
    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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  • 7
    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.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-5217
    Keywords: Scheduling ; Schur-convexity ; rearrangement inqualities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Diese Note behandelt das Problem, die Spaltenelemente einer reellen Matrix so zu permutieren, daß eine reellwertige Funktion der Zeilensummen minimiert wird. Der Spezialfall der Minimierung der maximalen Zeilensumme wurde jüngst von mehreren Autoren [1, 4, 6, 7] untersucht. Hier betrachten wir primär den Fall, daß die Matrix nur zwei Spalten hat und die Zielfunktion Schur-konvex ist.
    Notes: Abstract This note deals with the problem of permuting elements within columns of a real matrix so as to minimize a real-valued function of row sums. The special case dealing with minimization of maximum row sum has been studied by several authors [1, 4, 6, 7] recently. Here we are concerned primarily with the case in which the matrix has two columns only and the function is Schur-convex.
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  • 9
    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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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-5217
    Keywords: Scheduling ; open shop
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We consider open shop problems with unit processing times,n jobs have to be processed onm machines. The order in which a given job is processed on the machines is not fixed. For each job a release time or a due date may be given. Additional, we consider the restriction that every machine must perform all corresponding operations without any delay time. Unit time open shop problems with release times to minimize total completion time were unsolved up to now for both allowed and forbidden delay times. We will solve these problems in the case of two and three machines. Furthermore we will give polynomial algorithms for several no-delay-problems with due dates.
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