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Tree based models and algorithms for the preemptive asymmetric Stacker Crane problem

Hervé Kerivin, Mathieu Lacroix, Alain Quilliot, Hélène Toussaint (2011)

RAIRO - Operations Research

In this paper we deal with the preemptive asymmetric stacker crane problem in a heuristic way. We first present some theoretical results which allow us to turn this problem into a specific tree design problem. We next derive from this new representation an integer linear programming model together with simple and efficient greedy and local search heuristics. We conclude by presenting experimental results which aim at both testing the efficiency of our heuristic and evaluating the impact of the...

Trivial Cases for the Kantorovitch Problem

Serge Dubuc, Issa Kagabo, Patrice Marcotte (2010)

RAIRO - Operations Research

Let X and Y be two compact spaces endowed with respective measures μ and ν satisfying the condition µ(X) = v(Y). Let c be a continuous function on the product space X x Y. The mass transfer problem consists in determining a measure ξ on X x Y whose marginals coincide with μ and ν, and such that the total cost ∫ ∫ c(x,y)dξ(x,y) be minimized. We first show that if the cost function c is decomposable, i.e., can be represented as the sum of two continuous functions defined on X and Y, respectively,...

Two characterizations of Pareto minima in convex multicriteria optimization

Sanjo Zlobec (1984)

Aplikace matematiky

Two conditions are given each of which is both necessary and sufficient for a point to be a global Pareto minimum. The first one is obtained by studying programs where each criterion appears as a single objective function, while the second one is given in terms of a "restricted Lagrangian". The conditions are compared with the familiar characterizations of properly efficient and weakly efficient points of Karlin and Geoffrion.

Two hedging points policy for an unreliable manufacturing system

Ryszarda Rempała (2002)

Applicationes Mathematicae

This paper deals with an unreliable manufacturing system in which limited backlog is allowed. An admissible production policy is described by two decision parameters: upper and lower hedging points. The objective is to find the optimum hedging points so as to minimize the long run average expected cost under an additional condition. The condition expresses a constraint for the limiting probability of the event that the system stays at the lower hedging point, which corresponds to a limit of backlog....

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