We propose a parallel algorithm which uses bothMonte-Carlo and quasi-Monte-Carlo methods. A detailed analysis of thisalgorithm, followed by examples, shows that the estimator's efficiencyis a linear function of the processor number. As a concrete applicationexample, we evaluate performance measures of a multi-class queueingnetwork in steady state.

The aim of this paper is to present a new branch and boundmethod for solving the Multi-Processor Flow-Shop. This method is based on the relaxation of the initial problem to m-machine problems corresponding to centers. Release dates and tails are associated with operations andmachines. The branching scheme consists in fixing the inputs of a critical centerand the lower bounds are those of the m-machine problem. Several techniques for adjusting release dates and tails have also been introduced. As shown byour personal study, the overall method is very efficient.

In this paper, a model of the load transfer on a fullyconnected net is presented. Each processor can accept at most K tasks.A load difference of two tasks between two processors is a prohibitedsituation and when it may appear, an immediat and instantaneous transferis decided.The performances of the system are evaluated by the following indices:the reject probability, the throughput, the mean response time, thestationary probability distribution for a processor to host i tasks.The aim of this study is to evaluate the load transfer inpact thanks tothe comparison between the values of the indices without transfer andwith transfer. In particular the asymptotic behaviour for massivelyparallel systems is studied and interpreted. Calculated with an idealsituation, these comparisons yield upper bounds on the benefits that canbe expected from a transferring policy. Beyonds, the opportunity of thetransfer according to the values of the parameters can be studied. Themean number of transfers executed within a time unit and the mean numberof transfers of a given task are calculated. At last values of theindices when the number of accepted tasks K grows to infinity isstudied.

We describe an O.R. technique which plans the allotment of time of the collaborators of a big company. The proposed method not only considers the immediate profitability of the company, but also thetraining of the collaborators in order to guarantee the success of the company'srising generation. The proposed method uses a greedy approach and constitutes therefore a simple and fast tool for decision makers. It has beensuccessfully implemented in an important Swiss bank society.

Let X and Y be two compact spaces endowed withrespective 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 onX x Y whose marginals coincide with μ and ν, and such thatthe total cost ∫ ∫ c(x,y)dξ(x,y) be minimized. We firstshow that if the cost function c is decomposable, i.e., can berepresented as the sum of two continuous functions defined on X andY, respectively, then every feasible measure is optimal. Conversely,when X is the support of μ and Y the support of ν and whenevery feasible measure is optimal, we prove that the cost function isdecomposable.

The Algorithm in this paper is designed to find theshortest path in a network given time-dependent cost functions. It hasthe following features: it is recursive; it takes place bath in abackward dynamic programming phase and in a forward evaluation phase; itdoes not need a time-grid such as in Cook and Halsey and Kostreva andWiecek's "Algorithm One”; it requires only boundedness (above andbelow) of the cost functions; it reduces to backward multi-objectivedynamic programming if there are constant costs. This algorithm has beensuccessfully applied to multi-stage decision problems where the costsare a function of the time when the decision is made. There are examplesof further applications to tactical delay in production scheduling andto production control.

Given a graph with colored edges, a Hamiltonian cycle iscalled alternating if its successive edges differ in color. The problemof finding such a cycle, even for 2-edge-colored graphs, is triviallyNP-complete, while it is known to be polynomial for 2-edge-coloredcomplete graphs. In this paper we study the parallel complexity of finding such a cycle, if any, in 2-edge-colored complete graphs. We givea new characterization for such a graph admitting an alternatingHamiltonian cycle which allows us to derive a parallel algorithm forthe problem. Our parallel solution uses a perfect matching algorithmputting the alternating Hamiltonian cycle problem to the RNC class. Inaddition, a sequential version of our parallel algorithm improves thecomputation time of the fastest known sequential algorithm for thealternating Hamiltonian cycle problem by a factor of $O(\sqrt {n} )$ .

We first motivate and define a notion of asymptoticdifferential approximation ratio. For this, we introduce a new class ofproblems called radial problems including in particular the hereditaryones. Next, we validate the definition of the asymptotic differentialapproximation ratio by proving positive, conditional and negativeapproximation results for some combinatorial problems. We first derive adifferential approximation analysis of a classical greedy algorithm forbin packing, the “first fit decreasing”. Next we deal with minimumvertex-covering-by-cliques of a graph and the minimumedge-covering-by-complete-bipartite-subgraphs of a bipartite graph anddevise a differential-approximation preserving reduction from the formerto the latter. Finally, we prove two negative differential approximationresults about the ability of minimum vertex-coloring to be approximatedby a polynomial time approximation schema.

In this paper, we develop some stochastic dominancetheorems for the location and scale family and linear combinations ofrandom variables and for risk lovers as well as risk averters thatextend results in Hadar and Russell (1971) and Tesfatsion (1976). Theresults are discussed and applied to decision-making.

Our concern here, is the characterization of dissimilarity indexes defined over finite sets, whose spatial representation is spherical. Consequently, we propose a methodology (NormedMultiDimensional Scaling) to determine the spherical euclidean representation of a set ofitems best accounting for the initial dissimilarity between items. Thismethodology has the advantage of being graphically readable on individual qualitiesof projection like the normed PCA, of which it constitutes a generalization. Moreover, it avoids the arbitrary character of spherical encoding which the use of similitude functions currently used in MDS, implies.

We address the 3-Machine Assembly-Type Flowshop Scheduling Problem (3MAF). This problem is known to be NP-complete in the strongsense. We propose an exact branch and bound method based on a recursiveenumeration of potential inputs and outputs of the machines. Using this algorithm,several large size instances have been solved to optimality.

The relations between automatic clustering methods and inferentiel statistical models have mostely been studied when the data involves only one set. We propose to study these relations in the caseof data involving two sets. We shall look at cross clustering methods assuggested by Govaert [6]; we show that these methods, like the simple clusteringmethods, can be considered as a clustering approach of a mixture model. Weintroduce the notion of crossed mixture from a concret example and define thenotions of likelihood and associated clustered likelihood. Then, we study therelations which exist between the crossed mixture models and simple models and weshow that these relations are completely similar to those which exist betweenthe crossed clustering methods and simple clustering methods.

Fractional programming consists in optimizing a ratio oftwo functions subject to some constraints. Different versions of thismodel, linear or nonlinear, have applications in various fields likecombinatorial optimization, stochastic programming, data bases, andeconomy. Three resolution methods are presented: direct solution,parametric approach and solution of an equivalent problem.

This paper presents an application of Multiple Attribute Utility Theory onstrategic choices concerning energy transportation. The environmental assessmentof a network reinforcement strategy is emphasized. Our assessment bringsabout to consider multidimensional variables in MCDM. However, Multi-AttributedUtility Theory (MAUT) cannot, as a practical matter, manage such variables. We therefore work out a methodology to transform multidimensional variablesinto unidimensional ones. We apply it then to a pratical case. From the application, we draw some conclusions on Multi-Attributed Utility Theoryand on its interest for strategic choices dealing with environmental consequences.

We consider a generalized proximal point method (GPPA) forsolving the nonlinear complementarity problem with monotone operators inRn . It differs from the classical proximal point method discussedby Rockafellar for the problem of finding zeroes of monotone operatorsin the use of generalized distances, called φ-divergences,instead of the Euclidean one. These distances play not only aregularization role but also a penalization one, forcing the sequencegenerated by the method to remain in the interior of the feasible set,so that the method behaves like an interior point one. Under appropriateassumptions on the φ-divergence and the monotone operator weprove that the sequence converges if and only if the problem hassolutions, in which case the limit is a solution. If the problem doesnot have solutions, then the sequence is unbounded. We extend previousresults for the proximal point method concerning convex optimizationproblems.

Comparing q-ary relations on a set ${\cal O}$ ofelementary objects is one of the most fundamental problems ofclassification and combinatorial data analysis. In this paper thespecific comparison task that involvesclassification tree structures (binary or not) is considered in thiscontext. Two mathematical representationsare proposed. One is defined in terms of a weighted binary relation; the second uses a 4-ary relation.The most classical approaches to tree comparison are discussed in thecontext of a set theoretic representation of these relations. Formalandcombinatorial computing aspects of a construction method for a verygeneralfamily of association coefficients between relations are presented. The main purpose of this article is to specify the componentsof this construction, based on a permutational procedure, when thestructuresto be compared are classification trees.

An algebraic and combinatorial approach to the study ofthe Quadratic Assignment Problem produced theoretical results that canbe applied to (meta) heuristics to give them information about theproblem structure, allowing the construction of algorithms. In thispaper those results were applied to inform a Simulated Annealing-typeheuristic (which we called RedInv-SA). Some results from tests withknown literature instances are presented.