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.