Dans cet article nous caractérisons, par les facettes, l'enveloppe convexe des vecteurs caractéristiques des hyperplans d'un espace projectif fini et d'un espace affine fini.

Le traditionnel problème d'ordonnancement de type flowshop se généralise en un problème d'optimisation matricielle dansl'algèbre Max-Plus. Une famille de bornes inférieures est présentée pour ce nouveau problème et la preuve est apportée que ces bornes généralisent les bornes de Lageweg et al.

In this paper, a graph partitioning problem that arises in the design ofSONET/SDH networks is defined and formalized. Approximation algorithms withperformance guarantees are presented. To solve this problem efficiently inpractice, fast greedy algorithms and a tabu-search method are proposed andanalyzed by means of an experimental study.

In this paper we consider the problem of scheduling precedence task graphs inparallel processing where there can be disturbances in computation andcommunication times. Such a phenomenon often occurs in practice, due to ourinability to exactly predict the time because of system intrusion like cache miss and packet transmission time in mediums like ethernet etc. We propose a method based on the addition of some extra edges to protect the initial scheduling from performing badly due to such changes and provide an upper bound on theperformance guarantee for the scheduling algorithms. Moreover, this construction guarantees a result at least as goodas the result obtained for the initial static scheduling.We also show that this construction is a minimal set in context of partially on-line scheduling.

This paper studies the issue of well-posednessfor vector optimization. It is shown thatcoercivity implies well-posedness without any convexity assumptionson problem data.For convex vector optimization problems,solution sets of such problems are non-convex in general,but they are highly structured. By exploring such structures carefully via convex analysis,we are able to obtaina number of positive results, including a criterion for well-posedness in terms of that of associated scalar problems.In particularwe show that a well-known relative interiority conditioncan be used as a sufficient condition for well-posedness in convexvector optimization.

In this paper we consider a like-queue production system in which server startupand breakdowns are possible. The server is turned on (i.e. begins startup)when N units are accumulated in the system and off when the system is empty.We model this system by an M[x]/M/1 queue withserver breakdowns and startup time under the N policy. The arrival rate varies according to the server's status:off, startup, busy, or breakdown.While the server is working, he is subject tobreakdowns according to a Poisson process. When the server breaks down, he requires repairat a repair facility, where the repair time follows the negative exponential distribution.We study the steady-state behaviour of the system size distribution atstationary point of time as well as the queue size distribution at departure point of timeand obtain some useful results.The total expected cost function per unit time is developed to determine the optimal operatingpolicy at a minimum cost. This paper provides the minimum expected cost and the optimal operatingpolicy based on assumed numerical values of the system parameters. Sensitivity analysis is also provided.

In this paper, we study the problem of computing a minimum cost Steiner tree subject to a weight constraint in a Halin graph where each edge has a nonnegative integer cost and a nonnegative integer weight. We prove the NP-hardness of this problem and present a fully polynomial time approximation scheme for this NP-hard problem.

We present a transformation for stochastic matrices and analyze theeffects of using it in stochastic comparison with the strong stochastic(st) order. We show that unless the given stochastic matrix is row diagonallydominant, the transformed matrix provides better st bounds on the steady state probability distribution.

Les méthodes de points intérieurs en programmation linéaireconnaissent un grand succès depuis l'introductionde l'algorithme de Karmarkar. La convergence de l'algorithme repose sur unefonction potentielle qui, sous saforme multiplicative, fait apparaître un exposant p. Cet exposantest, de façongénérale, choisi supérieur au nombre de variables n du problème.Nous montrons dans cetarticle que l'on peut utiliser des valeurs dep plus petites que n. Ceci permet d'améliorer le conditionnement dela méthode au voisinage de la solution optimale.

In this paper, we study a heuristic algorithm for global optimization, which is based on the Ψ-transformation. We illustrate its behavior first, on a set of continuous non-convex objective functions – we search the global optimum of each function. Then, we give an example from combinatorial optimization. It concerns the optimization of scheduling rules parameters of a manufacturing system. Computational results are presented, they look encouraging.

A recently introduced dualization technique for binary linear programs with equality constraints, essentially due to Poljak et al. [13], and further developed in Lemaréchal and Oustry [9], leads to simple alternative derivations of well-known, important relaxations to two well-known problems of discrete optimization: the maximum stable set problem and the maximum vertex cover problem. The resulting relaxation is easily transformed to the well-known Lovász θ number.

This paper is concerned with scheduling when the data are not fully knownbefore the execution. In that case computing a complete schedule off-linewith estimated data may lead to poor performances. Some flexibility must beadded to the scheduling process. We propose to start from a partial schedule and to postpone the complete scheduling until execution, thus introducing what we call a stabilizationscheme. This is applied to the m machine problem with communicationdelays: in our model an estimation of the delay is known at compile time; but disturbances due to network contention, link failures, ... may occur at execution time. Hence the processor assignment and a partial sequencing on each processor are determined off-line. Some theoreticalresults for tree-like precedence constraints and an experimental study show the interest of this approach compared with fully on-line scheduling.

The classical colouring models are well known thanks in large part to their applications to scheduling type problems; we describe the basic concepts of colourings together with a number of variations and generalisations arising from scheduling problems such as the creation of school schedules. Some exact and heuristic algorithms will be presented, and we will sketch solution methods based on tabu search to find approximate solutions to large problems. Finally we will also mention the use of colourings for creating schedules in sports leagues and for computer file transfer problems. This paper is an extended version of [37].

Retrial queueing systems are characterized by the requirement that customersfinding the service area busy must join the retrial group and reapply forservice at random intervals. This paper deals with the M/G/1 retrial queuesubjected to breakdowns. We use its stochastic decomposition property toapproximate the model performance in the case of general retrial times.

In this paper, we focus on some specific optimization problems from graphtheory, those for which all feasible solutions have an equal sizethat depends on the instance size.Once having provided a formal definition of this class ofproblems, we try to extract some of its basic properties; most ofthese are deduced from the equivalence, under differentialapproximation, between two versions of a problem π which onlydiffer on a linear transformation of their objective functions.This is notably the case of maximization and minimization versionsof π, as well as general minimization and minimization withtriangular inequality versions of π. Then, we prove that somewell known problems do belong to this class, such as special casesof both spanning tree and vehicles routing problems. Inparticular, we study the strict rural postman problem(called SRPP) and show that both the maximization and theminimization versions can be approximately solved, in polynomialtime, within a differential ratio bounded above by 1/2.From these results, we derive new bounds for standard ratiowhen restricting edge weights to the interval [a,ta] (theSRPP[t] problem): we respectively provide a 2/(t+1)- and a(t+1)/2t-standard approximation for the minimization and themaximization versions.

This paper is the continuation of the paper “Autour de nouvelles notions pour l'analyse desalgorithmes d'approximation: Formalisme unifié et classesd'approximation” where a new formalism for polynomialapproximation and its basic tools allowing an “absolute”(individual) evaluation the approximability properties ofNP-hard problems have been presented and discussed. Inorder to be used for exhibiting a structure for theclass NPO (the optimization problems of NP),these tools must be enriched with an “instrument” allowingcomparisons between approximability properties of differentproblems (these comparisons must be independent on any specificapproximation result of the problems concerned). This instrumentis the approximability-preserving reductions. We show how tointegrate them in the formalism presented and propose thedefinition of a new reduction unifying, under a specific point ofview a great number of existing ones. This new reduction allowsalso to widen the use of the reductions, restricted until noweither between versions of a problem, or between problems, inorder to enhance structural relations between frameworks. Theyallow, for example, to study how standard-approximation propertiesof a problem transform into differential-approximation ones (forthe same problem, or for another one). Finally, we apply theseveral concepts introduced to the study of the structure (andhardness) of the instances of a problem. This point of view seemsparticurarly fruitful for a better apprehension of the hardness ofcertain problems and of the mechanisms for the design of efficientsolutions for them.

In the present paper a complete procedure for solvingMultiple Objective Integer Linear Programming Problems is presented. The algorithm can be regarded as a corrected form and an alternative to the method that was proposed by Gupta and Malhotra. A numerical illustration is given to show that this latter can miss some efficient solutions. Whereas, the algorithm stated bellow determines all efficient solutions without missing any one.

We show that a particular dynamic priority given to jobs in a multitasks operating system of computers is a deteriorating jobs or a delaying jobs scheduling. Under some assumptions we also show that it is an index rule. To do this, we present the tool of bandit processes to solve stochastic scheduling problems on a single machine.

In this paper a two-stage algorithm for finding non- dominated subsets of partially ordered setsis established. A connection is then made with dimension reduction in time-dependentdynamic programming via the notion of a bounding label, a function that boundsthe state-transition cost functions. In this context, the computational burden is partitionedbetween a time-independent dynamic programming step carried out on the bounding label anda direct evaluation carried out on a subset of “real" valued decisions. A computationalapplication to time-dependent fuzzy dynamic programming is presented.

This paper considers two backup schemes for a database system: a database is updated at a nonhomogeneous Poisson process and an amount of updated files accumulates additively. To ensure the safety of data, full backups are performed at time NT or when the total updated files have exceeded a threshold level K, and between them, cumulative backups as one of incremental backups are made at periodic times iT(i = 1,2,...,N - 1). Using the theory of cumulative processes, the expected cost is obtained, and an optimal number N* of cumulative backup and an optimal level K* of updated files which minimize it are analytically discussed. It is shown as examples that optimal number and level are numerically computed when two costs of backup schemes are given.