It is well known that each tree metric M has a unique realization as a tree, and that this realization minimizes the total length of the edges among all other realizations of M. We extend this result to the class of symmetric matrices M with zero diagonal, positive entries, and such that mij + mkl ≤ max{mik + mjl, mil + mjk} for all distinct i,j,k,l.

In telecommunications network design, one of the most frequentproblems is to adjust the capacity on the links of the network in order to satisfy a set of requirements. In the past, theserequirements were demands based on historical data and/or demographic predictions. Nowadays, because of new technologydevelopment and customer movement due to competitiveness, thedemands present considerable variability. Thus, network robustness w.r.t demand uncertainty is now regarded as a majorconsideration. In this work, we propose a min-max-min formulation and a methodology to cope with this uncertainty. We model the uncertainty as the convex hull of certain scenarios and show thatcutting plane methods can be applied to solve the underlying problems. We will compare Kelley, Elzinga-Moore and bundle methods.


The Progressive Second Price mechanism (PSP), recently introduced byLazar and Semret to share aninfinitely-divisible resource among users through pricing, has been shown to verifyvery interesting properties. Indeed, the incentive compatibilityproperty of that scheme, and the convergence toan efficient resource allocation where established, using the frameworkof Game Theory.Therefore, that auction-based allocation and pricing scheme seemsparticularly well-suited to solve congestion problems intelecommunication networks, where the resource to share is theavailable bandwidth on a link.This paper aims atsupplementing the existing results by highlighting some properties of thedifferent equilibria that can be reached. We precisely characterize the possible outcomes of thePSP auction game in terms of players bid price: when the bid fee (cost of a bid update) tends to zero then the bid price of all users at equilibrium gets close to the so-called market clearing price of the resource. Therefore, observing an equilibrium of the PSP auction game gives some accurate information about the market clearing price of the resource.

In this paper we, firstly, present a recursive formula of theempirical estimator of the semi-Markov kernel. Then a non-parametricestimator of the expected cumulative operational time forsemi-Markov systems is proposed. The asymptotic properties of thisestimator, as the uniform strongly consistency and normality aregiven. As an illustration example, we give a numerical application.

Most systems are characterized by uncertainties that cause throughput to be highly variable, for example, many modern production processes and services are substantially affected by random yields. When yield is random, not only is the usable quantity uncertain, but the random yield reduces usable capacity and throughput in the system. For these reasons, strategies are needed that incorporate random yield. This paper presents the analysis of the newsvendor model with a general random yield distribution, including the derivation of the optimal order quantity. Results are shown to converge to the basic newsvendor model for the case of perfect yield, and are further demonstrated using the case of general multiplicative random yield. Results have significant impact on both manufacturing and service sectors since the newsvendor model applies to many real-world situations.

The m-subspace polytope is defined as the convex hull of the characteristic vectors of all m-dimensional subspaces ofa finite affine space. The particular case of the hyperplane polytopehas been investigated by Maurras (1993) and Anglada and Maurras (2003), who gave a complete characterization of the facets. The general m-subspace polytope that we consider shows a much more involved structure, notably as regards facets. Nevertheless, several families of facets are established here. Then the group of automorphisms of the m-subspace polytope is completely described and the adjacency of vertices is fully characterized.


Clique family inequalities a∑v∈W xv + (a - 1)∈v∈W , xv ≤ aδ form an intriguing class of valid inequalities for the stable set polytopes of all graphs. We prove firstly that their Chvátal-rank is at most a, which provides an alternative proof for the validity of clique family inequalities, involving only standard rounding arguments.Secondly, we strengthen the upper bound further and discuss consequences regarding the Chvátal-rank of subclasses of claw-free graphs.


Given a graph G = (V,E) and a “cost function” $f: 2^V\rightarrow\mathbb{R}$ (provided by an oracle), the problem [PCliqW] consists in finding a partition into cliques of V(G) of minimum cost. Here, the cost of a partition is the sum of the costs of the cliques in the partition.We provide a polynomial time dynamic program for the case where G is an interval graph and f belongs to a subclass of submodular set functions, which we call “value-polymatroidal”.This provides a common solution for various generalizations of the coloringproblem in co-interval graphs such as max-coloring,“Greene-Kleitman's dual”, probabilist coloring and chromatic entropy. In the last two cases, this is the first polytime algorithm for co-interval graphs. In contrast, NP-hardness of related problems is discussed. We also describe an ILP formulation for [PCliqW] which gives a common polyhedral framework to express min-max relations such as ${\overline{\chi}}=\alpha$ for perfect graphs and the polymatroid intersection theorem. This approach allows to provide a min-max formula for [PCliqW] if G is the line-graph of a bipartite graph and f is submodular.However, this approach fails to provide a min-max relation for [PCliqW] if G is an interval graphs and f is value-polymatroidal.

This paper is devoted to the exact resolution of a strongly NP-hard resource-constrained scheduling problem, the Process Move Programming problem, which arises in relation to the operability of certain high-availability real-time distributed systems. Based on the study of the polytope defined as the convex hull of the incidence vectors of the admissible process move programs, we present a branch-and-cut algorithm along with extensive computational results demonstrating its practical relevance, in terms of both exact and approximate resolution when the instance size increases.

Given a weighted undirected graph G = (V,E),a tree (respectively tour) cover of an edge-weighted graph is a set of edges which forms a tree (resp. closed walk) and covers every other edge in the graph. The tree (resp. tour) cover problem is of finding a minimum weight tree (resp. tour) cover of G. Arkin, Halldórsson and Hassin (1993) give approximation algorithms with factors respectively 3.5 and 5.5. Later Könemann, Konjevod, Parekh, and Sinha (2003) study the linear programming relaxations and improve both factors to 3. We describe in the first part of the paper a 2-approximation algorithm for the metric case of tree cover.In the second part, we will consider a generalized version of tree (resp. tour) covers problem which is to find a minimum tree (resp. tours) which covers a subset D ⊆ E of G.We show that the algorithms of Könemann et al.can be adapted for the generalized tree and tours covers problem with the same factors.

A co-biclique of a simple undirected graph G = (V,E) is the edge-set of two disjoint complete subgraphs of G.(A co-biclique is the complement of a biclique.)A subset F ⊆ E is an independent of G if there is a co-biclique B such that F ⊆ B, otherwise F is a dependent of G. This paper describes the minimal dependents of G. (A minimal dependent is a dependent C such that any proper subset of C is an independent.) It is showed that a minimum-cost dependent set of G can be determined in polynomial time for any nonnegative cost vector $x\in \mathbb Q_+^E$ . Based on this, we obtain a branch-and-cut algorithm for the maximum co-biclique problem which is, given a weight vector $w\in \mathbb Q_+^E$ , to find a co-biclique B of G maximizing w(B) = ∑e∈B we .

The minimum cost multiple-source unsplittable flow problem isstudied in this paper. A simple necessary condition to get asolution is proposed. It deals with capacities and demands and canbe seen as a generalization of the well-known semi-metriccondition for continuous multicommdity flows. A cutting planealgorithm is derived using a superadditive approach. Theinequalities considered here are valid for single knapsackconstraints. They are based on nondecreasing superadditivefunctions and can be used to strengthen the relaxation of anyinteger program with knapsack constraints. Some numericalexperiments confirm the efficiency of the inequalities introducedin the paper.

We discuss the use of operations research methods for computer-aided design of mechanical transmission systems. We consider how to choose simultaneously transmission ratios and basic design parameters of transmission elements (diameters, widths, modules and tooth number for gears, diameters of shafts). The objectives, by the order of importance, are: to minimize the deviation of the obtained speeds from desired; to maximize the transmission life; to minimize the total mass. To solve this problem, we propose a multi-level decomposition scheme in combination with methods of quadratic and dynamic programming. Some industrial cases are solved. For these cases, the developed software tool improves the design decisions by decreasing total metal consumption of the transmission as much as 7–10% and considerable simplifies the work of the designer.

This paper addresses a one-machine scheduling problem in which the efficiency of the machine is not constant, that is the duration of a task is longer in badly efficient time periods. Each task has an irregular completion cost. Under the assumption that the efficiency constraints are time-periodic, we show that the special case where the sequence is fixed can be solved in polynomial time. The general case is NP-complete so that we propose a two-phase heuristic to find good solutions. Our approach is tested on problems with earliness-tardiness costs.

L'opérateur de moyenne pondérée est très souvent utilisé pour définir une valeur v(a) à des entités a à partir de performances xj(a), j=1,...,n. Cet opérateur fait intervenir des poids spécifiquesw j comme multiplicateurs de la performance relative à la je composante. Ceci induit des possibilités de compensation des mauvaises performances par les meilleures qui peuvent être jugées inacceptables dans certains contextes concrets. En vue d'atténuer ces possibilités de compensation, on peut faire intervenir une seconde pondération à l'aide de poids de rangq r qui affectent le rôle que joue, dans la définition de v(a), la performance xj(a) en fonction du rang r qu'elle occupe dans un rangement des meilleures valeurs aux moins bonnes.Je commencerai par décrire trois exemples issus de contextes réels dans lesquels cette double pondération est nécessaire. Ensuite, je présenterai successivement un premier opérateur que j'ai introduit en 1996 sous le nom de moyenne ordonnée doublement pondérée (MO2P) et un second, proposé en 1997 par Torra [Int. J. Intell. Syst.12 (1997) 153–166.] “weighted ordered weighted average” (WOWA). Ces deux opérateurs n'étant signifiants que si les performances xj(a) se situent sur une même échelle d'intervalle E, je terminerai en proposant un autre type d'opérateur pouvant convenir lorsque E est une échelle purement ordinale.



The line balancing problem consits in assigning tasks to stations in orderto respect precedence constraints and cycle time constraints. In thispaper, the cycle time is fixed and the objective is to minimize the numberof stations. We propose to use metaheuristics based on simulated annealingby exploiting the link between the line balancing problem and the binpacking problem. The principle of the method lies in the combinationbetween a metaheuristic and a bin packing heuristic. Two representationsof a solution and two neighboring systems are proposed and the methods arecompared with results from the literature. They are better or similar totabu search based algorithm.


We address a multi-item capacitated lot-sizing problem with setup times that arises in real-world production planning contexts. Demand cannot be backlogged, but can be totally or partially lost. Safety stock is an objective to reach rather than an industrial constraint to respect. The problem is NP-hard. We propose mixed integer programming heuristics based on a planning horizon decomposition strategy to find a feasible solution. The planning horizon is partitioned into several sub-horizons over which a freezing or a relaxation strategy is applied. Some experimental results showing the effectiveness of the approach on real-world instances are presented. A sensitivity analysis on the parameters of the heuristics is reported.

This paper deals with a special case of Project Scheduling problem: there is a project to schedule, which is made up of activities linked by precedence relations. Each activity requires specific skills to be done. Moreover, resources are staff members who master fixed skill(s). Thus, each resource requirement of an activity corresponds to the number of persons doing the corresponding skill that must be assigned to the activity during its whole processing time. We search for an exact solution that minimizes the makespan, using a Branch-and-Bound method.