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 spécifiqueswj 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 rangqr 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.



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.

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.

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.

The line balancing problem consits in assigning tasks to stations in order to respect precedence constraints and cycle time constraints. In this paper, the cycle time is fixed and the objective is to minimize the number of stations. We propose to use metaheuristics based on simulated annealing by exploiting the link between the line balancing problem and the bin packing problem. The principle of the method lies in the combination between a metaheuristic and a bin packing heuristic. Two representations of a solution and two neighboring systems are proposed and the methods are compared with results from the literature. They are better or similar to tabu search based algorithm.


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.