Gestion conjointe de production et qualité appliquée aux lignes de production non fiables

RÉSUMÉ Cette recherche s'intéresse aux lignes de production non fiables formées de plusieurs machines satisfaisant une demande fixe de produits finis de type unique et comprenant des stocks d'encours à capacité fixe. Deux types de machines sont considérés ici: un type de machine dont une partie de la production est non conforme aux normes de la qualité et un autre type de machine dont la production est 100 % conforme. La thèse est organisée selon trois contributions principales. L'objectif visé dans la première partie est de développer des modèles d'analyse de performance et des techniques d'optimisation efficaces pour le réglage des paramètres de conception suivant une approche de contrôle de type CONWIP (Constant Work-In-Process). Notre recherche s'inscrit dans le courant des approches de décomposition des ateliers de fabrication. L'analyse de la performance de ces systèmes aléatoires discrets/continus repose essentiellement sur les équations de Kolmogorov et le principe de la demande moyenne. De plus, nous introduisons des blocs de construction formés de paires de stock local-machine globale. La machine globale commune à toutes ces paires permet alors d'introduire une mesure de corrélation importante entre tous les blocs de construction quelle que soit la distance des stocks qui entrent dans leur composition. Ceci permet de créer des liens entre blocs de construction de la décomposition qui se situent au-delà de leurs voisinages respectifs, comme c'est le cas dans d'autres méthodes de décomposition. Cet aspect de corrélation des machines est caractéristique de la stratégie de production CONWIP. De plus, dans notre modélisation globale, la dynamique totale du stock dans la boucle CONWIP est considérée comme étant essentiellement affectée par les statistiques de fiabilité de la machine M1, et la probabilité de disponibilité des pièces dans le stock (n-1), reflétant ainsi l'opinion que le CONWIP est une forme de Kanban imposée à une collection de machines.----------ABSTRACT This research is concerned with unreliable production lines. Two types of machines are considered here: a machine for which part of the production is part substandard in quality and a machine whose production is 100% in conformity. The thesis is organized according to three principal contributions. In the first part of our research and for a given choice of the maximum allowable total storage parameter, the performance of constant work-in-process (CONWIP) disciplines in unreliable transfer lines subjected to a constant rate of demand for parts is characterized via a tractable approximate mathematical model. For a (n-1) machines CONWIP loop, the model consists of n multi-state machine single buffer building blocks, separately solvable once a total of (n-1)2 unknown constants shared by the building blocks are initialized. The multi-state machine is common to all building blocks, and its n discrete states approximate the joint operating state of the machines within the CONWIP loop; each of the first (n-1) blocks maps into a single internal buffer dynamics, while the nth building block characterizes total work-in-process (wip) dynamics. The blocks correspond to linear n component state equations with boundary conditions. The unknown (shared) constants in the block dynamics are initialized and calculated by means of successive iterations. The performance estimates of interest, mean total wip, and probability of parts availability at the end buffer in the loop are obtained from the model and validated against the results of Monte-Carlo simulations. In the second part of our research, we address the optimal production control problems for an unreliable manufacturing system that produces items that can be regarded as conforming or non conforming. A new stochastic hybrid state Markovian model with three discrete states, also called modes is introduced. The first two, operational sound and operational defective are not directly observable, while the third mode, failure, is observable. Production of defective parts is respectively initiated and stopped at the random entrance times to and departure times from the defective operational mode. The intricate piecewise-deterministic dynamics of the model are studied, and the associated Kolmogorov equations are developed under the suboptimal class of hedging policies

Optimal planning of buffer sizes and inspection station positions

The problem of buffer sizing and inspection stations positioning in unreliable production lines is a complex mixed integer nonlinear optimization problem. In this problem, we have a production line with n machines and n fixed-size (storage) buffers in series. The machines produce parts that are either conforming or nonconforming, and the line includes inspection stations that reject the nonconforming pats. The goal is to find the optimal buffer sizes, the number and positions of the inspection stations, and satisfy the customer demand on conforming parts while minimizing the total cost. We present in this paper an exact method to solve this complex manufacturing problem. We also present new theoretical results on buffer-size bounds, stationarity, and cost function convexity permitting to significantly reduce the problem complexity. These theoretical and algorithmic developments allow solving to optimality instances with up to 30 machines tools developed previously cannot solve

Multilevel hybrid method for optimal buffer sizing and inspection stations positioning

Designing competitive manufacturing systems with high levels of productivity and quality at a reasonable cost is a complex task. Decision makers must face numerous decision variables which involve multiple and iterative analysis of the estimated cost, quality and productivity of each design alternative. This paper adresses this issue by providing a fast algorithm for solving the buffer sizing and inspection positioning problem of large production lines by combining heuristic and exact algorithms. We develop a multilevel hybrid search method combining a genetic algorithm and tabu search to identify promising locations for the inspection stations and an exact method that optimizes rapidly (in polynomial time) the buffers' sizes for each location. Our method gives valuable insights into the problem, and its solution time is a small fraction of that required by the exact method on production lines with 10-30 machines