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Ce papier est consacré a un système de production à deux niveaux qui a une cadence de fabrication élevée et un contrôle de la qualité intégré. Le niveau haut comporte une seule machine qui approvisionne alternativement les deux machines du niveau bas. Le contrôle de la qualité est implémenté à l'entrée de chaque machine du niveau bas. Ce système de production est capable de produire des pièces de types différents. L'objectif consiste à minimiser le coût total conséquence du changement d'outils au niveau haut et du rejet des lots qui contiennent au moins une pièce défectueuse. Nous étudions le cas particulier (machines identiques au niveau bas) et le cas général.

Hierarchical production planning systems attract today much attention of both management scientists and practitioners. Hierarchical production planning systems are often decomposed into three decision-making levels, i.e. a medium term level, a short term level, and a very short term level. This paper presents a medium term production planning model. At first, all machines which can perform the same operation are aggregated. Group technology is used to decompose the system into several subsystems, then specific attention is given on how to aggregate the subsystems. Similarly, parts are aggregated. We end up with an aggregate planning model involving production subsystems and part families.

In this paper, we use event graphs, a paricular type of Petri nets, to evaluate job-shops when manufacturing times are random variables and the control is defined as the sequence of product types at the entrance of each machine. Under very general assumptions, we prove that the cycle time of the system converges in probability to a constant and asymptotically tends in distribution to a normal distribution whose standard deviation tends to zero. We also provide a lower bound of the main cycle time. We finally derive from the previous results a heuristic algorithm which leads to a near optimal solution of the problem (an optimal solution being the minimal work-in-process which allows the maximal productivity, i.e. the minimal cycle time, knowing the control).

Ce papier est consacré au problème de gestion de stocks à deux niveaus. La demande est connue sur [0,N], où N est l'horizon du problème. Les coûts de stockage et de commande sont supposés concaves et non décroissants. Nous montrons que la politique optimale est, pour le niveau haut, identique à la politique optimale bien connue du cas mono-produit. Au niveau bas, les propriétés de cette politique sont plus compliquées, surtout lorsque l'on trouve plusieurs stocks à ce niveau. Dans la suite, nous considérons ce cas général.

We present an algorithm which considers a set of product types and a set of machine types. The algorithm works out a partition of p subsets of product types, called product families, and a partition of q subsets of machine types, called production subsystems such that : either p = q and there exists a one-to-one relationship between and product families production subsystems, or p = q + 1 (or q = p + 1) and there exists a one-to-one relationship between r product families and production subsystems where r is the minimum value of p and q. The supplementary subset of product (or machine) types has non corresponding subset of machine (or product) types. In both cases the partitions obtained maximize a criterion which is the weighted sum of normalized processing times of each product family in its related production subsystem and the complements of normalized processing times of each product family outside its related production subsystem. In the latter case the supplementary subset of product (or machine) types contains only products which have insignificant processing times (or machines which are only rarely or briefly involved by product transformation). We prove the convergence of our algorithm and give some numerical results. The presentation is closed with the description of an implementation of the algorithm for large data sets.

We study the relationship between buffer capacity and productivity in a system consisting of a flexible cell feeding several dediciated machines. The processing times at both the flexible cell and the dedicated machines are random variables. Each dedicated machine has a finite local buffer to hold parts that are waiting to be processed and the flexible cell is required to produce parts according to specified production ratios. We develop a simple analytic estimate for machine utilization in steady state for this system. Such an analytic estimate may be useful in the planning stages of this kind of manufacturing system both in terms of understanding the tradeoff between increasing buffer capacity and utilization and in estimating the appropriate size and distribution of buffers in the system. Comparison with simulation for the case of exponential processing times indicate that the estimate works reasonably well.

This paper is devoted to the two-product problem with joint production costs and independent inventory costs. It gives an algorithm which leads to the optimal policy in the infinite horizon case. This algorithm is the extension of the celebrated E0Q formula which was obtained for the mono-product problem.

The scheduling of parts in a production system is an NP-complete problem. To search an optimal solution is incompatible with the "real time" constraint. The usual procedures (clusters-job, introduction of constraints on the fabrication starting time, hierarchical schedulind) all contribute to vanish the combinatorial aspect of the problem. We propose to memorize some behaviour-classes and to use them in order to choose the management rule in relation with the aimed targets. A numerical example will describe this approach.

Ce papier donne un algorithme qui conduit à une partition d'un ensemble de n objets en p classes (p << n). L'objectif est de minimiser la somme des inerties des p classes. Nous montrons une méthode pour obtenir une bonne situation initiale.

Dans la suite, nous proposons deux méthodes utilisables pour classer les résultats obtenus en utilisant différentes règles pour gérer un système de production. L'objectif essentiel de ce travail est d'obtenir des classes de résultats qu'il est possible de qualifier et de représenter simplement.