Commande des systèmes de production non fiables avec contrôle de la qualité

Abstract

This work deals with the problem of optimal stochastic control of an unreliable production system with quality control. The system consists of a single machine producing a single type of product (M1P1) subject to random failures and repairs and must satisfy a constant rate customer demand. The machine produced with a defective rate, in order to reduce the amount of bad parts that would go to the customer, a product inspection is done. It is done continuously and consists of controlling a part or fraction of the production. Good products are put back on the production line, while bad products are destroyed. The objective of this work is to propose an optimal production policy that will minimize the total cost consisting of holding and backlog cost, the inspection cost, the waste cost and the cost of returned parts by the customer. The decision variables are the production rate of the system and the fraction of production to be controlled. The state variable is the inventory level of finished products. We have developed a stochastic optimal control model of the problem posed by using homogeneous Markov chains to describe the system (machine dynamics). Applying the control theory based on dynamic programming, we developed optimum conditions that were of the Hamilton-Jacobi-Bellman (HJB) type. By a numerical approach of resolution of these equations (Kushner and Dupuis, 1992), we obtained an optimal policy with critical threshold. A simulation approach combined with experimental designs and surface methodology response allowed us to obtain the optimal values of the policy parameters that minimize the total production cost. From the simulation model, we have treated several scenarios to bring variability to our system. First, we introduced a constraint to average outgoing quality of products (AOQ) that would end up at the customer. This allowed to establish an equation which can determine the fraction to be controlled according to the desired level of quality. Then, we considered a probability of error during the control of the quality of the products, thus making it possible to determine in this case, the parameters of the production policy according to the probability. Finally, we have dealt with the case of a production system where the defective rate varies with the age of the machine. A numerical approach of resolution of this system allowed us to obtain an optimal production policy with critical threshold and a preventive maintenance policy. A simulation approach combined with the experimental designs and the methodology surface response allowed to obtain the critical thresholds and the fractions to be controlled for each period where the defective rate stay constant. We have shown for all the cases treated that the production policy depends on the level of inventory, a sensitivity analysis allowed to validate these results.

Date	12 Feb 2019
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	Jean-Pierre Kenné (Supervisor) & Ali Gharbi (Co-supervisor)