Commande optimale stochastique des systèmes manufacturiers en boucle fermée

Abstract

The work presented in this thesis aims to jointly develop optimal strategies to control the production and maintenance in a hybrid manufacturing system integrating remanufacturing and in the presence of uncertainties. Machines breakdowns and repairs, customer demand, return of end-of-life products, deterioration of machines and quality of manufactured products are the main considered sources of uncertainties in this thesis. Taking all these random aspects into account makes the optimization problem very complex. We will divide this problem into five (5) sub-problems by gradually integrating these aspects to better understand their impacts on the control policies. The contributions of this thesis are presented in five (5) phases. The first phase deals with a problem of planning production and replacement activities for a manufacturing system in a context of deterioration. The random phenomena examined in this phase are machine breakdowns and repairs. We assume that the machine undergoes a progressive deterioration while in operation and that the machine failure rate is a function of its age. When a failure occurs, minimal repairs are carried out. When the machine reaches a certain level of degradation, it is replaced. Due to minimal repairs, the dynamics of the system is affected by its history and semi-Markov processes have been used for modeling. A numerical resolution of the optimality conditions, described by the Hamilton-Jacobi-Bellman (HJB) equations, led to the solution of the problem studied. The second phase of the study permits to integrate into the production system of the first the random aspects of customer demand and the quality of the parts produced. The effect of the deterioration phenomenon on the machine, caused by the machine aging and minimal repairs, is mainly observed in its availability and the quality of the parts produced. We consider that the failure rate and the defective rate depend on the age of the machine. The integration of random demand and quality behaviour led us to propose a new modeling approach by developing the second-order optimality conditions of HJB type. Optimal control policies are determined by numerical methods. In the third phase, we studied a hybrid system consisting of one manufacturing machine and one remanufacturing machine. The machines are non-identical and unreliable. The modeling of their dynamics has been done using homogeneous Markov chains. In addition to uncertainties of the previous two (2) phases, we consider the uncertainties about customer demand and product returns. The solution was obtained numerically by solving the second-order HJB equations, and our results have been confirmed by numerical analysis. In the fourth phase of this work, we took into account the deterioration of the remanufacturing machine in the context of a hybrid manufacturing/remanufacturing system. In this phase, we considered production systems in which the heterogeneous nature of the returned products involves an imperfect repair process on the machine. In addition to this deterioration, the machines are subject to random breakdowns and repairs. A new mathematical modeling approach is proposed for the underlying class of problems related to machines history. This new approach is based on the extension of the state space and leads to a Markovian decision model; which in turn allows us to apply the powerful techniques developed for the stochastic optimization of such models. Then, the manufacturing, remanufacturing and replacement policies have been determined by the same numerical tools as those of previous phases. Sensitivity analyzes have been developed to show the relevance of the proposed approach. The fifth phase complements the previous models, since we extend the concept of the deterioration effect of the hybrid system on both machines to solve more realistic and complex industrial problems. The first machine is used for ordinary manufacturing activities, and its deterioration effect randomly affects its availability and the quality of its parts produced. The second machine deals with activities of remediation of defective products of the first machine and remanufacturing of returned products at end-of-life. The effect of the deterioration on the availability of the second machine is captured by the remediation process of the flow of defectives parts. Since the deterioration of the first machine causes the second machine to fail, it will have to be replaced by a new one that will restore the hybrid system parameters to the initial conditions when a certain level of degradation is reached. The goal is to determine the optimal production plan for manufacturing, remediation and remanufacturing, as well as the replacement strategy while minimizing the total cost. Since the process of deterioration leads to a memory process, we have developed a semi-Markovian decision model to describe this dynamic. The optimality conditions of the second-order HJB type have been solved by numerical methods and the structure of the joint control policy has been validated by a sensitivity analysis.

Date	11 Apr 2018
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	Jean-Pierre Kenné (Supervisor) & Ali Gharbi (Co-supervisor)