des id´ees `a travers la d´efinition de nouveaux probl`emes d’ordonnancement : Probl`eme d’ordonnancement avec des contraintes de temps (Probl`eme with Time Constraints-P T C) et Probl`eme d’ordonnancement avec l’´etat de sant´e des ´equipements (Problem with Equipment Health Factor-P EHF ). P T C et P EHF ont des objectifs multicrit`eres. P T C est un probl`eme d’ordonnancem- ent des familles de jobs sur des machines parall`eles non identiques en tenant compte des temps de setup et des contraintes de seuil de temps. L’objectif est de planifier les familles de jobs sur les machines en minimisant la somme des dates de fin et les pertes de qualification des machines. La complexit´e de ce probl`eme r´eside dans le fait que ce n’est pas seulement une d´ecision d’affectation de jobs sur une machine, mais aussi de s´election de la famille appropri´ee afin de maintenir les qualifications. Nous avons d´emontr´e que ce probl`eme est NP-difficile. Le probl`eme P EHF est une extension de P T C. Il consiste `a ordonnancer des familles de jobs sur des machines parall`eles non identiques avec des contraintes de temps et en int´egrant la ”sant´e” de l’´equipement (EHF ). L’objectif est d’ordonnancer les familles de jobs diff´erents sur les machines tout en minimisant la somme des dates de fin, les pertes de qualification des machines et en optimisant le rendement attendu qui r´esulte de l’affectation d’une machine `a un job. Ce rendement est d´efini comme une fonction de EHF et de la criticit´e des jobs.
Pour r´esoudre ces probl`emes des programmes lin´eaires en nombre entiers, des heuristiques et m´eta-heuristique ont ´et´e propos´ees, test´ees et analys´ees.
0.9
Perspectives
Des pistes de recherche peuvent ˆetre propos´ees concernant la r´esolution et la mod´elisation des probl`emes d´efinis dans cette cette th`ese. Mais avant, il nous semble important d’aller un peu plus loin dans l’´etude de la complexit´e des probl`emes d´efinis dans cette th`ese. En effet, nous avons pu montrer que les probl`emes sont NP-difficile sans pouvoir montrer si leur complexit´e est au sens faible ou au sens fort. Une r´eflexion dans ce sens compl`eterait cette ´etude complexit´e.
J’ai propos´e dans cette th`ese des m´ethodes exactes (programmation lin´eaire) pour PTC et PEHF qui donnent des solutions pour des tailles d’instances relativement petites. Il paraˆıt important d’investiguer d’autres approches pour de plus grandes instances. La g´en´eration de colonnes nous paraˆıt ˆetre une premi`ere approche s´erieuse.
dans la conception de produit exigent de v´erifier en temps r´eel que les ma- chines soient qualifi´ees. Pour s’assurer que la qualification est correcte- ment faite et pr´ecise, des wafers tests (Send Ahead Wafers-SAW ) sont en- voy´es en ´eclaireur pour que les machines fonctionnent dans les sp´ecifications voulues. Il s’agit ici, d’int´egrer l’ordonnancement des SAW dans le processus d’ordonnancement global tout en minimisant le nombre de SAW qui coˆutent chers.
General Introduction
Semiconductor industry is one of the most complex industries. The very large number of processes and the variety in their types are major sources of complexity. In this industry, the wafer is the principle element. A wafer undergoes several hundreds operations. This is due to the fact that processes in semiconductor manufacturing facilities are of a reentrant type, i.e. wafers visit the same machines many times. These environment characteristics and many other aspects, make scheduling in such industries, a complex issue.
Fabrication processes of semiconductors are very precise and require a high level of accuracy. Reliable equipment are required and right recipe parameters should be provided. Advanced Process Control (APC) systems ensure that each process is done following predefined specifications and that each equipment is reliable to process different product types.
In fact, both scheduling and Advanced Process Control (APC) aim at improving the overall fabrication efficiency, and more precisely to maximize the throughput and to minimize the manufacturing cost. There are various types of scheduling strategies and techniques which are used in those indus- tries. Nevertheless, scheduling in semiconductor manufacturing facilities is even more complicated. The difficulty comes from the complex environment and the related high cost of machines and their corresponding maintenance requirements. Many scheduling techniques in semiconductor manufacturing were studied in the literature and research is still active in this domain.
Advanced Process Control has become an indispensable element in the fabrication process with the aggressive competition for better quality and higher productivity. APC utilizes wide variety of techniques in order to keep processes at their specification levels and to survey tools for existing and/or possible defects. To accomplish such goals, statistical techniques, data min- ing, control charts and control loops are used. The use of such techniques showed a noticeable improvement in throughput, on Overall Equipment Ef-
Most of existing semiconductor fabs use scheduling systems which have no relation with process control systems and vice-versa. The objective of this research work concerns the integration of two systems: Scheduling and Advanced Process Control. Here are some questions (not exhaustive related to this integration): What are the benefits of a collaboration between these two systems? What are the challenging problems and the solution approaches that may be proposed? And thereafter, how can we integrate scheduling and APC issues? In this thesis, we try to answer these questions.
Reading Plan This thesis is composed of six chapters. Below, the contents of each chapter are summarized.
• Chapter 1 provides an overview on processes, scheduling and Advanced Process Control in semiconductor manufacturing, where a description of semiconductor manufacturing processes is given. Also, scheduling issues and problems are outlined and a summary on Advanced Process Control components and techniques is provided.
• Chapter 2 addresses the contributions done in the integration of schedul- ing and Advanced Process Control. In this chapter, different inte- gration issues, possibilities and perspectives are discussed and major integration problems are proposed. Two of the proposed problems, Problem with Time Constraints (P T C) and Problem with Equipment Health Factors (P EHF ) are considered, studied and analyzed in this thesis.
• Chapter 3 presents a literature review concerning the selected problems (P T C and P EHF ). Complexity is addressed. Time indexed mixed integer linear programming models are proposed.
• Chapter 4 reports numerical results on the mathematical programming models. Objective functions are considered as a weighted sum of differ- ent criteria. These weights are defined in preference vectors. Different types of preference vectors are studied and analyzed. A lexicographical order of criteria is considered. Moreover, an example of the ǫ-constraint method is also provided. A sensitivity study on the Time Constraint (threshold ) is also done. The results showed the strong compromise
0.9 Perspectives
between the different criteria of the objective functions for both prob- lems. Numerical experiments showed limitations on the number of jobs, machines and families that a standard solver can handle, which led to developing approximate solution approaches.
• Chapter 5 addresses several constructive heuristics and a metaheuristic (Simulated Annealing, SA) to solve large instances. The performance of dedicated heuristics, a recursive algorithm and SA depends on the considered objectives.
• The last chapter concludes this thesis and various perspectives are pro- posed and discussed.
Chapter 1
Semiconductor Manufacturing:
Processes, Scheduling and
Advanced Process Control
1.1
Introduction
In this chapter, we give an overview on the fabrication processes and their different procedures in semiconductor manufacturing. We also address some important scheduling issues. A general overview about Advanced Process Control (APC) is also given, which explores its different components.