ISyE 8803D Formal Methods in Operations Engineering Instructor Spyros Reveliotis Spring 2007

Course Objectives Familiarize the student with a set of formal frameworks that are applicable to the modeling, analysis and control of contemporary operations. Exemplify the systematic and effective use of abstract mathematical frameworks in the study of more concrete applications, like manufacturing system control, modeling and analysis of guidepath-based transportation systems, and workflow management. Introduce additional concepts and results in the IE curriculum that are lying on the interface of IE with Computer Science and Control Theory. Motivate additional research ideas.

A motivational example: Part flow control in an FMS R3R3 R2R2 R1R1 J 1 : R 1  R 2  R 3 J 2 : R 3  R 2  R 1

Cluster Tools: A (potential) FMS implementation in contemporary semiconductor manufacturing

Another example: Traffic Management in an AGV System

A more “realistic” problem context: The 300mm FAB

A transportation example

Internet-based business workflow management

A unifying modeling abstraction: Sequential Resource Allocation Systems (RAS) A set of (re-usable) resource types R = {R i, i = 1,...,m}. Finite capacity C i for each resource type R i. a set of job types J = {J j, j = 1,...,n}. An (partially) ordered set of job stages for each job type, {p jk, k = 1,..., j }. A resource requirements vector for each job stage p, a p [i], i = 1,...,m. Jobs release their currently held resources only upon allocation of the resources requested for their next stage Sequential RAS deadlock: A RAS state in which there exists a subset of jobs s.t. every job in this subset in order to proceed requires some resource(s) currently allocated to some other job in this subset.

Logical vs Performance Control of Sequential RAS Resource Allocation System Behavioral Correctness Efficiency

An Event-Driven RAS Control Scheme RAS Domain Logical Control System State Model Performance Control Configuration Data Feasible Actions Admissible Actions EventCommanded Action

The theoretical foundations of the proposed framework Control Theory “Theoretical” Computer Science Operations Research Discrete Event Systems

Course Outline 1. Introduction: a.Motivating applications and the underlying problems b.The unifying abstraction: Sequential Resource Allocation Systems c.The proposed decomposition of the RAS control problem to logical and performance control d.The underlying methodology (Discrete Event Systems theory), the book and its complements 2. Logical Modeling, Analysis and Control of Operations a.The RAS deadlock problem and the optimal deadlock avoidance policy: Basic characterizations b.Introduction to formal languages and finite state automata (FSA) c.Introduction to supervisory control (SC) theory d.Supervisory control with uncontrollable and/or unobservable events e.Complexity considerations and Polynomial-Kernel Deadlock Avoidance Policies f.Petri nets (PN) as an alternative modeling framework for DES behavior g.PN-based modeling and analysis of the RAS deadlock avoidance problem

Course Outline (cont.) 3. Performance-oriented modeling, analysis and control of Operations –a.Stochastic Timed Automata, Generalized Semi-Markov Processes and their relationship to Markov and Semi-Markov processes –b.An Introduction to Queueing theory with emphasis on (Markovian) Queueing networks –c.Controlled Markov Chains, Markov Decision Processes (MDP), and their application to the RAS scheduling problem –d.Analysis and Control of non-Markovian Queueing systems BCMP networks Multi-class queueing networks and their application to semiconductor manufacturing systems: stability/efficiency and bounds for the performance of some well-known dispatching policies (Introduction to fluid and Brownian modeling and analysis of queueing systems ?) Computing efficient scheduling policies through Approximate Dynamic Programming (ADP).

Textbook and Course References 1.Textbook: C. Cassandras and S. Lafortune, “Introduction to Discrete Event Systems”, Kluwer Academic Publishers, Supplements: (excerpts from some of these texts will be provided during the course development) a.S. Reveliotis, “Real-Time Management of Resource Allocation Systems”, Kluwer Academic Publishers, to appear. b.H. Chen and D. Yao, “Fundamentals of Queueing Networks”, Springer, c.D. Yao (ed.), “Stochastic Modeling and Analysis of Manufacturing Systems”, Springer- Verlag, d.J. Buzacott and J. G. Shanthikumar, “Stochastic Models of Manufacturing Systems”, Prentice Hall, e.N. Viswanadham and Y. Narahari, “Performance Modeling of Automated Manufacturing Systems”, f.S. Gershwin, “Manufacturing Systems Engineering”, Prentice Hall, g.S. Sethi and Q. Zhang, “Hierarchical Decision Making in Stochastic Manufacturing Systems”, Birkhauser, h.D. Bertsekas, “Dynamic Programming and Optimal Control: Vols 1&2”, 3rd ed., Athena Scientific, i.D. Bertsekas and J. Tsitsiklis, “Neuro-Dynamic Programming”, Athena Scientific, Papers and/or other material cited in class.

Course policies Course Prerequisites It is expected that attending students will possess the following background: 1.Familiarity with the basic concepts of stochastic modeling and analysis, to the extent covered in ISyE 6650 or some equivalent course. 2.Familiarity with the basic optimization models and algorithms covered in ISyE 6669 or some equivalent course. Evaluation Procedures Course grades will be based on: 1.Homework assignments 2.A term paper / project 3.Class participation. Satisfy academic curiosity and learn while having fun!