ISyE 8803DFormal 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

R3R2R1

J1 : R1 R2 R3 J2 : R3 R2 R1

Cluster Tools: A (potential) FMS implementation in

contemporary semiconductor manufacturing

Another example: Traffic Management in an AGV

System

W1 W2

W3W4

DockingStation

Type - 1Deadlock

Type - 2Deadlock

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

A transportation example

http://www.cities21.org/Redmond.htm

Internet-based business workflow management

A unifying modeling abstraction:Sequential Resource Allocation Systems (RAS)

• A set of (re-usable) resource types R = {Ri, i = 1,...,m}.

• Finite capacity Ci for each resource type Ri.

• a set of job types J = {Jj, j = 1,...,n}.

• An (partially) ordered set of job stages for each job type, {pjk, k = 1,...,j}.

• A resource requirements vector for each job stage p, ap[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

ResourceAllocation

System

ResourceAllocation

System

BehavioralCorrectnessBehavioral

CorrectnessEfficiencyEfficiency

An Event-Driven RAS Control Scheme

RAS Domain

Logi

cal

Con

trol

Sys

tem

Sta

te M

odel

Per

form

ance

Con

trol

Configuration Data

FeasibleActions

AdmissibleActions

Event CommandedAction

The theoretical foundations of the proposed framework

ControlTheory

“Theoretical” Computer Science

OperationsResearch

DiscreteEventSystems

Course Outline1. Introduction:

a. Motivating applications and the underlying problemsb. The unifying abstraction: Sequential Resource Allocation Systemsc. The proposed decomposition of the RAS control problem to logical and

performance controld. The underlying methodology (Discrete Event Systems theory), the book and

its complements

2. Logical Modeling, Analysis and Control of Operationsa. The RAS deadlock problem and the optimal deadlock avoidance policy:

Basic characterizationsb. Introduction to formal languages and finite state automata (FSA)c. Introduction to supervisory control (SC) theoryd. Supervisory control with uncontrollable and/or unobservable eventse. Complexity considerations and Polynomial-Kernel Deadlock Avoidance

Policiesf. Petri nets (PN) as an alternative modeling framework for DES behaviorg. 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 References1. Textbook: C. Cassandras and S. Lafortune, “Introduction to Discrete Event Systems”,

Kluwer Academic Publishers, 1999.

2. 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, 2001.c. D. Yao (ed.), “Stochastic Modeling and Analysis of Manufacturing Systems”, Springer-

Verlag, 1994. d. J. Buzacott and J. G. Shanthikumar, “Stochastic Models of Manufacturing Systems”,

Prentice Hall, 1993.e. N. Viswanadham and Y. Narahari, “Performance Modeling of Automated Manufacturing

Systems”, 1992.f. S. Gershwin, “Manufacturing Systems Engineering”, Prentice Hall, 1994.g. S. Sethi and Q. Zhang, “Hierarchical Decision Making in Stochastic Manufacturing

Systems”, Birkhauser, 1994.h. D. Bertsekas, “Dynamic Programming and Optimal Control: Vols 1&2”, 3rd ed., Athena

Scientific, 2005.i. D. Bertsekas and J. Tsitsiklis, “Neuro-Dynamic Programming”, Athena Scientific, 1996.

3. Papers and/or other material cited in class.

Course policies

• Course PrerequisitesIt 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 ProceduresCourse grades will be based on:

1. Homework assignments2. A term paper / project3. Class participation.

• Satisfy academic curiosity and learn while having fun!