Post on 16-Jan-2016
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!