Instructor: Spyros Reveliotis homepage: IE7201: Production & Service Systems Engineering Fall 2008

“Course Logistics” Office Hours: By appointment Course Prerequisites: ISYE 6650 (Familiarity with probability, stochastic modeling and basic queueing theory) and ISYE 6669 (Familiarity with optimization concepts and formulations, and basic Linear Programming theory) Grading policy: –Homework: 50% (more like take-home exams…) –Project: 25% –Class Participation: 25% Reading Materials: –Course Textbook: C. Cassandras and S. Lafortune, Introduction to Discrete Event Systems, 2nd Ed., Springer –Additional material will be distributed during the course development

Course Objectives Provide an understanding and appreciation of the different resource allocation and coordination problems that underlie the operation of production and service systems. Enhance the student ability to formally characterize and study these problems by referring them to pertinent analytical abstractions and modeling frameworks. Develop an appreciation of the inherent complexity of these problems and the resulting need of simplifying approximations. Systematize the notion and role of simulation in the considered problem contexts. Define a “research frontier” in the addressed areas.

Our basic view of the considered systems Production System: A transformation process (physical, locational, physiological, intellectual, etc.) Organization InputsOutputs Materials Capital Labor Manag. Res. Goods Services The production system as a process network Stage 5 Stage 4 Stage 3 Stage 2Stage 1 SuppliersCustomers

A strategic perspective on the operation of the considered systems Differentiation (Quality; Uniqueness; e.g., Luxury cars, Fashion Industry, Brand Name Drugs) Cost Leadership (Price; e.g., Wal-Mart, Southwest Airlines, Generic Drugs) Responsiveness (Reliability; Quickness; Flexibility; e.g., Dell, Overnight Delivery Services) Competitive Advantage through which the company market share is attracted

Some typical Performance Measures operationalizing the corporate strategy Production rate or throughput, i.e., the number of jobs produced per unit time Production capacity, i.e., the maximum sustainable production rate Expected cycle time, i.e., the average time that is spend by any job into the system (this quantity includes both, processing and waiting time). Average Work-In-Process (WIP) accumulated at different stations Expected utilization of the station servers. Remark: The above performance measures provide a link between the directly quantifiable and manageable aspects and attributes of the system and the primary strategic concerns of the company, especially those of responsiveness and cost efficiency.

The need for behavioral control R3R3 R2R2 R1R1 J 1 : R 1  R 2  R 3 J 2 : R 3  R 2  R 1

Cluster Tools: An FMS-type of environment in contemporary semiconductor manufacturing

Another example: Traffic Management in an AGV System

A more “realistic” example: A typical fab layout

An example taken from the area of public transportation

A more avant-garde example: Computerized workflow management

A modeling abstraction: Sequential Resource Allocation Systems 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. A distribution characterizing the processing time requirement of each processing stage. Protocols characterizing the job behavior (e.g., typically jobs will release their currently held resources only upon allocation of the resources requested for their next stage)

Behavioral or 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

Theoretical foundations Control Theory “Theoretical” Computer Science Operations Research Discrete Event Systems

Course Outline 1. Qualitative / Behavioral modeling of the considered RAS Languages and (Finite State) Automata An introduction to (Ramadge & Wonham) Supervisory Control theory Petri nets Application of the above frameworks to the liveness-enforcing supervision of RAS 2, Timed models: towards performance analysis of the considered RAS Timed Automata and Petri nets Dioid / (max, +) Algebras Applications in Queueing Systems and in the development of efficient cyclical schedules for contemporary cluster tools 3. Stochastic Timed Automata Stochastic Clock Structures and Stochastic Timed Automata Generalized Semi-Markov Process (GSMP) and its connection to Simulation Markov and Semi-Markov Processes as specializations of the GSMP model Generalized Stochastic Petri nets (GSPN)

Course Outline (cont.) 4. The stochastic scheduling problem in the considered RAS Formulation of the scheduling problem for RAS with Markovian Dynamics in the GSPN modeling framework Approximation of non-Markovian dynamics through the method of stages Introduction to Markov Decision Process (MDP) theory and Dynamic Programming (DP) Approximate DP: current trends and their potential application in the RAS scheduling problem 5. Queueing-theoretic-based analysis and control of the considered RAS Introduction to the theory of Open and Closed Markovian Queueing networks BCMP networks Performance evaluation and stability analysis of multi-class queueing networks An introduction to fluid-based modeling, analysis and control of queuing systems 6. Application of MDP theory in inventory control The optimality of (S,s) policies Introduction to the theory of multi-echelon inventory systems Hedging point strategies

Reading Assignment Please, read Chapter 1 in your textbook.

An informal introduction to the RAS logical control problem

A motivational example: Deadlock Avoidance in an FMS R3R3 R2R2 R1R1 J 1 : R 1  R 2  R 3 J 2 : R 3  R 2  R 1

q 0 q J 21 J q J 22 J q 1 11 J q 2 21 J q 3 12 J q 4 22 J q J 21 J q J 12 J 21 J q J 21 J 22 J Modeling the underlying RAS behavior

q 0 q J 21 J q J 22 J q 1 11 J q 2 21 J q 3 12 J q 4 22 J q J 21 J q J 12 J 21 J q J 21 J 22 J Finite State Automata-based modeling: Safe vs. Unsafe Region

The Optimal Logical Control Policy q 0 q J 21 J q J 22 J q 1 11 J q 2 21 J q 3 12 J q 4 22 J q J 21 J q J 12 J 21 J q J 21 J 22 J q 6 13 J q 5 11 J 12 J q 7 23 J q 8 21 J 22 J q 9 11 J 13 J q J 13 J q 11 J 12 J 13 J q J 23 J q J 23 J q J 22 J 23 J

Complexity and other complicating effects State Safety is an NP-complete problem in sequential RAS (by reduction of the SAT problem) State Transition Diagram (STD) size: Uncontrollable and/or unobservable events where: C = max resource capacity Q = max number of stages supported by a resource m = number of resource types

The “nature” of the available results Special RAS structure admitting an optimal logical control policy of polynomial complexity w.r.t the RAS size Polynomial-Kernel (PK-) RAS logical control policies: Sub- optimal policies that are of polynomial complexity –RUN (Resource Upstream Neighborhood) –RO (Resource Ordering) –Banker’s algorithm –etc. An analytical framework for –interpreting the correctness of the above policies, and –enabling the “automatic” validation and synthesis of new members from this class of policies