IE7201: Production & Service Systems Engineering
Spring 2016
Instructor: Spyros Reveliotis
e-mail: spyros@isye.gatech.edu
homepage: www.isye.gatech.edu/~spyros
“Course Logistics”
•
Office Hours: By appointment
•
Course Prerequisites:
– ISYE 6761 (Familiarity with basic probability concepts and Discrete Time
Markov Chain theory)
– ISYE 6669 (Familiarity with optimization concepts and formulations, and
basic Linear Programming theory)
•
Grading policy:
– Homework: 20%
– Midterm Exam: 40%
– Final Exam: 40%
•
Reading Materials:
– Course Textbook: Fundamentals of Queueing Theory, by D. Gross, J. G.
Shortle, J. M. Thompson and C. M. Harris, J. Wiley & Sons, Inc., 2008.
– 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.
Course Outline
1. Introduction: Course Objectives, Context, and Outline
– Contemporary organizations and the role of Operations Management (OM)
– Corporate strategy and its connection to operations
– The organization as a resource allocation system (RAS)
– The underlying RAS management problems and the need for understanding the impact of the
underlying stochasticity
– The basic course structure
2. Modeling and Analysis of Production and Service Systems as Continuous-Time Markov Chains
– A brief overview of the key results of the theory of Discrete-Time Markov Chains
– Bucket Brigades
– The Exponential Distribution and the Poisson Process
– Continuous-Time Markov Chains (CT-MC)
– Birth-Death Processes and the M/M/1 Queue
• Transient Analysis
• Steady State Analysis
– Modeling more complex behavior through CT-MCs
• Single station systems with multi-stage processing, finite resources and/or blocking effects
• Open (Jackson) and Closed (Gordon-Newell) Queueing networks
Course Outline (cont.)
3. Accommodating non-Markovian behavior
– Phase-type distributions and their role as approximating distributions
– The M/G/1 queue
– Priority Queues
– The G/G/1 queue
– The essence of “Factory Physics”
– (Reversibility and BCMP networks)
4. Performance Control of Production and Service systems
– Controlling the “event rates” of the underlying CT-MC model (an informal introduction
of the dual Linear Programming formulation in standard MDP theory)
– A brief introduction of the theory of Markov Decision Processes (MDPs) and of Dynamic
Programming (DP)
– An introduction to Approximate DP
– An introduction to dispatching rules and classical scheduling theory
– Buffer-based priority scheduling policies, Meyn and Kumar’s performance bounds and
stability theory
Course Outline (cont.)
5. Behavioral Control of Production and Service Systems
–
–
–
–
Behavioral modeling and analysis of Production and Service Systems
Resource allocation deadlock and the need for liveness-enforcing supervision (LES)
Petri nets as a modeling and analysis tool
A brief introduction to the behavioral control of Production and Service Systems
Our basic view of the considered systems
• Production System: A transformation process (physical,
locational, physiological, intellectual, etc.)
Inputs
•Materials
•Capital
•Labor
•Manag. Res.
Outputs
Organization
•Goods
•Services
• The production system as a process network
Stage 1
Stage 2
Stage 4
Suppliers
Stage 3
Stage 5
Customers
The major functional units of a modern
organization
Strategic Planning:
defining the organization’s mission and
the required/perceived core competencies
Production/
Operations:
product/service
creation
Finance/
Accounting:
monitoring of
the organization
cash-flows
Marketing:
demand
generation
and
order taking
Fit Between Corporate and Functional
Strategies (Chopra & Meindl)
Corporate Competitive Strategy
Product
Development
Strategy
Supply Chain
or Operations
Strategy
Information Technology Strategy
Finance Strategy
Human Resources Strategy
Marketing
and Sales
Strategy
Corporate Mission
• The mission of the organization
–
–
–
–
defines its purpose, i.e., what it contributes to society
states the rationale for its existence
provides boundaries and focus
defines the concept(s) around which the company can rally
• Functional areas and business processes define their
missions such that they support the overall corporate
mission in a cooperative and synergistic manner.
Corporate Mission Examples
• Merck: The mission of Merck is to provide society with superior
products and services-innovations and solutions that improve the
quality of life and satisfy customer needs-to provide employees with
meaningful work and advancement opportunities and investors with a
superior rate of return.
• FedEx: FedEx is committed to our People-Service-Profit philosophy.
We will produce outstanding financial returns by providing totally
reliable, competitively superior, global air-ground transportation of
high-priority goods and documents that require rapid, time-certain
delivery. Equally important, positive control of each package will be
maintained utilizing real time electronic tracking and tracing systems.
A complete record of each shipment and delivery will be presented
with our request for payment. We will be helpful, courteous, and
professional for each other, and the public. We will strive to have a
completely satisfied customer at the end of each transaction.
A strategic perspective on the operation of
the considered systems
Responsiveness (Reliability; Quickness; Flexibility;
e.g., Dell, Overnight Delivery Services)
Competitive Advantage through which
the company market share is attracted
Cost Leadership (Price;
e.g., Wal-Mart, Southwest
Airlines, Generic Drugs)
Differentiation (Quality; Uniqueness;
e.g., Luxury cars, Fashion Industry,
Brand Name Drugs)
The operations frontier, trade-offs,
and the operational effectiveness
Responsiveness
Cost Leadership
Differentiation
The primary “drivers” for achieving strategic fit in
Operations Strategy
(adapted from Chopra & Meindl)
Corporate Strategy
Operations Strategy
Efficiency
Facilities
Responsiveness
Inventory
Transportation
Information
Market
Segmentation
The course perspective:
Modeling, analyzing and controlling workflows
Some Key Performance measures
• 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.
Some key issues to be addressed in
this course
• How do I get good / accurate estimates of the
performance of a certain system configuration?
• How do I design and control a system to support
certain target performance?
• What are the attributes that determine these
performance measures?
• What are the corresponding dependencies?
• Are there inter-dependencies between these
performance measures and of what type?
• What target performances are feasible?
Queueing Theory:
A plausible modeling framework
• Quoting from Wikipedia:
Queueing theory (also commonly spelled queuing theory) is the
mathematical study of waiting lines (or queues).
The theory enables mathematical analysis of several related
processes, including arriving at the (back of the) queue, waiting in the
queue (essentially a storage process), and being served by the
server(s) at the front of the queue.
The theory permits the derivation and calculation of several
performance measures including the average waiting time in the
queue or the system, the expected number waiting or receiving
service and the probability of encountering the system in certain
states, such as empty, full, having an available server or having to wait
a certain time to be served.
Factory Physics
(a term coined by W. Hopp & M. Spearman)
The employment of fundamental concepts
and techniques coming from the area of
queueing theory in order to characterize,
analyze and understand the dynamics of
(most) contemporary production systems.
The underlying variability
• But the actual operation of the system is
characterized by high variability due to a large host
of operational detractors; e.g.,
–
–
–
–
–
–
machine failures
employee absenteeism
lack of parts or consumables
defects and rework
planned and unplanned maintenance
set-up times and batch-based operations
Analyzing a single workstation with
deterministic inter-arrival and processing times
Case I: ta = tp = 1.0
B1
M1
TH
WIP
1
1
Arrival
2
3
4
Departure
5
t
TH = 1 part / time unit
Expected CT = tp
Analyzing a single workstation with
deterministic inter-arrival and processing times
Case II: tp = 1.0; ta = 1.5 > tp
B1
WIP
M1
TH
Starvation!
1
1
Arrival
2
3
4
Departure
5
t
TH = 2/3 part / time unit
Expected CT = tp
Analyzing a single workstation with
deterministic inter-arrival and processing times
Case III: tp = 1.0; ta = 0.5
B1
M1
TH
WIP
3
Congestion!
2
1
1
Arrival
2
3
4
Departure
5
t
TH = 1 part / time unit
Expected CT  
A single workstation with variable interarrival times
Case I: tp=1; taN(1,0.12) (ca=a / ta = 0.1)
B1
M1
TH
WIP
3
2
TH < 1 part / time unit
Expected CT  
1
1
Arrival
2
3
4
Departure
5
t
A single workstation with variable interarrival times
Case II: tp=1; taN(1,1.02) (ca=a / ta = 1.0)
B1
M1
TH
WIP
3
2
TH < 1 part / time unit
Expected CT  
1
1
Arrival
2
3
4
Departure
5
t
A single workstation with variable
processing times
Case I: ta=1; tpN(1,1.02)
B1
M1
TH
WIP
3
2
TH < 1 part / time unit
Expected CT  
1
1
Arrival
2
3
4
Departure
5
t
Remarks
• Synchronization of job arrivals and completions
maximizes throughput and minimizes experienced cycle
times.
• Variability in job inter-arrival or processing times
causes starvation and congestion, which respectively
reduce the station throughput and increase the job cycle
times.
• In general, the higher the variability in the inter-arrival
and/or processing times, the more intense its disruptive
effects on the performance of the station.
• The coefficient of variation (CV) defines a natural
measure of the variability in a certain random variable.
The propagation of variability
W1
B1
W2
M1
B2
Case I: tp=1; taN(1,1.02)
Case II: ta=1; tpN(1,1.02)
WIP
WIP
3
3
2
2
1
1
1
W1 arrivals
2
3
TH
M2
4
5
W1 departures
t
1
W2 arrivals
2
3
4
5
t
Remarks
• The variability experienced at a certain station
propagates to the downstream part of the line due to the
fact that the arrivals at a downstream station are
determined by the departures of its neighboring upstream
station.
• The intensity of the propagated variability is modulated
by the utilization of the station under consideration.
• In general, a highly utilized station propagates the
variability experienced in the job processing times, but
attenuates the variability experienced in the job interarrival times.
• A station with very low utilization has the opposite
effects.
Automation and the need for
behavioral control
R1
R2
J1 : R1  R2  R3
R3
J2 : R3  R2  R1
Cluster Tools:
An FMS-type of environment in
contemporary semiconductor manufacturing
Another example:
Traffic Management in an AGV System
Type - 2
Deadlock
W1
W2
Type - 1
Deadlock
W3
W4
Docking
Station
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 = {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,...,lj}.
• A resource requirements vector for each job stage p, ap[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
Admissible
Actions
Configuration Data
RAS Domain
Performance Control
Feasible
Actions
Logical Control
Event
System State Model
An Event-Driven RAS Control Scheme
Commanded
Action
Theoretical foundations
Control
Theory
“Theoretical”
Computer
Science
Discrete
Event
Systems
Operations
Research