ISYE OMSA-6644
Simulation and Modeling for Engineering and Science
Course Description
This course covers modeling of discrete-event dynamic systems and introduces simulationbased methods for using these models to solve engineering design and analysis problems.
Prerequisites
You will be expected to come in knowing a bit of basic calculus, probability, and statistics. But don’t worry too much – we’ll provide bootcamps on that material so as to make the class pretty much self-contained. In addition, this course will involve extensive computer programming, so it would be nice to have at least a little experience in something like Excel, just to bring back the programming memories.
Course Goals
• Learn how to develop simulation models and conduct simulation studies.
• Become familiar with the organization of simulation languages. In particular, we will do a great deal of modeling with Arena, a comprehensive simulation package with animation capabilities.
• Review statistical aspects including input analysis, random variate generation, output analysis, and variance reduction techniques.
Grading Policies
• There will be two midterms and a final exam. Test questions are typically multiple choice or T/F.
• There will be 11 Homework assignments (not as bad as it sounds). There will be a bunch of bonus questions spread throughout the semester, which you can do to earn a few extra points. HWs that are late will suffer a 10x% deduction, where x is the number of days late, with x = 3 being the upper bound on the allowed lateness. So plan ahead!
• We will have a project, which you can select from among several theory- and applications-oriented topics. You will be allowed to work in small groups.
• You must achieve an overall weighted average of 60% to pass the course.
• Work hard and you will be rewarded – Grading is usually pretty generous. 😊
• Grading Disputes:
o Let’s be winners, not whiners. We are happy to discuss grades, but please make reasonable requests. 😊
o To this end, we will generously provide various bonus point opportunities throughout the course; but because of this lovely act of kindness, we will not accept any test grade whining for matters involving up to 4 points. (Makes great sense, eh?!)
Mother Teresa: “Wow, that’s something nice that I would do!”
o If you really, really want to request a regrade (for matters involving more than 4 points), simply fill out the convenient form that can be found at http://www.isye.gatech.edu/%7Esman/courses/gradegrovel.pdf. o Here is some sage advice on whining: https://www.youtube.com/watch? v=Ow0lr63y4Mw.
• Grading Breakdown
Homework 10%
Project 10%
Midterm Exam 1 25%
Midterm Exam 2 25%
Final Exam 30%
Bonus Opportunities 2.5%
TOTAL 102.5%
Timing Policy
• The Modules follow a logical sequence, so they (mostly) need to be done in order.
• Quizzes must be completed during the time allotted on the schedule.
• You will have access to the course content for the scheduled duration of the course.
Exam Policy
• For Quiz x (x = 1,2,3), you are allowed to use x sheets of paper, either 8.5”x11” or A4, with handwritten or printed notes (both sides of the sheet, 2x sides total).
• For all quizzes, you are allowed a blank sheet of paper for scratch work. (All OMS Analytics and OMS CS students will be proctored; you will have to show the front and back of the blank sheet while you are being proctored.)
• You are also allowed to bring any reasonable calculator.
• You will not be allowed to use packages such as Excel, Arena, R, etc. during the exams.
Attendance Policy
• This is a fully online course.
• Login on a regular basis to complete your work, so that you do not have to spend a lot of time reviewing and refreshing yourself regarding the content.
Student Honor Code
All GT students should abide by the Georgia Tech Student Honor Code.
• Review the Georgia Tech Student Honor Code:
https://osi.gatech.edu/content/honor-code
• You are responsible for completing your own work.
• Any GT student suspected of behavior in violation of the Georgia Tech Honor Code will be referred to Georgia Tech’s Office of Student Integrity.
Communication
• Always be courteous and nice (see Netiquette below).
• Please make sure that your subject line PRECISELY states what problem you are asking about, as failure to do so causes everyone a great deal of time trying to figure out what you need. For instance, “Fall 2018 Practice Test 3, Question 5a”.
Netiquette
• Netiquette refers to etiquette that is used when communicating on the Internet. Review the Core Rules of Netiquette. When you are communicating via email, discussion forums or synchronously (in real-time), please use correct spelling, punctuation, and grammar consistent with the academic environment and scholarship1.
• We expect all participants in Georgia Tech’s MS in Analytics program, (learners, faculty, teaching assistants, staff) to interact respectfully. You must always play nice
Conner, P. (2006–2014). Ground Rules for Online Discussions, Retrieved 8/14/2020 from https://tilt.colostate.edu/TipsAndGuides/Tip/128
Course Materials
• All content and course materials can be accessed online.
• There is no required textbook for this course, though students are encouraged to find copies of the following references:
• Law, A. M., Simulation Modeling and Analysis, 5th edition, McGraw-Hill Education, New
York, 2015. [This textbook is most for the “theory” aspects of the course.]
• Kelton, W. D., Sadowski, R. P., and Zupick, N. B., Simulation with Arena, 6th edition,
McGraw-Hill, New York, 2015. [This book covers the Arena simulation language.]
• If you want to review probability and statistics, you can get a free pdf version of my book A First Course in Probability and Statistics here. You can also buy an el cheapo softbound version here. We’ve heard that this makes the perfect Independence Day gift!
Technology/Software Requirements
• Internet connection (DSL, LAN, or cable connection desirable)
• R statistical software (free download; see cran.r-project.org)
• Arena simulation software
• Arena is free! Get it here (but make sure to click the “Student” option on the “Job Type” menu)!
• Arena requires a Windows operating system to run on your computer.
• If you don’t have Windows, you can run Arena thru ISyE’s Virtual Lab.
• Arena (and our corresponding lecture material) is currently transitioning to a new version, so the latest Arena version doesn’t perfectly match what’s in the notes. The good news is that everything still works. 😊
• Adobe Acrobat PDF reader (free download; see https://get.adobe.com/reader/)
Disabilities and Special Circumstances
• If you have a disability requiring special accommodations, please make an appointment with the ADAPTS office to discuss the appropriate procedures. Their website is http://disabilityservices.gatech.edu
COVID-19 Related Precautions
Student Illness or Exposure to COVID-19
Course Topics and Pacing Schedule
Weeks Course Topics Release Dates (all times EASTERN)
Week 1
Lesson 1: Getting to Know You
Lesson 2: Syllabus
Lesson 3: Whirlwind Tour
Lesson 4: Whirlwind Tour – History
Lesson 5: What Can We Do for You
Lesson 6: Some Baby Examples
Lesson 7: More Baby Examples
Lesson 8: Generating Randomness
Week 2
Lesson 1 [OPTIONAL]: Calculus Primer
Lesson 2 [OPTIONAL]: Saved By Zero! Solving Equations
Lesson 3 [OPTIONAL]: Integration
Lesson 4 [OPTIONAL]: Integration Computer Exercises
Lesson 5: Probability Basics
Weeks Course Topics Release Dates (all times EASTERN)
Lesson 7: Great Expectations
Lesson 8: Functions of a Random Variable
Lesson 9: Jointly Distributed Random Variables
Lesson 10 [OPTIONAL]: Conditional Expectation
Lesson 11: Covariance and Correlation
Lesson 12: Probability Distributions
Lesson 13: Limit Theorems
Lesson 14 [OPTIONAL]: Introduction to Estimation
Lesson 15 [OPTIONAL]: Maximum Likelihood Estimation
Lesson 16 [OPTIONAL]: Confidence Intervals
Week 3
Lesson 1: Stepping Through Differential Equation
Lesson 2: Monte Carlo Integration
Lesson 3: Monte Carlo Integration Demo
Lesson 4: Making Some Pi
Lesson 5: A Single-Server Queue
Lesson 6: An (s,S) Inventory System
Lesson 7: An (s,S) Inventory System Demo
Lesson 8: Simulating Random Variables
Lesson 9: Simulating Random Variables Demo
Lesson 10: Spreadsheet Simulation
Module 4: General Simulation Principles
Lesson 1: Steps in a Simulation Study
Lesson 2: Some Useful Definitions
Lesson 3: Time-Advance Mechanisms
Lesson 4: Two Modeling Approaches
Weeks Course Topics Release Dates (all times EASTERN)
Week 4
Lesson 1: Introduction Lesson 2: Process-interaction Lesson 3: Let’s Meet Arena!
Lesson 4: The Arena Basic Template
Lesson 5: Create-Process-Dispose Modules
Lesson 6: The Process Module
Lesson 7: Resource, Schedule, and Queue Spreadsheets
Lesson 8: The Decide Module
Lesson 9: The Assign Module
Lesson 10: Attribute, Variable, and Entity Spreadsheets
Lesson 11: Arena Internal Variables
Lesson 12: Displaying Stuff
Lesson 13: Batch, Separate, and Control
Week 5
Lesson 15: Two-Channel Manufacturing Example
Lesson 16: Fake Customers
Lesson 17: The Advanced Process Template
Lesson 18: Resource Failures + Maintenance
Lesson 19: The Blocks Template
Lesson 20: The Joy of Sets
Lesson 21: Description of Call Center
Lesson 22: Call Center Demo Lesson 23: An Inventory Model Lesson 24: One Line vs Two Lines?
Lesson 25 [OPTIONAL]: A Re-entrant Queue
Lesson 26 [OPTIONAL]: SMARTS Files and Rockwell Demos Lesson 27: A Manufacturing System Demo
Lesson 28: Mfg System Details: Advanced Transfer Panel
Lesson 29: Mfg System Details: Sequences
Weeks Course Topics Release Dates (all times EASTERN)
Lesson 31: Mfg System Details: Model Walk-Through
Lesson 32: Mfg System Details: Transporters and Conveyors
Week 6
Lesson 1: Introduction
Lesson 2: Some Lousy Generators
Lesson 3: Linear Congruential Generators
Lesson 4: Tausworthe Generators
Lesson 5: Generalization of LCGs
Lesson 6: Choosing a Good Generator – Some Theory
Lesson 7: Choosing a Good Generator – Statistics Tests, Intro
Lesson 8: Choosing a Good Generator – Goodness-of-Fit Tests
Lesson 9: Choosing a Good Generator – Independence Tests I
Week 7
Lesson 2: Inverse Transform Method
Lesson 3.1: ITM – Continuous Examples
Lesson 3.2: ITM – Continuous Examples DEMO 1
Lesson 3.3: ITM – Continuous Examples DEMO 2
Lesson 4: Inverse Transform Method – Discrete Examples
Lesson 5 [OPTIONAL]: ITM – Empirical Distributions
Lesson 6.1: Convolution Method
Lesson 6.2: Convolution Method DEMO
Lesson 7: Acceptance-Rejection Method
Lesson 8 [OPTIONAL]: Proof of the A-R Method
Lesson 9.1: A-R Method – Continuous Examples
Lesson 9.2: A-R Method – Continuous Examples DEMO
Weeks Course Topics Release Dates (all times EASTERN)
a.m. – Th Aug 4 at 11:59 p.m.
Test Topix for ISyE 6644, Summer 2022
• As GT students, you are expected to formulate problems and solution strategies which are more than mere rote regurgitation of material you learned in class. Thus, you shouldn’t be surprised if some questions cover natural extensions of material from class.
• I’ll supply all necessary tables, e.g., N(0,1), t, and χ2, but you can feel free to use your own.
TEST 1 TOPIX
1. Intro Material
a. Definition of simulation
b. Advantages and disadvantages of simulation
c. History of simulation
d. Typical questions and applications
2. Calculus, Probability, and Statistics Review
a. Calculus [not really responsible for this material, except I might make you search for a zero]
i. Basic definitions
ii. Derivatives
iii. Solving for zeros iv. Integration
v. Numerical integration
b. Probability Preliminaries
i. Conditional probability
ii. Independent events
iii. Definition of random variable iv. Discrete RV’s and probability mass function
v. Continuous RV’s and probability density function
vi. Cumulative distribution function
c. Simulating RV’s (first pass)
i. Discrete uniform distribution
ii. General discrete distribution
iii. Inverse Transform Theorem for continuous RV’s iv. Exponential (and other) continuous distributions via IVT.
v. Generating U(0,1)’s via desert island algorithm, including walk-through of pseudo-code.
d. Expected Values
i. Definition
ii. Discrete and continuous examples of expected value
iii. Law of the Unconscious Statistician
iv. Moments, central moments, variance, standard deviation
v. Discrete and continuous examples of LOTUS
vi. Moment generating function
vii. Examples and properties of mgf’s
e. Functions of a RV
i. Discrete examples
ii. Continuous examples
iii. IVT methods (again) with examples iv. Relationship with LOTUS
f. Jointly distributed RV’s
i. Definition of joint cdf
ii. Marginal cdf’s
iii. Joint and marginal pmf’s iv. Joint and marginal pdf’s
v. Examples for discrete and continuous cases
vi. Independent RV’s
vii. Conditional pmf’s and pdf’s
viii. Conditional expectation [this won’t be on the test] ix. Double expectation E(E(Y|X)) = EY, including examples [this won’t be on the test]
g. Covariance and correlation
i. Definitions
ii. Relationship between independence and correlation
iii. Examples
iv. Miscellaneous properties (e.g., Var(X+Y), bounds on correlation, etc.)
h. Probability distributions
i. Discrete distributions
1. Bernoulli
2. Binomial
3. Geometric
4. Poisson (including discussion on Poisson processes) ii. Continuous distributions
1. Uniform
2. Exponential (including memoryless property)
3. Erlang, Gamma distributions
4. Triangular
5. Normal (including Standard Normal)
6. Other sampling distributions (including chi-square, t, F, and various relationships with each other)
i. Limit theorems
i. Linear combinations of independent normal (including distribution of sample mean)
ii. Convergence in distribution
iii. Law of Large Numbers iv. Central Limit Theorem for independent and identically distributed data.
v. Examples
j. Statistics Tidbits [this material will eventually be covered in modules 8, 9, 10, so it’s in fair territory to have it on the Final! ]
i. Properties of sample mean and sample variance
ii. Confidence intervals for the mean and variance
3. Hand Simulations
a. “Simulating” a differential equation
b. Monte Carlo integration
c. Determining π via simulation (dart tossing on a circle and sphere)
d. Single-server queue (including FIFO and LIFO service disciplines)
e. (s,S) inventory system
f. Simulating RV’s (repeats some material from the Prob/Stats review)
g. Spreadsheet simulation (e.g., stock portfolio in Excel)
4. General Simulation Principles
a. Steps in a simulation study
b. List of various simulation definitions (e.g., event, system state, simulation clock, etc.)
c. Event-Scheduling vs. Process Interaction modeling approaches
d. How are events processed?
e. Future events list + extended example
f. Simulation languages – what to look for
Plus, the first few Arena mini-topix below…
5. Arena
a. Layout of Arena screen (panels, modules, etc.)
b. Basic Process template: CREATE-PROCESS-DISPOSE modules
c. SEIZE-DELAY-RELEASE inside of the PROCESS module.
d. Resource, Schedule, Queue, Entity, and other spreadsheets
e. DECIDE module – probabilistic and conditional routing
f. ASSIGN module
TEST 2 TOPIX
Everything from Test 1 + the following (with less emphasis placed on the Test 1 material)…
g. Simple examples, e.g. (partial list),
i. Single-server queue
ii. Parallel servers
iii. Schedules for servers iv. Multiple arrival streams
h. Displays, graphics, etc.
i. BATCH and SEPARATE modules
j. Run set-up and control
k. More-sophisticated queueing networks (e.g., two-channel manufacturing example, call center example)
i. Advanced Process modules (e.g., SEIZE, DELAY, RELEASE modules)
ii. Some primitive blocks (e.g., QUEUE)
iii. Use of “pretend” customers iv. Nonhomogeneous Poisson arrivals
v. Use of resource sets, including how to prioritize servers
vi. Use of submodels
l. Inventory processes
m. Crazy examples such as re-entrant queues
n. SMARTS files and other Rockwell examples
o. Manufacturing systems
i. Advanced Transfer modules (e.g., ROUTE, ENTER, LEAVE)
ii. Sequences of customer visitation locations
iii. Advanced sets of sequences iv. Transporters and conveyors
6. Uniform Random Number Generation
a. Overview – desirable properties of a pseudo-random number generator
b. Some generators we won’t use, e.g.,
i. PRN’s from tables
ii. Midsquare
c. Linear congruential generators
i. Cycling
ii. 16807 desert island generator (again)
iii. RANDU (a bad generator)
d. Tausworthe generator
e. Combined generators
i. L’Ecuyer’s generator of cycle length 2191
ii. Mersenne Twister
f. Some theoretical considerations, e.g., from Knuth’s book
g. Statistical tests for randomness
i. Goodness-of-fit test – Chi-squared
i. Runs tests for independence
1. Runs up and down
2. Runs above and below the mean
3. Autocorrelation test [this won’t be on the test]
7. Random Variate Generation
a. Inverse Transform Theorem (yet again)
i. Proof
ii. Discrete example adaptations
iii. Continuous examples
1. East ones such as Exponential, Weibull, etc.
2. Slightly harder examples such as Triangle distribution
3. Normal distribution, both exact and approximate methods iv. Special case methods, e.g., Geometric
v. Empirical distributions [this won’t be on the test]
b. Convolution method
i. Binomial
ii. Triangle
iii. Erlang iv. CLT
1. Desert island sum of Uniforms to generate Normal
2. Normal approximation to Poisson (including continuity correction)
v. Cauchy
1. Cauchy’s add up to another Cauchy
2. IVT method
3. Ratio of two Normals
c. Acceptance-Rejection methods
i. Trivial Uniform example
ii. Some discussion on general method
iii. Proof of the general method [don’t expect to see this on the test, unless I’m in a really bad mood!]
iv. Examples involving polynomial and half-normal p.d.f.’s
v. Poisson distribution
d. Composition
e. Special-case techniques
i. Box-Muller method for Normal distribution
ii. Extensions of B-M, e.g., Cauchy, Chi-squared.
iii. Generating min’s and max’s of iid RV’s, e.g., min of iid Exponentials.
TEST 3 (FINAL) TOPIX
Everything in the freaking course, including the following new stuff (with less emphasis placed on the Tests 1 and 2 material)…
f. Multivariate Normal
i. Definition in 2 and then >2 dimensions
ii. Cholesky decomposition method for generating realizations (exact expression in 2 dimensions, algorithm for >2 dimensions)
g. Stochastic processes
i. Markov chains
ii. Poisson processes
iii. Nonhomogeneous Poisson processes (via thinning method) iv. Time series
1. MA(1)
2. AR(1)
3. EAR(1)
4. ARTOP
v. M/M/1 queue waiting times
vi. Brownian motion
1. Definition and history
2. Elementary properties, including covariance structure
3. General CLT
4. How to generate
5. Geometric BM and financial applications
8. Input Analysis
a. General discussion
i. Careful about GIGO with respect to simulation input
ii. What makes a good distribution
iii. Identification of obvious distributions
b. Estimation review
i. Unbiased estimators
1. Definition
2. Sample mean
3. Sample variance
4. Other examples such as Unif(0,θ)
ii. Mean squared error
iii. Maximum likelihood estimators
1. Definition
2. Examples such as Exponential
3. Two-dimensional examples such as Normal with unknown mean and variance
4. Other tougher examples such as Unif(0,θ) and Gamma
5. Invariance Property + examples iv. Method of Moments [this won’t be on the test (sorry, MoM!)]
c. Goodness-of-fit tests for input distributions
i. Chi-squared for Exponential
ii. Chi-squared for Weibull, including search techniques such as bisection and Newton
iii. Kolmogorov-Smirnov iv. More goodness-of-fit tests
d. Problem Children
i. Little or no data
ii. Data from an unusual distribution
iii. Nonstationary data iv. Multivariate / correlated data
e. Arena Input Analyzer demo
9. Output Analysis
a. Introduction
i. The need for output analysis in a proper statistical study
ii. Simulation data isn’t iid normal, and this is a problem
iii. Types of output analysis – finite-horizon (terminating) and steady-state
b. A mathematical interlude related to the fact that the variance of the sample mean isn’t Var(Xi)/n, and its consequences [I might ask you to calculate the variance of the sample mean for a specific process, but nothing else.]
c. Finite-horizon (terminating) simulations
i. Examples
ii. Confidence intervals for mean performance via the method of
Independent Replications
d. Initialization problems
e. Steady-state analysis for a single system
i. Examples
ii. Confidence intervals for the steady-state mean via the method of Batch
Means
iii. Properties of Batch Means [The more-mathematical aspects of this topic this won’t be on the test.]
iv. Overlapping Batch Means
v. Other methods
10. Comparing Systems
a. Classical confidence interval for the mean of one normal population
b. Classical confidence interval to compare the means of two normal systems
i. Variance completely unknown
ii. Paired-t CI
iii. Use in simulation scenarios
c. Variance reduction techniques
i. Common random numbers
ii. Antithetic random numbers [no theory related to this will be on the test] iii. Control variates [this won’t be on the test]
d. Ranking and selection methods to compare means of >2 systems
i. Definition of problem
ii. Relevance to simulation
iii. Indifference-zone approach iv. Normal means selection problem
• Bechhofer’s single-stage procedure
• Extensions
v. Bernoulli parameter selection problem
• Sobel and Huyett single-stage procedure
• Extensions vi. Multinomial cell selection problem
• Multinomial review and motivation
• Bechhofer, Elmaghraby, and Morse single-stage procedure • Extensions
