Companies in many industries can employ stochastic OR to improve
their business practices and increase profitability. For example, in the
financial services sector, planners, analysts, and portfolio managers use
stochastic modeling to manage their assets and liabilities and optimize their
portfolios. When choosing investment vehicles, it is critical to be able to
view a variety of outcomes under multiple factors and conditions, some of which
are stochastic. Another example is that the insurance industry relies heavily
on stochastic modeling to predict how company balance sheets will look at a given
point in the future.
Imagine that you are a store manager. How do you manage your
inventory level? High inventory implies higher costs. On the other hand, low
inventory usually leads to out of stock. What is your optimal inventory
decision while considering the uncertainty of future demand?
Another example we will explore in the class: imagine that you are
the manager of an airline call center. If you expect the number of calls to
increase by 20~50% since a holiday is coming, how many additional agents should
you add to handle the higher demand? More agents imply higher costs, while less
agents may increase customer waiting. We will model the call center as a
queueing system and apply queueing theory to find a good decision.
In this class, we will cover several important stochastic models
in Operations Research:
In the term project, students will develop Monte Carlo simulation
(using basic Excel) to analyze how various investment portfolios may perform
based on the probability distribution of individual stock returns and determine
good investment decisions.
Instructor: Professor
Chun-Hung Chen
Email: cchen9@gmu.edu
Office: Engineering Building,
Room 2213
Zoom link: provided in the BB
Phone: 703-993-3572
Fax: 703-993-1521
Office Hours: Thursday 3:30 - 4:30PM; Friday 9:30-10:30AM
Teaching Assistant: Ms. Farzana Sultana
Email (preferred): fsultan5@gmu.edu
Phone: 405-269-6031
Course Description as per
Catalog: Survey of
probabilistic methods for solving decision problems under uncertainty,
probability review, decision theory, queuing theory, inventory models,
forecasting, Markov chain models, and simulation are covered. Emphasis on
modeling and problem solving.
Course Learning Outcomes:
Required Text: W. L. Winston, "Operations Research:
Applications and Algorithms" 4th edition, 2004. Two copies of the textbook
have been placed on reserve at the Johnson Center Library. It may be borrowed
for 2 hours at a time. To borrow the book, you will need the call number:
T57.6.W645 2004.
Prerequisites: STAT 334, 344, 346, or MATH 351, or
equivalent.
Grading: There are two options:
In either option, a typical scale
will be applied to determine the final letter grade, i.e., B- for >80; B for
>83; B+ for >87; A- for >90; A for >93; etc.
In-class quiz:
Two quizzes will be given each week: one before the
middle break and another one near the end of the class.
Examinations:
The two exams will be held in class. Make
up exam questions will be MUCH HARDER than regular exam questions.
There is no final exam. We will do a term project near the end of
the semester.
Term Project is about the use of Monte Carlo simulation.
Students will develop simulation (using basic Excel) to analyze how various
investment portfolios may perform and determine good investment decisions.
Details will be given during the semester. The goal is to learn how a
stochastic modeling tool can be easily applied to real-life problems, and to
appreciate the power of simulation.
Computing Use: Basic Excel.
Use of
Generative-AI programs: It's
important to view Generative-AI programs as tools, like calculators. They
should not be used as solvers for assignment/exam problems.
Canvas (to
log in, please click here):
Homework
assignments, solutions, ppt files of lectures, lecture recording, and sample
exam questions can be downloaded at Canvas.
Specifically,
1. You can download ppt files of lectures in the
"Modules" section.
2.
Lecture
recordings from previous years are
available in the "Modules" section.
3. Homework
assignments and term project are available in the "Assignments" section.
4. Solutions to
homework will be posted in the "Modules" section after
submission deadline.
5. Sample exam
questions and their solutions can be downloaded in
the "Modules" section.
Recordings of Lectures:
All of our new lectures will be recorded. If you miss a class, you should go to
watch those recordings to catch up with the teaching materials and the
announcements made in classes. There are two types of recordings:
1.
Recordings
of new lectures.
2.
Lecture
recordings from previous years. This is also useful in the case when we encounter technical
issues when we record the new lectures. This is also useful if you want to make
better preparation before the class.
Both types of recordings are
available in the "Modules" section.
General Rules:
1. Homework must be submitted as a single pdf file through
Blackboard.
2.
Late
homework is always allowed. No need to get advanced permission. However, the
penalty for late homework is 25% for the first day and then 5%
per day. No exemption.
3.
No
collaborations are allowed for homework, although discussions are encouraged.
4.
Comments are
strongly encouraged.
5.
No cheating.
Course
Outline & Reading Assignment:
|
|
Topics |
Time (week) |
Reading Assignment |
|
A |
Introduction |
1 |
|
|
B |
Probability review |
2 |
Chapter 12 |
|
C |
Inventory Models |
3 |
Chapters 15 & 16 |
|
D |
Markov chains |
2 |
Chapter 17 |
|
E |
Queueing theory |
2 |
Chapter 20 |
|
F |
Simulation (using basic Excel) |
2 |
Skim Chapters 21, 22, 23 |
Go to Professor Chun-Hung Chen's Page
Additional Policies and Administrative Notes
Statement regarding use of Generative AI tools:
Student Use of Electronic Devices:
Closings and cancellations: In the event of inclement weather or another major event, the university announces class cancellation, delay of classes and changes to administrative office hours through the university switchboard, 703-993-1000; the George Mason home page; GMU-TV; and local radio and television stations.
Communication Policy: Mason Email (GMU Email):
Students are responsible for the content of university communications sent to
their George Mason University email account and are required to activate their
account and check it regularly. All communication from the university, college,
school, and program will be sent to students solely through their Mason email
account. Additional Modes of communication include emails to/from the
instructor or Canvas.
Emergency Preparedness: In the event of an emergency, we will follow GMU procedures. You may want to register with Mason Alert.
Privacy: Students must
use their GMU email account to receive important University information, including messages related
to this class.
Student Resources:
Information and links
regarding these and other student support offices are available on our Student Support Resources on Campus page.
Patriot Pass:
Once you sign up for your
Patriot Pass, your passwords will be synchronized, and you will use your
Patriot Pass username and password to log in to the following systems: Canvas,
University Libraries, MasonLive, myMason, Patriot Web, Patiot Connect, Stellic,
Virtual Computing Lab, and WEMS. [See https://password.gmu.edu/index.jsp ].
University Policies:
Students must follow
university policies. [See http://universitypolicy.gmu.edu ].
Responsible Use of Computing:
Students must follow the
university policy for the Responsible Use of Computing. [See http://universitypolicy.gmu.edu/policies/responsible-use-of-computing/ ].
Name and Pronouns Statement:
If you wish, please share
your name and gender pronouns with me and how best to address you in class via
email or during class introductions. You may address me as Dr./Prof. Chen or
just Professor in emails and verbally.
All-inclusive Diversity, Access
and Engagement:
The
programs and services offered by George Mason University are open to all who
seek them. George Mason does not discriminate on the basis of race, color,
religion, ethnic national origin (including shared ancestry and/or ethnic characteristics),
sex, disability, military status (including veteran status), sexual
orientation, gender identity, gender expression, age, marital status, pregnancy
status, genetic information, or any other characteristic protected by law.
After an initial review of its policies and practices, the university affirms
its commitment to meet all federal mandates as articulated in federal law, as
well as recent executive orders and federal agency directives. https://oacc.gmu.edu/
https://hr.gmu.edu/all-inclusive-diversity-access-and-engagement/
Anti-Racism Statement:
As a member of the George Mason
University community, the Volgenau School of Engineering plays an integral role
in building an educational environment that is committed to anti-racism and
inclusive excellence. An anti-racist approach to higher education acknowledges
the ways that individual, interpersonal, institutional, and structural
manifestations of racism against Black individuals and other people of color
contribute to inequality and injustice in our classrooms, on our campuses, and
in our communities and it strives to provide our community members with
resources to interrupt cycles of racism so as to cultivate a more equitable,
inclusive, and just environment for all of our students, staff, faculty,
alumni, and friends, regardless of racial background.
To be anti-racist means:
We believe that the work of
anti-racism starts with each individual and that in cultivating an anti-racist
approach to research, scholarship, and practice, our students will build a
skill set rooted in principles of equity, inclusion, and justice that they will
carry with them throughout their lives.
For more information on how
to continuously cultivate the practice of anti-racism, see this guide from the
National Museum of African American History and Culture on how to be
anti-racist:
https://nmaahc.si.edu/learn/talking-about-race/topics/being-antiracist
Student Services:
University Libraries:
The Mason library provides
resources for both in-class [See http://library.gmu.edu/]
and distance students. [See http://library.gmu.edu/distance ].
Writing Center:
The George Mason University
Writing Center staff provides a variety of resources and services (e.g., tutoring,
workshops, writing guides, handbooks) intended to support students as they work
to construct and share knowledge through writing. You can now sign up for an
Online Writing Lab (OWL) session or for a face-to-face session in the Writing
Center, which means you set the date and time of the appointment! Learn more
about the Online Writing Lab (OWL) (found under Online Tutoring).
Counseling and Psychological
Services:
The George Mason University
Counseling and Psychological Services (CAPS) staff consists of professional
counseling and clinical psychologists, social workers, and counselors who offer
a wide range of services (e.g., individual and group counseling, workshops, and
outreach programs) to enhance students' personal experience and academic performance
[See http://caps.gmu.edu ].
Common Policies Affecting All Courses at George Mason University
Updated August 2024
These four policies affect students in all courses at George Mason University. This Course Policy Addendum must be made available to students in all courses (see Catalog Policy AP.2.5).
Additional policies affecting this course, and additional resources or guidance regarding these policies, may be provided to students by the instructor.
Academic Standards exist to promote authentic scholarship, support the institution's goal of maintaining high standards of academic excellence, and encourage continued ethical behavior of faculty and students to cultivate an educational community which values integrity and produces graduates who carry this commitment forward into professional practice.
As members of the George Mason University community, we are committed to fostering an environment of trust, respect, and scholarly excellence. Our academic standards are the foundation of this commitment, guiding our behavior and interactions within this academic community. The practices for implementing these standards adapt to modern practices, disciplinary contexts, and technological advancements. Our standards are embodied in our courses, policies, and scholarship, and are upheld in the following principles:
Violations of these standards - including but not limited to plagiarism, fabrication, and cheating - are taken seriously and will be addressed in accordance with university policies. The process for reporting, investigating, and adjudicating violations is outlined in the university's procedures. Consequences of violations may include academic sanctions, disciplinary actions, and other measures necessary to uphold the integrity of our academic community.
The principles outlined in these academic standards reflect our collective commitment to upholding the highest standards of honesty, acknowledgement, and uniqueness of work. By adhering to these principles, we ensure the continued excellence and integrity of George Mason University's academic community.
Student responsibility: Students are responsible for understanding how these
general expectations regarding academic standards apply to each
course, assignment, or exam they participate in; students should ask their
instructor for clarification on any aspect that is not clear to them.
Disability Services at George Mason University is committed to upholding the letter and spirit of the laws that ensure equal treatment of people with disabilities. Under the administration of University Life, Disability Services implements and coordinates reasonable accommodations and disability-related services that afford equal access to university programs and activities. Students can begin the registration process with Disability Services at any time during their enrollment at George Mason University. If you are seeking accommodations, please visit https://ds.gmu.edu/ for detailed information about the Disability Services registration process.
Disability Services is located in Student Union Building I (SUB I), Suite 2500. Email: ods@gmu.edu. Phone: (703) 993-2474.
Student responsibility: Students are responsible for registering with Disability Services and communicating about their approved accommodations with their instructor in advance of any relevant class meeting, assignment, or exam.
The Family Educational Rights and Privacy Act (FERPA) governs the disclosure of education records for eligible students and is an essential aspect of any course. Students must use their GMU email account to receive important University information, including communications related to this class. Instructors will not respond to messages sent from or send messages regarding course content to a non-GMU email address.
Student responsibility: Students are responsible for checking their GMU email regularly for course-related information, and/or ensuring that GMU email messages are forwarded to an account they do check.
As a part of George Mason University's commitment to providing a safe and
non-discriminatory learning, living, and working environment for all members
of the University community, the University does not discriminate on the basis of sex or gender in any of its education or
employment programs and activities. Accordingly, all non-confidential employees, including your faculty member, have a
legal requirement to report to the Title IX Coordinator, all relevant details
obtained directly or indirectly about any incident
of Prohibited Conduct (such as sexual harassment, sexual assault,
gender-based stalking,
dating/domestic violence). Upon notifying the Title IX Coordinator of
possible Prohibited Conduct, the Title IX Coordinator will assess the report
and determine if outreach is required. If outreach is required, the individual the report is about (the
"Complainant") will receive a communication, likely in the form of an
email, offering that person the option to meet with a representative of the
Title IX office.
For more information about non-confidential employees, resources, and Prohibited Conduct, please see University Policy 1202: Sexual and Gender-Based Misconduct and Other Forms of Interpersonal Violence. Questions regarding Title IX can be directed to the Title IX Coordinator via email to TitleIX@gmu.edu, by phone at 703-993-8730, or in person on the Fairfax campus in Aquia 373.
Student opportunity: If you prefer to speak to someone confidentially, please contact one of Mason's confidential employees in Student Support and Advocacy (SSAC), Counseling and Psychological Services (CAPS), Student Health Services (SHS), and/or the Office of the University Ombudsperson.
Go to Professor
Chun-Hung Chen's Page