Stochastic Operations Research (OR) is concerned with complex
systems that operate under randomness and uncertainty, and
aims to develop mathematical models and techniques for the analysis and
optimization of such systems. In data analytics, stochastic OR is an important
foundation for Prescriptive Analytics, which is a process that analyzes data
and provides instant recommendations on how to optimize business practices to
suit multiple predicted outcomes with consideration of system randomness and
future uncertainty.
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.
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 will
increase by 20~50% since a holiday is coming, how many additional agents should
you add to handle the higher demand? More agents implies
higher costs, while less agents may increase customer waits. 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 distributions of
individual stock returns and determine good decisions.
Instructor: Professor
Chun-Hung Chen
Email: cchen9@gmu.edu
Office: Engineering Building,
Room 2213
Phone: 703-993-3572
Fax: 703-993-1521
Office Hours: Wednesday 3:30 - 4:30PM; Friday 9:30-10:30AM
Teaching Assistant: Mr. Bahador Dodge
Email: bdodge @gmu.edu
Office: Engineering Building, Room 2216
Zoom link: provided in the BB
Office Hours: Wednesdays 6:00-7:00pm and Thursdays 3:00-4:00pm (The TA
is assisting multiple classes with many students. To minimize your waiting
time, you are advised to send an email to TA in advance. Thus
he can give you a suggested best time to arrive.)
Required Text: W. L. Winston, "Operations Research:
Applications and Algorithms" 4rd edition, 2004.
Two copies of the text books 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.
Library Resource Assistant: Theresa Calcagno; tcalcagn@gmu.edu;
703-993-3712
Prerequisites: STAT 344, or MATH 351, or equivalent.
Grading: Homework 5%; Term Project 15%, Two exams 80%
(higher one 45%, lower one 35%). 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.
Examinations: There will be two take-home exams. The exam
runs from 4:30pm of the day to 11:00pm of the next
day. 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 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.
Recordings of New 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.
To access the new recordings, after you log onto your blackboard
and get into our class, please choose "tool" and click "Class Collaborate Ultra". After you enter
Collaborate, click the menu on the upper left corner of the Collaborate window
and then choose "Recordings".
Blackboard (to
log in Bb, please
click here):
1. You can download the ppt files of lectures at
"Course Content" section.
2.
Lecture
recordings of from previous years are available at
"Course Content" section.
3. Homework
assignments and term project are available at "Assignment"
section.
4. Solutions to
homework will be posted at "Assignment" section after submission deadline.
5. Sample exam
questions and their solutions can be downloaded at "Assignment" section.
Class Format:
1. This is a hybrid
class, including in-person meetings at classroom (Enterprise Hall 277) and
online teaching via Blackboard.
2. No matter which
section you enroll, you are welcome to attend the classroom section (Enterprise
Hall 277) and meet with the instructor face-to-face.
3. No matter which
section you enroll, to save your transportation time, you are welcome to attend
the online section through
Blackboard. After you log into your blackboard and get into our class, please
choose "tool" and click "Class Collaborate Ultra". Then you
will see the link to join the class.
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 & Probability
review |
2 |
Chapter 12 |
|
B |
Decision making under
uncertainty |
1.5 |
Chapter 13 |
|
C |
Inventory Models |
3 |
Chapters 15 & 16 |
|
D |
Markov chains |
2 |
Chapter 17 |
|
E |
Queueing theory |
2 |
Chapter 20 |
|
F |
Simulation (using basic Excel) |
1.5 |
Chapters 21, 22, & 23 |
Go to Professor Chun-Hung Chen's Page
Additional University Policies
Academic Standards:
GMU
Common Course Policies - Stearns Center for Teaching and Learning
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Standards exist to promote authentic scholarship, support the institution's
goal of maintaining high standards of academic excellence, and encourage
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University Calendar:
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with Disabilities:
Students with disabilities who seek accommodations in a course must be registered with the George Mason University Office of Disability Services (ODS) and inform their instructor, in writing, at the beginning of the semester GMU Common Course Policies - Stearns Center for Teaching and Learning
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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).
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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. I use she/her for myself, and you may address me as Dr. Last Name in emails and verbally.
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George Mason University promotes a living and learning environment for outstanding growth and productivity among its students, faculty, and staff. Through its curriculum, programs, policies, procedures, services, and resources, Mason strives to maintain a quality environment for work, study, and personal growth. An emphasis on diversity and inclusion throughout the campus community is essential to achieve these goals. Diversity is broadly defined to include such characteristics as, but not limited to, race, ethnicity, gender, religion, age, disability, and sexual orientation. Diversity also entails different viewpoints, philosophies, and perspectives. Attention to these aspects of diversity will help promote a culture of inclusion and belonging and an environment where diverse opinions, backgrounds, and practices have the opportunity to be voiced, heard, and respected. The reflection of Mason's commitment to diversity and inclusion goes beyond policies and procedures to focus on behavior at the individual, group, and organizational levels. The implementation of this commitment to diversity and inclusion is found in all settings, including individual work units and groups, student organizations and groups, and classroom settings; it is also found with the delivery of services and activities, including, but not limited to, curriculum, teaching, events, advising, research, service, and community outreach. Acknowledging that the attainment of diversity and inclusion are dynamic and continuous processes and that the larger societal setting has an evolving socio-cultural understanding of diversity and inclusion, Mason seeks to continuously improve its environment. To this end, the university promotes continuous monitoring and self-assessment regarding diversity. The aim is to incorporate diversity and inclusion within the philosophies and actions of the individual, group, and organization, and to make improvements as needed.
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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:
To make constant, conscious decisions to interrupt racism and cultivate equity, inclusion, and justice for people of all racial backgrounds, and in particular those from Black communities and other communities of color, who are most likely to bear the direct and indirect costs of systems of white supremacy;
To interrogate histories of white supremacy and white-dominant culture, and to examine the ways in which these histories have impacted our individual beliefs, our interpersonal relationships, our institutional and structural policies and processes, and our entire society;
To make a commitment to being responsible for our own relationships to, and actions within, systems of white supremacy; and
To cultivate a practice of self-awareness and self-reflection that allows us to critically evaluate our own role in upholding white supremacy and identify the ways we can interrupt cycles of racism at the individual, interpersonal, institutional, and structural levels.
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