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.
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 stocks. 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 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 investment 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: Ms. Raina Joy Saha
Email: rsaha3@gmu.edu
Office: Engineering Building, Room 2216
Office Hours: Tuesday 3:00 - 5:00 PM, and Thursday 3:00 - 4:00 PM
Prerequisites: STAT 346, or MATH 351, or equivalent.
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.
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.
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.
Class Format and in-class quiz:
The instructor will come to the classroom to give
lectures in person. It is preferred that students also come to the classroom.
However, students can choose to attend
the class online through Blackboard, except taking exams. After you log into your blackboard and get into
our class, please choose "tool". and click "Blackboard
Collaborate Ultra". Then you will see the link to join the class.
Two quizzes will be given in each class: one
before the middle break and another one near the end of the class. To encourage
class participation, the instructor will ask several questions during the
lecture. If you choose to attend the class online, you have
to answer one instructor's question before each quiz in order to be
qualified to take that quiz online. To answer questions online, please unmute
your microphone and speak out. Further details will be given during classes.
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 the teaching
materials and the announcements made in classes.
To access the new recordings, after you log into
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):
Homework assignments, solutions, ppt files of
lectures, lecture recording, and sample exam questions can be downloaded at
Blackboard. Specifically,
1.
You can
download 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.
General Rules:
1. Homework must be submitted as a single pdf file through
Blackboard via myMason
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 |