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 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
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 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.
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.
General Rules:
1. No matter which
section you enroll, you are welcome to attend the classroom section (Enterprise
Hall 274) and meet with the instructor face-to-face.
2. 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.
3.
Homework
must be submitted as a single pdf file through Blackboard via myMason
4.
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.
5.
No
collaborations are allowed for homework, although discussions are encouraged.
6.
Comments are
strongly encouraged.
7.
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 |