OR 442/MATH 442

Stochastic Operations Research

Fall 2023

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: Thursday 3:00 - 5:00 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:

  1. Default option (with quiz): Homework 5%; Two exams, 30% each; Term project 10%; Quiz in class 30% (four lowest ones will be dropped). Total is 105/100.
  2. No-quiz option: Homework 5%; Two exams, 42.5% each; Term project 10%. Total is 100/100. To choose this option, let the instructor know by the end of the fourth 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 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:



Time (week)

Reading Assignment






Probability review


Chapter 12


Inventory Models


Chapters 15 & 16


Markov chains


Chapter 17


Queueing theory


Chapter 20




Chapter 24


Simulation (using basic Excel)


Skim Chapters 21, 22, 23


Go to Professor Chun-Hung Chen's Page