MATH441/OR441 Operations Research I

Fall 2007


George Mason University

Department of Systems Engineering and Operations Research


Tuesday and Thursday 3:00pm-4:15pm,

Thompson Hall, Room 222


Instructor: Yifan Liu

Office: Science & Technology Building II, Room 125;

Phone: (703)993-4620; fax (703)993-1521


Office Hour: Wednesday 12:00-1:00pm, and 6:00-7:00pm, or by appointment




Text: Wayn. L. Winston, Operations Research Applications and Algorithms, Fourth Edition, 2003.


Course Website: All course material will be posted on WebCT.


Course Summary: This course will introduce the basic mathematical ideas and methods of Deterministic Operations Research. We will discuss modeling real life problems, the basic concepts of Linear Programming (LP), and methods for solving LP problems. We are going to discuss briefly some concepts of nonlinear optimization and their applications. There will be a project, which requires modeling real life problems using MPL languages available for downloading from the Internet (


Tentative Course Schedule (subject to slight change, depending on the pace of the course)


Date                Topic                                                                                      Chapters

8/28                 Introduction to Operations Research                                      1

8/30                 Linear Programming (I)                                                          3.1-3.2


9/4                   Linear Programming (II)                                                         3.3-3.4

9/6                   Linear Programming (III)                                                       3.5-3.9


9/11                 The Simplex Method (I)                                                         4.1-4.2

9/13                 The Simplex Method (II)                                                        4.5


9/18                 The Simplex Method (III)                                                      4.6-4.8

9/20                 The Simplex Method (IV)                                                      4.12


9/25                 Sensitivity Analysis & Duality (I)                                          6.1-6.2

9/27                 Sensitivity Analysis & Duality (II)                                         6.3


10/2                 (Tuesday classes do not meet this week because of Columbus Day recess)

10/4                 Sensitivity Analysis & Duality (III)                                       6.5-6.7


10/9                 Sensitivity Analysis & Duality (IV)                                       6.8-6.9

10/11               Review


10/16               The Transportation Problem (I)                                               7.1                  

10/18               Midterm (Transportation problem NOT on midterm)     


10/23               The Transportation Problem (II)                                             7.2

10/25               Networks (I)                                                                           8.1-8.2


10/30               Networks (II)                                                                          8.3, 8.6

11/1                 Integer Programming (I)                                                         9.1-9.2


11/6                 (Instructor out for conference, class cancelled)

11/8                 (Instructor out for conference, class cancelled)


11/13               Integer Programming (II)                                                        9.3

11/15               Integer Programming (III)                                                      9.5


11/20               Integer Programming (IV)                                                      9.7                  

11/22               Nonlinear Programming (I)                                                     11.1-11.3


11/27               Nonlinear Programming (II)                                                   11.4, 11.6

11/29               Nonlinear Programming (III)                                                  11.8


12/4                 Nonlinear Programming (IV)                                                  11.9

12/6                 Review


12/11               Final Exam


Note: Sensitivity Analysis & Duality seems to be the most difficult part of this course according to the feedback from last year. Be prepared to spend more time on preview before coming to the class, and on the homework.




Class Participation: 10%. According to the suggestions from the students last year, and from other professors, I will try to use the examples different from those in the textbook to illustrate the same content, and leave the textbook examples for you to read before and after class, so that you will have more examples to understand the stuff better. Therefore, class participation is mandatory, and coming to most of the lectures counts for 5%. From time to time, I will offer chances for the students to volunteer to do some in-class exercises on the board, on which 3% based. The rest 2% is awarded for other kinds of active participation, such as asking or answering good questions in class.


Homework: 10%. At the end of each class, I will assign 1 or 2 problems for homework, which will be collected, graded and returned in a weekly pattern as follows:

  1. The homework will be collected 12 times, on each Thursday starting from 9/6 till 12/6, excluding 10/18 (so that you have more time to prepare for the midterm) and 11/8 (class cancelled)
  2. All homework will be graded. The lowest two scores will be dropped, and the rest 10 will count 1% each towards your final grade.
  3. All problems assigned will be collected on the Thursday in the following week (or one more week later if that Thursday is 10/18 or 11/8). That is, Tuesday problems won’t be collected until at least 9 days later, and Thursday problems won’t be collected until at least one week later.
  4. All collected homework will be graded within one week, and be returned to you the following Thursday, with the exceptions for exam preparation:
    1. The homework collected on 10/11 will be returned to you on 10/16.
    2. The homework collected on 12/6 can be picked up in my office on 12/10, the reading day.

In these case, you have sometime to go over the last homework before the exams.

You are strongly recommended to do the problems before the next class, so that you can be better prepared for the new lecture.


Midterm: 25%. Thursday, 10/18, class time, open book, open notes, NO computer allowed (calculator OK).


Computational Project: 20%. Use MPL languages software, available for downloading from, for a real-life problem. The project problem will be assigned shortly after the midterm, and be due on 12/11 when the final exam starts. The grading of the project is composed of three parts: Formulation (6%), Programming (8%), and Writing (6%).


Final Exam: 35%. Tuesday, 12/11, 1:30-4:15pm, open book, open notes, NO computer allowed (calculator OK). Final exam will be mainly based on the part not covered in the mid-term, but may use some of the knowledge learned in the first half of the semester.


Make-up exams will only be given for extreme situations (religious reasons, family emergency, sickness, conference or business trips, etc.), and only if I am contacted before the exam is given and full arrangements are established. Early leave for the winter break does NOT qualify for an alternative time for the final exam.