2024 Faculty Courses School of Engineering Undergraduate major in Industrial Engineering and Economics
Advanced Operations Research
- Academic unit or major
- Undergraduate major in Industrial Engineering and Economics
- Instructor(s)
- Tomomi Matsui
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Tue / 3-4 Fri
- Class
- -
- Course Code
- IEE.A330
- Number of credits
- 200
- Course offered
- 2024
- Offered quarter
- 1Q
- Syllabus updated
- Mar 14, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course covers some mathematical methods in operations research. The topics include, transportation problems, routing problems, network design problems, AHP and DEA. We also review some statistical models including Markov chain, queueing theory, and models for choice behavior. We discuss some topics related to game thery, e.g., stable marriage, spatial interaction model, linear production game, and social choice theory.
The objective of this course is to let students learn basic methods in operations research.
Course description and aims
By completing this course, students will have the necessary tools to do the following:
(1) Understand fundamental properties of optimization models
(2) Understand fundamental properties of statistical models
(3) Understand fundamental properties of some models related to game theory
Keywords
optimization problem, statistical model, game theory
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
In each class we give a lecture in the first half and then assign some exercise problems in the last half.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | overview of the lecture | Details will be given in each lecture. |
| Class 2 | basic algorithms | understand the basic algorithms |
| Class 3 | linear programming | understand the mathematical structure and algorithms of linear programming |
| Class 4 | duality theorem | understand the mathematical structure of duality theorem |
| Class 5 | data envelopment analysis | understand the mathematical structure and algorithms of the data envelopment analysis |
| Class 6 | shortest path problem and assignment problem | understand the mathematical structure and algorithms of shortest path problems and assignment problems |
| Class 7 | maximum flow problem | understand the mathematical structure and algorithms of maximum flow problems |
| Class 8 | graph coloring problem | understand the mathematical structure and algorithms of graph coloring problem |
| Class 9 | Mid-term Exam | check the level of understanding of the classes 1-８ topics |
| Class 10 | social choice theory | understand the mathematical structure of the social choice theory |
| Class 11 | integer programming | understand the mathematical structure and algorithms of the integer programming |
| Class 12 | Markov chain | understand the mathematical structure of Markov chains |
| Class 13 | analytic hierarchy process | understand the mathematical structure and algorithms of analytic hierarchy process |
| Class 14 | queueing theory | understand the mathematical structure of queueing theory |
| Class 15 | summary |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None
Reference books, course materials, etc.
M. Mori and T. Matsui, ``Operations Research,'' Asakura Publishing Co., Ltd., 2004.
Evaluation methods and criteria
To Be Determined (Regular face-to-face lessons: Midterm and final exams 70%, exercise problems 30%.）
Related courses
- IEE.A206 ： Operations Research
- IEE.A430 ： Numerical Optimization
Prerequisites
In principle, undergraduate students of Department of Industrial Engineering and Economics, and undergraduate students of the 4-university union course can attend the class.
It is desirable to have completed ‘‘Operations Research.’’
Contact information (e-mail and phone) Notice : Please replace from ”[at]” to ”@”(half-width character).
matsui.t.af[at]m.titech.ac.jp