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.
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
optimization problem, statistical model, game theory
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
---|---|---|---|---|
- | - | ✔ | - | ✔ |
In each class we give a lecture in the first half and then assign some exercise problems in the last half.
Course schedule | Required learning | |
---|---|---|
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 | End-term Exam | check the level of understanding of the classes 10-14 topics |
None
M. Mori and T. Matsui, ``Operations Research,'' Asakura Publishing Co., Ltd., 2004.
Midterm and final exams 70%, exercise problems 30%.
No prerequisites are necessary, but enrollment in related courses is desirable.