### 2018　Mathematical Economics

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Undergraduate major in Industrial Engineering and Economics
Instructor(s)
Shioura Akiyoshi
Class Format
Lecture
Media-enhanced courses
Day/Period(Room No.)
Tue7-8(W935)  Fri7-8(W935)
Group
-
Course number
IEE.B337
Credits
2
2018
Offered quarter
2Q
Syllabus updated
2018/4/6
Lecture notes updated
2019/6/17
Language used
Japanese
Access Index ### Course description and aims

Many of the mathematical problems arising in the fields of economics and industrial engineering can be formulated as problems of finding optimal solutions or stable solutions.
In this course, the instructor will cover optimization problems related to discrete solutions and other related problems. The instructor will explain the mathematical structure and algorithms of those problems, while also touching on their connection to economics and industrial engineering.

Recently, discrete optimization problems often appear in various aspects in economics and industrial engineering.
Knowledge related to discrete optimization theory is necessary for approaching various problems in economics and industrial engineering from a mathematical standpoint.
We would like students to acquire such knowledge through this course.

### Student learning outcomes

Students in this course will learn the following for problems of finding optimal solutions and problems of finding stable solutions.
(1) Gain an understanding of and be able to explain models dealt with in each problem.
(2) Gain an understanding of the structure and various properties of solutions in each problem, and be able to explain in mathematical language.
(3) Be able to explain the procedure of methods (algorithms) for finding the optimum solution and stable solution of each problem, and learn to actually calculate the solutions for simple examples.
(4) Gain an understanding of and be able to explain the links been economics and industrial engineering and each problem.

### Keywords

discrete optimization problem, combinatorial optimization problem, mathematical programming problem,
stable solution, stable matching

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

### Class flow

The instructor will cover various problems in each class, and explain the structure of solutions, how the solutions are found, as well as their connection to economics and industrial engineering.
Before class ends, the instructor will present exercise problems covered in that day's class, which the students will solve by the following class in report format.
The instructor will explain solutions to exercise problems at the start of the following class, and students will grade the reports themselves.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Guidance, Minimum Spanning Tree Problem explain the goal of this lecture
Class 2 Minimum Spanning Tree Problem understand the mathematical structure and algorithms of the minimum spanning tree problem
Class 3 Shortest Path Problem understand the mathematical structure and algorithms of the shortest path problem
Class 4 Maximum Cardinality Matching Problem understand the mathematical structure and algorithms of the maximum cardinality matching problem
Class 5 Maximum Weight Matching Problem understand the mathematical structure and algorithms of the maximum weight matching problem
Class 6 Maximum Flow Problem understand the mathematical structure and algorithms of the maximum flow problem
Class 7 Minimum-Cost Flow Problem understand the mathematical structure and algorithms of the minimum-cost flow problem
Class 8 Mid-term Exam check the level of understanding of the classes 1-7 topics
Class 9 Knapsack Problem and Traveling Salesman Problem understand the difficulty of the knapsack problem and the traveling salesman problem, and explain algorithms for finding approximate solutions
Class 10 Exchange of Goods understand the mathematical structure and algorithms of the goods exchange problem
Class 11 Exchange of Goods understand the mathematical structure and algorithms of the goods exchange problem
Class 12 One-to-one Stable Matching Problem understand the mathematical structure and algorithms of the one-to-one stable matching problem
Class 13 One-to-one Stable Matching Problem understand the mathematical structure and algorithms of the one-to-one stable matching problem
Class 14 One-to-many Stable Matching Problem understand the mathematical structure and algorithms of the one-to-many stable matching problem
Class 15 End-term Exam check the level of understanding of the classes 9-14 topics

### Textbook(s)

None.
Handouts will be distributed at the beginning of each class.

### Reference books, course materials, etc.

Kazuo Murota, Akiyoshi Shioura: Discrete Convex Analysis and Optimization Algorithms, Asakura Shoten, 2013 (in Japanese).
Toyotaka Sakai: Introduction to Market Design, Minerva Shobo, 2010 (in Japanese).
Debasis Mishra: Mathematical Programming with Application to Economics, http://www.isid.ac.in/~dmishra/mp.html

### Assessment criteria and methods

Mid-term exam (40%), End-term exam (40%), report (20%)

### Related courses

• IEE.A206 ： Operations Research
• IEE.A330 ： Advanced Operations Research
• IEE.A201 ： Basic Mathematics for Industrial Engineering and Economics
• IEE.B205 ： Noncooperartive Game Theory

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

No prerequisites are necessary, but enrollment in related courses is desirable.

### Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

shioura.a.aa[at]m.titech.ac.jp

### Office hours

Any time. An appointment by e-mail is desirable. 