Mathematical programming is a method for maximizing (minimizing) an objective function under constraints. The problems handled
by this method are also called mathematical programming problems or optimization problems, and appear very often as mathematical
models of engineering problems. For example, a production planning problem to produce a product with limited resources and
maximize profit, or a transportation problem to minimize the cost of transporting a product from multiple factories to a delivery
destination.
In this class, students learn how to solve basic linear and nonlinear programming problems. In addition, students will learn how to perform calculations using Excel.
In this class, students learn how to solve basic linear and nonlinear programming problems. In addition, students will learn how to perform calculations using Excel.
The purpose of this class is to understand the purpose of mathematical programming and to be able to calculate not only by
hand but also by using a computer.
- To be able to solve linear programming problems.
- To be able to solve nonlinear programming problems.
- To be able to solve mathematical programming problems using Excel.
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | Introduction to mathematical programming problems, typical linear programming problems, and graphical solution methods | Read through the handouts and the textbook p.1-p.6, p.23-p.41 and solve the problems in the handouts before class. After class, review and solve the questions and examples. | 190minutes |
| 2. | Simplex method 1 | Read through the handouts and the textbook p.41-p.53 and solve the problems in the handouts before class. After class, review and solve the questions and examples. | 190minutes |
| 3. | Simplex method 2 | Read through the handouts and the textbook p.41-p.53 and solve the problems in the handouts before class. After class, review and solve the questions and examples. | 190minutes |
| 4. | Two stage simplex method | Read through the handouts and the textbook p.54-p.66 and solve the problems in the handouts before class. After class, review and solve the questions and examples. | 190minutes |
| 5. | Duality and Sensitivity Analysis | Read through the handouts and the textbook p.83-p.98 and solve the problems in the handouts before class. After class, review and solve the questions and examples. | 190minutes |
| 6. | Lagrange's Method of Undetermined Multipliers | Read through the handouts and solve the problems in the handouts before class. After class, review and solve the questions and examples. | 190minutes |
| 7. | Karush-Kuhn-Tucker Condition | Read through the handouts and the textbook p.127-p.139 and solve the problems in the handouts before class. After class, review and solve the questions and examples. | 190minutes |
| 8. | Descent method | Read through the handouts and the textbook p.139-p.144 and solve the problems in the handouts before class. After class, review and solve the questions and examples. | 190minutes |
| 9. | Examination and its explanation | Preparation of examination. | 190minutes |
| 10. | Excel Basics (Functions and Logical Functions) | Read through the handouts, study by video, and solve practice problems on the handouts before class. | 190minutes |
| 11. | Linear and nonlinear problems with Excel (using solvers) | Read through the handouts and the textbook p.66-p.82 and solve the problems in the handouts before class. After class, review and solve the questions and examples. | 190minutes |
| 12. | Solving 1- and 2-variable descent methods with Excel | Read through the handouts, study by video, and solve practice problems on the handouts before class. | 190minutes |
| 13. | Descent Method Solution with VBA | Read through the handouts, study by video, and solve practice problems on the handouts before class. | 190minutes |
| 14. | Examination and its explanation | Preparation of examination. | 190minutes |
| Total. | - | - | 2660minutes |
| Reports and little examinations | Examination 1 | Examination 2 | Total. | |
|---|---|---|---|---|
| 1. | 10% | 15% | 25% | |
| 2. | 10% | 15% | 25% | |
| 3. | 50% | 50% | ||
| Total. | 20% | 30% | 50% | - |
Examinations and reports will be examples, exercises, and questions of the same level as those in the handouts or textbook.
Examination 1 (45%), examination 2 (15%), reports (40%) will be converted into 100 points, of which 60 points or more will be considered passing.
Examination 1 (45%), examination 2 (15%), reports (40%) will be converted into 100 points, of which 60 points or more will be considered passing.
Review Differential and Integral Calculus 1, Linear Algebra 1, and Differential and Integral Calculus 2
- Course that cultivates an ability for utilizing knowledge
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | 該当しない |
Last modified : Fri Mar 18 23:01:08 JST 2022