Operations Research (OR) is a field in which people use mathematical and engineering methods to study optimization problems in Business and Management, Economics, Computer Science, Civil Engineering, Electrical Engineering, etc.
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Operations Research (3): Theory
国立台湾大学課程信息
This course is appropriate for students with experience Calculus, Linear Algebra, and Probability.
您將學到的內容有
Understand the theoretical properties of linear programs, integer programs, and nonlinear programs.
Apply the mathematical properties to reduce the complexity of real-world problems or to solve it.
您將獲得的技能
- Theory
- Business Analytics
- Mathematical Optimization
This course is appropriate for students with experience Calculus, Linear Algebra, and Probability.
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国立台湾大学
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授課大綱 - 您將從這門課程中學到什麼
Course Overview
In the first lecture, after introducing the course and the importance of mathematical properties, we study the matrix way to run the simplex method. Being more familiar with matrices will help us understand further lectures.
Duality
In this week, we study the theory and applications of linear programming duality. We introduce the properties possessed by primal-dual pairs, including weak duality, strong duality, complementary slackness, and how to construct a dual optimal solution given a primal optimal one. We also introduce one important application of linear programming duality: Using shadow prices to determine the most critical constraint in a linear program.
Sensitivity Analysis and Dual Simplex Method
In the past two weeks, we study the simplex method and the duality. On top of them, the dual simplex method is discussed in this lecture. We apply it to one important issue in sensitivity analysis: evaluating a linear programming model with a new constraint. A linear programming model with a new variable is also discussed.
Network Flow
In this lecture, we introduce network flow models, which are widely used for making decision regarding transportation, logistics, inventory, project management, etc. We first introduce the minimum cost network flow (MCNF) model and show hot it is the generalization of many famous models, including assignment, transportation, transshipment, maximum flow, and shortest path. We also prove a very special property of MCNF, total unimodularity, and how it connects linear programming and integer programming.
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- 5 stars96.87%
- 4 stars3.12%
來自OPERATIONS RESEARCH (3): THEORY的熱門評論
This is a good course. It provides necessary theoretical foundations.
Excellent intro into the vast world of optimization and operations research. Please make one on stochastic processes and programming next!
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