Learn the fundamental principles and practical applications of Operations Research through a comprehensive course covering essential optimization techniques and mathematical modeling. Begin with an introduction to linear programming before mastering various solution methods including simplex, Big-M, and two-phase approaches. Explore duality theory, sensitivity analysis, and parametric programming to understand how solutions behave under changing conditions. Progress through specialized topics including transportation problems, integer programming with branch-and-bound methods, and dynamic programming applications. Apply these concepts to real-world scenarios such as resource allocation, distribution logistics, and medical team deployment across countries. Master both geometric and algebraic interpretations of optimization problems while developing practical skills in model formulation and solution techniques.
Overview
Syllabus
- Chapter 1 Introduction of operations research
- Chapter 2 Setting model of linear programming
- 2.1 Linear Programming model(1)
- 2.2 Linear Programming Model(2)
- Chapter 3 The graphic method of linear programming
- Chapter 4 The simplex method of linear programming
- 4.1 Geometric Interpretation of the Simplex Method
- 4.2 Algebraic Interpretation of the Simplex Method
- 4.3 The Simplex Method in Tabular Form
- 4.4 Tie Breakings in the Simplex Method
- Chapter 5 Big-M and Two Phase method
- 5.1 The Artificial-Variable -Technique(1)
- 5.2 The Artificial-Variable -Technique(2)
- Chapter 6 Dual problem and Sensitivity analysis of linear programming
- 6.1 Introduction to Duality Theory
- 6.2 The Primal-Dual Relationships
- 6.3 Dual simplex method
- 6.4 Sensitivity analysis(1)
- 6.4 Sensitivity analysis(2)
- 6.5 Structural Sensitivity Analysis
- Chapter 7 Parametric programming
- 7.1 Parametric Linear Programming(1)
- 7.2 Parametric Linear Programming(2)
- Chapter 8 Transportation problem
- 8.1 P&T Company Distribution Problem
- 8.2 The transportation problem model
- 8.3 A Streamlined Simplex Method for the Transportation Problem
- 8.4 A Streamlined Simplex Method for the Transportation Problem (con't)
- Chapter 9 Integer programming
- 9.1 Integer programming model(1)
- 9.2 Integer programming model(2)
- 9.3 branch-and-bound method(1)
- 9.4 branch-and-bound method(2)
- 9.5 The Assignment Problem(1)
- 9.6 The Assignment Problem(2)
- Chapter 10 Dynamic Programming
- 10.1 A prototype example
- 10.2 Characteristics of Dynamic Programming Problem
- 10.3 A Example- Distributing medical teams to countries
- 10.4 Application of DP - Continuous Variable Type
Taught by
Manfeng Liu, Cuixia Wang, Yue Cai, and Wei Liang
