Chapter structure of the 2023-2025 course:
The previously discussed chapters are closely related to the Fundamental Planning Section (Chapters 1-5), which need to be listened to consecutively, as they cover the linear programming part that is essential for all universities. The subsequent chapters can be listened to independently, as there is no sequential relationship between them, and each university chooses its own chapters for explanation. Students can choose according to the syllabus.
Today we will discuss the last section of Chapter 8: Graphs and Networks, specifically 8.8 Solving Graph Theory Problems with MATLAB.
This section mainly explains how to use the Dijkstra algorithm implemented in MATLAB to solve the shortest path problem, using the previous examples 8-10 as a reference.
In the course, I briefly outlined some basic points about MATLAB and explained the implementation of this algorithm. More importantly, I emphasized how to use AI to help debug and understand the program, or guide AI in writing the program.
With the rapid development of AI technology, the era where we need to manually write code may be coming to an end. What we need to cultivate now is perhaps more about understanding the theory ourselves and being able to efficiently guide AI in its operations. Let AI help us with the coding!
Finally, we have completed Chapter 8!!!! Let’s celebrate!!!
The CCTALK course collection for this chapter has been launched (see the QR code at the end of the article), and it will be uploaded and reviewed on Bilibili soon.
See you in the next class on Network Planning Diagrams!
For detailed information about this lesson, please watch the video explanation: (Duration: 35min)
For information about my course resources, please understand first:
1. Series of Operations Research Courses. Please click:
[Huang Lijuan Operations Research | New Collection Course Introduction | 2023-2024 New Edition] Detailed Explanation of 13 Knowledge Points for Graduate Entrance Examination
[Teaching Notes] Operations Research | Common Questions and Answers (31 Questions) – Updated to 2024.12.02
[Teaching Notes] Operations Research | One Problem One Practice CCTALK Collection (270+ Problems), updated to 2024.12.02
[Teaching Notes] Huang Lijuan Operations Research | Graduate Entrance Examination Review Plan
[Huang Lijuan Operations Research] 2023-2024 Course Updates | Public Account Individual Lesson and Bilibili Individual Chapter Course (Two-Year) CCTALK Individual Chapter Course (One-Year)
[Huang Lijuan Operations Research] | Detailed Explanation of Knowledge Points, Sprint Review, and One Problem One Practice CCTALK Collection Introduction (Total 500+ Videos)
[Huang Lijuan Operations Research] Bilibili and Douyin Packaged Collection Course Introduction (One-Year and Two-Year)
[Huang Lijuan Operations Research] 2020 Edition Course | Public Account Individual Lesson and Bilibili, Douyin Individual Chapter Course (One-Year)
[Huang Lijuan Operations Research] One Problem One Practice | Public Account Individual Lesson, Bilibili Individual Chapter, Collection and Douyin Collection Course, up to 260+ Problems, continuously updated (One-Year and Two-Year)
Note 1: The 2020 Edition course notes have been completed and are expected to be published this year.
Note 2: CCTALK, Bilibili, and Douyin platforms are all open for registration.
Note 3: The recommended writing method for the assignment method on the table is in the push of the lesson “Adjustment and Improvement of Solutions”.
2. Complete Free Course Resources for Linear Algebra. Please click:
[Teaching Notes] Linear Algebra Course Review Materials | Complete Video Highlights
[Linear Algebra] One Problem One Practice | Orthogonal Transformation of Quadratic Forms – 2020 Graduate Entrance Examination Mathematics I
[Linear Algebra] One Problem One Practice | Using Inverse Matrix to Prove Cramer’s Rule – Foreign Trade University 2015 Doctoral Entrance Exam Questions
[Linear Algebra] One Problem One Practice | Least Squares Solution – Proof that the Equation Group Must Have a Solution
[Linear Algebra] One Problem One Practice | Proofs Related to Positive Definite Quadratic Forms – Certain University Doctoral Entrance Exam Questions
Note: This course was recognized as a “First-Class Undergraduate Course in Shaanxi Province” by the Shaanxi Provincial Department of Education in 2021, welcome everyone to recommend and learn.
3. Copyright Statement, Infringement Will Be Pursued. Please click:
Due to serious online infringement, my courses have been entrusted to a professional company and law firm for long-term rights protection.There will be annual lawsuits against some infringers. Updates on these cases will be provided in real time (the first case has already been adjudicated in favor, and enforcement of the judgment has been applied for). Please read carefully below about my online course copyright statement:
[Huang Lijuan Operations Research] Serious Statement on Long-Term Commissioning of Law Firms and Professional Companies for Rights Protection
Note: Thank you to all students who support genuine products and actively protect my intellectual property rights.
The following are the links to the recorded videos of the 2023-2025 edition:
Chapter 1 Linear Programming[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.1 Mathematical Model of Linear Programming[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.2 Standard Form of Linear Programming[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.3 Graphical Method of Linear Programming[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.4 Properties of Solutions to Linear Programming Problems 1 – Basic Concepts[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.4 Properties of Solutions to Linear Programming Problems 2 – Basic Theorems[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.5 Solving Linear Programming Problems Using the Simplex Method 1 – Introduction to the Simplex Method[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.5 Solving Linear Programming Using the Simplex Method 2 – Principles of the Simplex Method[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.5 Solving Linear Programming Problems Using the Simplex Method 3 – Simplex Tableau[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.5 Solving Linear Programming Using the Simplex Method 4 – Various Special Cases[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.6 Solving Linear Programming Using the Artificial Variable Method[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.7 Using Excel to Solve Linear Programming Problems[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.8 Applications of Linear Programming in Management 1 – Reasonable Material Cutting Problems[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.8 Applications of Linear Programming in Management 2 – Ingredient Problems[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.8 Applications of Linear Programming in Management 3 – Express Delivery Sorting Problems[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.8 Applications of Linear Programming in Management 4 – Advertising Combination Problems[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.8 Applications of Linear Programming in Management 5 – Production Scheduling Problems[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.8 Applications of Linear Programming in Management 6 – Continuous Investment Problems[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.8 Applications of Linear Programming in Management 7 – Cash Flow Management Problems[2023 Operations Research] Detailed Explanation of Knowledge Points | 1.8 Applications of Linear Programming in Management 8 – Production Storage ProblemsCCTALK New Version Chapter One Package Course Purchase Link:
Chapter 2 Dual Theory and Sensitivity Analysis[2023 Operations Research] Detailed Explanation of Knowledge Points | 2.1 Dual Linear Programming Problems[2023 Operations Research] Detailed Explanation of Knowledge Points | 2.2 Basic Properties of Dual Problems[2023 Operations Research] Detailed Explanation of Knowledge Points | 2.3 Economic Significance of Dual Solutions – Shadow Prices[2023 Operations Research] Detailed Explanation of Knowledge Points | 2.4 Dual Simplex Method[2023 Operations Research] Detailed Explanation of Knowledge Points | 2.5 Sensitivity Analysis of Linear Programming 1 – Changes in b[2023 Operations Research] Detailed Explanation of Knowledge Points | 2.5 Sensitivity Analysis of Linear Programming 2 – Changes in C[2023 Operations Research] Detailed Explanation of Knowledge Points | 2.5 Sensitivity Analysis of Linear Programming 3 – Changes in A and Adding Variables and Constraints[2023 Operations Research] Detailed Explanation of Knowledge Points | 2.6 Parameter Linear ProgrammingCCTALK New Version Chapter Two Package Course Purchase Link:
Chapter 3 Transportation Problems
[2023 Operations Research] Detailed Explanation of Knowledge Points | 3.1 Mathematical Model of Transportation Problems
[2023 Operations Research] Detailed Explanation of Knowledge Points | 3.2.1 Tabular Assignment Method – Determining Initial Basic Feasible Solution[2023 Operations Research] Detailed Explanation of Knowledge Points | 3.2.2 Tabular Assignment Method – Optimal Solution Determination[2023 Operations Research] Detailed Explanation of Knowledge Points | 3.2.3 Tabular Assignment Method – Closed Loop Adjustment Method and Several Special Problems[2023 Operations Research] Detailed Explanation of Knowledge Points | 3.3 Transportation Problems with Imbalanced Supply and Demand[2023 Operations Research] Detailed Explanation of Knowledge Points | 3.4 Transfer Problems[2023 Operations Research] Detailed Explanation of Knowledge Points | 3.5 Application Examples and Computer SolutionsCCTALK New Version Chapter Three Package Course Purchase Link:
Chapter 4 Linear Goal Programming[2023 Operations Research] Detailed Explanation of Knowledge Points | 4.1 Mathematical Model of Goal Programming[2023 Operations Research] Detailed Explanation of Knowledge Points | 4.2 Graphical Method of Goal Programming[2023 Operations Research] Detailed Explanation of Knowledge Points | 4.3 Simplex Method of Goal Programming[2023 Operations Research] Detailed Explanation of Knowledge Points | 4.4 Application Examples and Computer Solutions for Goal ProgrammingCCTALK New Version Chapter Four Package Course Purchase Link:
Chapter 5 Integer Linear Programming
[2023 Operations Research] Detailed Explanation of Knowledge Points | 5.1 Introduction to Integer Programming Problems
[2023 Operations Research] Detailed Explanation of Knowledge Points | 5.2 Branch and Bound Method
[2023 Operations Research] Detailed Explanation of Knowledge Points | 5.3 Cutting Plane Method
[2023 Operations Research] Detailed Explanation of Knowledge Points | 5.4 0-1 Integer Programming
[2023 Operations Research] Detailed Explanation of Knowledge Points | 5.5 Assignment Problems
[2023 Operations Research] Detailed Explanation of Knowledge Points | 5.6.1 Modeling and Application of Integer Programming – Selection of Investment Projects
[2023 Operations Research] Detailed Explanation of Knowledge Points | 5.6.2 Modeling and Application of Integer Programming – Duty Scheduling Problems
[2023 Operations Research] Detailed Explanation of Knowledge Points | 5.6.3 Modeling and Application of Integer Programming – Fixed Cost Problems
[2023 Operations Research] Detailed Explanation of Knowledge Points | 5.6.4 Modeling and Application of Integer Programming – Knapsack Problems
[2023 Operations Research] Detailed Explanation of Knowledge Points | 5.7 Using Excel to Solve Integer Programming Problems
CCTALK New Version Chapter Five Package Course Purchase Link:
Chapter 6 Nonlinear Programming
[2023 Operations Research] Detailed Explanation of Knowledge Points | 6.1.1 Basic Concepts of Nonlinear Programming Problems – Mathematical Models and Graphical Methods
[2023 Operations Research] Detailed Explanation of Knowledge Points | 6.1.2 Basic Concepts of Nonlinear Programming Problems – Optimality Conditions
[2023 Operations Research] Detailed Explanation of Knowledge Points | 6.1.3 Basic Concepts of Nonlinear Programming Problems – Convex (Concave) Functions and Convex Programming
[2023 Operations Research] Detailed Explanation of Knowledge Points | 6.1.4 Basic Concepts of Nonlinear Programming – Descent Iteration Algorithm[2023 Operations Research] Detailed Explanation of Knowledge Points | 6.2.1 Unconstrained Extremum Problems – One-Dimensional Search – Fibonacci Method[2023 Operations Research] Detailed Explanation of Knowledge Points | 6.2.2 Unconstrained Extremum Problems – One-Dimensional Search – 0.618 Method[2023 Operations Research] Detailed Explanation of Knowledge Points | 6.2.3 Solutions to Unconstrained Extremum Problems 1 – Gradient Method[2023 Operations Research] Detailed Explanation of Knowledge Points | 6.2.4 Solutions to Unconstrained Extremum Problems 2 – Conjugate Gradient Method[2023 Operations Research] Detailed Explanation of Knowledge Points | 6.2.5 Solutions to Unconstrained Extremum Problems 3 – Variable Scaling Method[2023 Operations Research] Detailed Explanation of Knowledge Points | 6.3.1 Constrained Extremum Problems – Optimality Conditions (K-T Conditions)[2023 Operations Research] Detailed Explanation of Knowledge Points | 6.3.2 Constrained Extremum Problems – Quadratic Programming[2023 Operations Research] Detailed Explanation of Knowledge Points | 6.3.3 Constrained Extremum Problems – Feasible Direction Method[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 6.3.4 Constrained Extremum Problems – Constrained Function Method – Exterior Point Method[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 6.3.5 Constrained Extremum Problems – Constrained Function Method – Interior Point MethodCCTALK New Version Chapter Six Package Course Purchase Link:
Chapter 7 Dynamic Programming
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 7.1.1 Basic Concepts of Dynamic Programming
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 7.1.2 Basic Equations of Dynamic Programming
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 7.2 Optimality Principle of Dynamic Programming
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 7.3.1 Solution Methods of Dynamic Programming – Backward Induction Method
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 7.3.2 Solution Methods of Dynamic Programming – Forward Induction Method
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 7.4.1 Management Applications of Dynamic Programming – One-Dimensional Discrete Resource Allocation Problems
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 7.4.1 Management Applications of Dynamic Programming – One-Dimensional Continuous Resource Allocation Problems
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 7.4.2 Management Applications of Dynamic Programming – Production Scheduling Problems
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 7.4.3 Management Applications of Dynamic Programming – Production and Storage Problems – Reproduction Points
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 7.4.4 Management Applications of Dynamic Programming – Uncertainty Procurement Problems (Stochastic Dynamic Programming)
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 7.4.5 Management Applications of Dynamic Programming – Composite System Work Reliability Problems
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 7.4.6 Management Applications of Dynamic Programming – Sorting Problems
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 7.4.7 Management Applications of Dynamic Programming – Equipment Renewal Problems
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 7.4.8 Management Applications of Dynamic Programming – Traveling Salesman Problem
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 7.4.9 Management Applications of Dynamic Programming – Revenue Management and Dynamic Pricing
CCTALK New Version Chapter Seven Package Course Purchase Link:
Chapter 8 Graphs and Networks
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 8.1 Basic Concepts of Graphs
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 8.2.1 Trees and Their Properties
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 8.2.2 Supporting Trees of Graphs
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 8.2.3 Minimum Spanning Tree Problem
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 8.3.1 Shortest Path Problem – Dijkstra Method
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 8.3.2 Shortest Path Problem – Successive Approximation Method
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 8.3.3 Applications of Shortest Path Problems
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 8.4.1 Maximum Flow Problem in Networks – Basic Concepts and Theorems
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 8.4.2 Maximum Flow Problem in Networks – Labeling Method to Find Maximum Flow
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 8.5 Minimum Cost Maximum Flow Problem
[2023-2024 Operations Research] Detailed Explanation of Knowledge Points | 8.6 Chinese Postman Problem
[2023-2025 Operations Research] Detailed Explanation of Knowledge Points | 8.7.1 Matching Problems – Basic Concepts and Theorems
[2023-2025 Operations Research] Detailed Explanation of Knowledge Points | 8.7.2 Matching Problems – Hungarian Algorithm for Maximum Matching in Bipartite Graphs
CCTALK New Version Chapter Eight Package Course Purchase Link:
