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EP30.FSF1121 — Network and Linear Optimization | Chương trình đào tạo NEU

EP30.FSF1121 — Network and Linear Optimization

Credits
3
Self-study hours
90
Showing intake
K68-2026

Course description

This course introduces fundamental concepts and techniques in Linear Programming and Network Optimization, two core areas of Operations Research. Students learn how to formulate optimization models, analyze feasible regions, and apply the simplex method, duality, and sensitivity analysis to solve linear programs. The course then develops structured optimization methods on networks, including spanning trees, shortest paths, maximum flows, and minimum-cost flows, together with primal and dual network simplex algorithms. Applications cover logistics, transportation, supply chains, and structural design. Practical sessions emphasize building and solving models using computational tools such as Excel Solver and Python. A group project reinforces modelling, analytical reasoning, teamwork, and technical communication skills.

Course requirements

Requirements for taking final /terminal exams

Students are allowed to take the final exam if their attendance score reaches 5 points or more (on the scale of 10).

Requirements for attending classes

Students are responsible for attending all classes. In case of absence from school due to force majeure reasons, sufficient and reasonable proofs must be provided. For each absence, 1 point will be deducted 1 point. Students who miss any classes more than 3 times, with or without reason, will be considered as failing to complete the course and have to re-register.

Students will be awarded points for constructive comments, these points are added to attendance points and group assignments.

Groups who do not submit the group work will receive a score of 0 (zero). Late submissions will be deducted for each day of late submission.

Requirements for in-class behaviour

The course is conducted on the principle of respecting learners and lecturers. Any behaviour that affects the teaching and learning process is strictly prohibited.

Students must come to class on time. Students who are late more than 10 minutes after class starts will not be allowed to attend the class. Do not make noise and affect others during the learning process.

Laptops and tablets are only used for the purpose of taking notes for and calculating for lectures and exercises, absolutely forbidden to use for other purposes.

Detailed content

The course content includes

  • Introduction to Linear Programming
  • Simplex Method I 
  • Degeneracy, Cycling, and Anti-Cycling Rules
  • Duality Theory 
  • Network Optimization Introduction & Spanning Trees
  • Network Simplex 
  • Applications
  • Structural Optimization

Lecturers

  • Nguyen Van Quy
  • Le Thi Anh
  • Phung Minh Duc
  • Bui Quoc Hoan
  • Tong Thanh Trung

Teaching plan

Week 1

Introduction to Linear Programming Managing a Production Facility The Linear Programming Problem Standard form Feasible region Basic feasible solutions
References
[1] Chapter 1 [2] Chapter 1
Activities
Lectures: Introduce the course structure, expectations, assessment. Explain LP concepts: feasible region, basic feasible solutions. In-class discussions: Students discuss real-world optimization problems they know. Clarify mathematical prerequisites and common modelling mistakes. In-class exercises: Simple formulation tasks (identify decision variables, constraints, objective).
Assessment
Criteria: Attendance, Responding & Behavior Tools: Appendix 2, Rubric 1 Method: Attendance Check & Work Assignment

Week 2

Chapter 1. Simplex Method I (Algorithmic Foundations 2.1. An example 2.2 The simplex method 2.2.1 Pivot Rule 2.2.2 Tableau mechanics 2.3 Initialization: Two-phase method 2.4 Unboundedness 2.5 Geometry 2.5.1 Extreme points 2.5.2 Polyhedral interpretation
References
[1] Chapter 2 [2] Chapter 2
Activities
Lectures: Explain tableau construction, pivot rules, basic feasible solutions. Introduce two-phase method, unboundedness, and geometric interpretation. In-class discussions: Discuss the meaning of pivot steps and basis changes. Students compare efficiency of different initialization methods. In-class exercises: Perform simplex steps on small LPs. Solve initial tableau exercises in groups.
Assessment
Criteria: Attendance, Responding & Behavior Tools: Appendix 2, Rubric 1 Method: Attendance Check

Learning resources

  • Linear Programming: Foundations and Extensions. Second Edition. Springer — Vanderbei, R. J., 2001
  • Linear Optimization in Applications — S. L. Tang, Hong Kong UP, 1999
  • Network Optimization: Continuous and Discrete Models — Bertsekas & Tsitsiklis, 1998
  • Network Optimization Problems: Algorithms — Du & Pardalos, Applications and Complexity, 1993
  • Lecture notes and slides

Week 4

Chapter 3. Degeneracy, Cycling, and Anti-Cycling Rules 3.1. Definition 3.2 Perturbation / Lexicographic Method 3.3 Bland’s Rule 3.4 Fundamental Theorem of Linear Programming
References
[1] Chapter 3 [2] Chapter 2
Activities
Lectures: Introduce degeneracy, cycling, lexicographic perturbation, Bland’s Rule. Discuss the Fundamental Theorem of Linear Programming. In-class discussions: Students analyze examples of cycling and why anti-cycling rules matter. Compare lexicographic vs Bland’s Rule. In-class exercises: Identify degenerate BFS in sample LPs. Apply Bland’s Rule on a provided tableau.
Assessment
Criteria: Attendance, Responding & Behavior Tools: Appendix 2, Rubric 1 Method: Attendance Check & Work Assignment

Week 5

Chapter 4. Duality Theory 4.1 Duality Theory 4.1.1 Motivation – Finding Upper Bounds 4.1.2 The Dual Problem 4.1.3 Weak Duality 4.1.4 Strong Duality 4.1.5 Complementary Slackness 4.2 Dual Simplex 4.2.1 Dual Simplex Method 4.2.2 Dual-Based Phase I Algorithm 4.2.3 Dual of General Form 4.2.4 Lagrangian Duality
References
[1] Chapter 5, 7 [2] Chapter 2
Activities
Lectures: Explain primal–dual relationships, weak/strong duality, complementary slackness. Introduce dual simplex method, sensitivity analysis, and parametric analysis. In-class discussions: Students interpret dual variables (shadow prices). Discuss the meaning of complementary slackness in economic terms. In-class exercises: Construct dual problems from primal forms. Perform one iteration of dual simplex. Practice interpreting Solver sensitivity reports.
Assessment
Criteria: Attendance, Responding & Behavior Tools: Appendix 2, Rubric 1 Method: Attendance Check & Work Assignment

Week 7

Review Midterm Test Assignment Giving
Activities
Review key concepts. Conduct midterm exam. Giving assignment
Assessment
Criteria: Calculation problems, Discussion questions Tools: Appendix 2, Rubric 2 Method: Written Exam

Week 8

Chapter 5. Network Optimization Introduction & Spanning Trees 5.1 Networks Optimization 5.1.1 Networks, graphs, arcs, nodes 5.1.1 Directed/Undirected graphs 5.1.2 Basic flow concepts 5.2 Spanning tress and Bases 5.2.1 Basic tructure 5.2.2 Tree representation
References
[1] Chapter 13 [3] Chapter 1
Activities
Lectures: Introduce network structures: nodes, arcs, flows, incidence matrices. Explain spanning trees, bases, and their role in network simplex. In-class discussions: Students compare LP bases and network bases. Discuss applications of spanning trees in logistics and design. In-class exercises: Build spanning trees manually from example graphs. Identify basic arcs and non-basic arcs.
Assessment
Criteria: Attendance, Responding & Behavior Tools: Appendix 2, Rubric 1 Method: Attendance Check & Work Assignment

Week 9

Chapter 6. Network Simplex 6.1 Primal Network simplex 6.1.1 Feasible tree solution 6.1.2 Pivoting edges 6.1.3 Cycle finding 6.2 Dual Network simplex 6.2.1 The Dual Network Simplex Method 6.2.2 Putting It All Together 6.2.3 The Integrality Theorem
References
[1] Chapter 13 [4] Chapter 1
Activities
Lectures: Present feasible tree solutions, cycle detection, pivoting in network simplex. Introduce dual network simplex and integrality properties. In-class discussions: Students analyze differences between primal vs dual network simplex. Discuss why network-structured LPs admit faster algorithms. In-class exercises: Perform one iteration of primal and dual network simplex. Identify entering and leaving arcs in simple network examples.
Assessment
Criteria: Attendance, Responding & Behavior Tools: Appendix 2, Rubric 1 Method: Attendance Check & Work Assignment

Week 11

Chapter 7. Applications 7.1 The Transportation Problem 7.2 The Assignment Problem 7.3 The Shortest-Path Problem 7.4 The Maximum-Flow Problem
References
[1] Chapter 14 [2] Chapter 3, 5
Activities
Lectures: Explain transportation and assignment formulations. Present shortest-path algorithms (Dijkstra/Bellman-Ford). Introduce maximum-flow algorithms and upper-bounded flows. In-class discussions: Compare transportation vs assignment structures. Discuss real-world applications in routing, logistics, and communications. In-class exercises: Solve transportation or assignment problems using step-by-step method. Compute shortest paths and flows on sample networks. Python/NetworkX practice on small datasets.
Assessment
Criteria: Attendance, Responding & Behavior Tools: Appendix 2, Rubric 1 Method: Attendance Check & Work Assignment

Week 14

Chapter 8. Structural Optimization 8.1 Incidence Matrices 8.2 Stability 8.3 Conservation Laws 8.4 Minimum-Weight Structural Design 8.5 Anchors Away
References
[1] Chapter 15
Activities
Lectures: Introduce incidence matrices, stability, conservation laws. Explain minimum-weight structural design and network reliability ideas. In-class discussions: Students discuss examples of structural networks (bridges, communication, energy). Compare structural optimization with classical network flows. In-class exercises: Build incidence matrices for given networks. Solve small structural optimization exercises.
Assessment
Criteria: Attendance, Responding & Behavior Tools: Appendix 2, Rubric 1 Method: Attendance Check & Work Assignment

Week 15

Summary and Revision Report Submission
Activities
Revision (TU) Groups present projects and answer questions Lecturer and class members comments
Assessment
Appendix 2, Rubrics 1, 3
Final exam
Activities
Students take exams according to give schedule
Assessment
According to the exam requirement Appendix 2, Rubric 2