Course Syllabus 2301677 Linear network optimization
1. Course ID 2301677
2. Credit 3
3. Course name Linear network optimization
4. Department Faculty of Science, Department of Mathematics and Computer Science
5. Semester First
6. Academic year 2555
7. Instructor Krung Sinapiromsaran, Ph. D., MHMK 309, 02-218-5156, [email protected] Boonyarit Intiyot, Ph. D., Chem II 213, 02-218-5225, [email protected] 8. Requirement
8.1. Prerequisite C. F.
8.2. Corequisite -
9. Course status Selective
10. Degree Master of Science, Applied Mathematics and Computational Science
11. Level Graduate
12. Hours/week
Lecture 3 hours:Tuesday 10:00-11:30 TAB 229 and Thursday 10:00-11:30 TAB 130
Lab -
Self-study 6
13. Course Description
(ภาษาไทย) แนวคิดและนิยามทางกราฟ ตัวแบบข่ายงาน วิธีซิมเพล็กซ์ข่ายงาน ปัญหาการขนส่ง ปัญหาการกำาหนดงาน การไหลของผลิตภัณฑ์
(English) Graph concepts and definition; network model; network simplex method; transportation problems;
assignment problems; multicommodity flows.
14. Course Outline
14.1.Behavioral objective: Student can
1. formulate the network flow model from a given problem;
2. perform the network simplex method to solve the given network model;
3. solve the given transportation problem;
4. solve the given assignment problem;
5. solve the multicommodity network flow problem;
14.2.Course details
1. Introduction to linear network optimization (3 hours)
a. Network terminology
b. Minimum-cost network flow problems
2. Network simplex method (9 hours)
a. Node-arc incidence matrix b. Bases and Rooted Spanning Trees c. Unimodularity
d. The Network Simplex method
e. Finding an Initial Basic Feasible Solution f. Degeneracy and cycling
g. Network flow problems with bounds on the flows
3. The transportation and assignment problem (9 hours)
a. The Transportation Problem
b. The Northwest Corner Rule and The Vogel Approximation Method c. The Transportation Simplex Algorithm
d. The Assignment Problem e. The Hungarian algorithm
4. The Out-of-kilter algorithm (9 hours)
a. The Out-of-kilter formulation of a minimal cost network flow problem b. Summary of the Out-of-kilter algorithm
c. A labeling procedure for the Out-of-kilter algorithm
d. Relaxation algorithm
5. Maximal flow, shortest path, Multicommodity flow and network synthesis problems (15 hours)
a. The maximal flow problem b. The shortest path problem
c. Polynomial shortest path algorithms for networks having arbitrary cost d. Multicommodity flows
e. Characterization of a basis for the multicommodity minimal-cost flow problem
14.3.Course plan
Week Date Content
1 5 – 8 June 2012 Network terminology and Minimum-cost network flow problems 2 11 – 15 June 2012 Node-arc incidence matrix; Bases and Rooted Spanning Trees;
Unimodularity
3 18 – 22 June 2012 The Network Simplex method; Finding an Initial Basic Feasible Solution;
Degeneracy and cycling
4 25 – 29 July 2012 Network flow problems with bounds on the flows
5 2 – 6 July 2012 The Transportation Problem; The Northwest Corner Rule and The Vogel Approximation Method
6 9 – 13 July 2012 The Transportation Simplex Algorithm
7 16 – 20 July 2012 The Assignment Problem; The Hungarian algorithm 8 23 – 27 July 2012 Midterm:Tuesday 24 July 2012, 13:00 – 16:00
9 30 July – 3 August 2012 The Out-Of-Kilter formulation of a minimal cost network flow problem 10 6 – 10 August 2012 A labeling procedure for the Out-of-kilter algorithm
11 14 – 17 August 2012 Relaxation algorithm 12 20 – 24 August 2012 The maximal flow problem 13 27 – 31 August 2012 The shortest path problem
14 3 – 7 September 2012 Polynomial shortest path algorithms for networks having arbitrary cost 15 10 – 14 September 2012 Multicommodity flows
16 17 – 21 September 2012 Characterization of a basis for the multicommodity minimal-cost flow problem
17 24 September – 12
October 2012 FINAL:Tuesday 25 September 2012, 13:00 – 16:00
14.4.Course media Board, LCD projector, computer with internet connection
14.5.Course evaluation 1. Assignments 20 %
2. Midterm 40 % Tuesday 24 July 2012, 13:00 – 16:00 3. Final 40 % Tuesday 25 September 2012, 13:00 – 16:00 15. References
1. Bazaraa, M. S., Jarvis, J. J. and Sherali, H. D., Linear programming and network flows, third edition, John Wiley & Sons, New York, 2005.
2. Winston, W. L., Introduction to mathematical programming: Applications and Algorithms, second edition, Duxbury Press, CA, 1995.
3. Winston, W. L., Operations research: Applications and Algorithms, third edition, Duxbury Press, CA, 1994.
16. Course Evaluation
16.1.Evaluation form Lecture 04 16.2.Course improvement -