Linear Optimization (IND 501) | GSÜ - ECTS Information Guide

Content

Objective

This course introduces basic theoretical principles and algorithms of linear programming, which provide a foundation for the other mathematical programming concepts and techniques. Furthermore, the course also introduces several different types of mathematical models, which can be used to model real-life applications, and the softwares GAMS and CPLEX, which can be used to solve large-scale linear programming problems. The objectives of the course are determined as follows:
• Introduce how to formulate mathematical models of the real-life applications
• Enable students to apply the linear optimization algorithms efficiently
• Enable students to use the softwares GAMS and CPLEX for large-scale linear optimization problems
• Facilitate the understanding of the theory of the other mathematical programming techniques

Course Learning Outcomes

Upon successful completion of this course, the student will be able to LO 1: Formulate real-life problems through mathematical models.
LO 2: Exemplify different types of the mathematical programming problems.
LO 3: Select the linear optimization algorithm which solves a specific problem most efficiently.
LO 4: Distinguish the differences among the linear optimization algorithms.
LO 5: Explain the problems that can be encountered while solving linear optimization problems and their solution procedures.
LO 6: Define some of the common concepts in linear and nonlinear optimization.
LO 7: Define some of the common concepts in deterministic and stochastic linear optimization.
LO 8: Analyze the results of linear programming problems.
LO 9: Solve large-scale linear programming problems through Professional softwares.
LO 10: Formulate real-life applications through different types of models and conclude which model suits best for the specific application

References

Bazaraa, M.S., Jarvis, J.J., Sherali, H.D., “Linear Programming and Network Flows”, 4. Edition, Wiley, New Jersey, 2010
Bertsimas, D., Tsitsiklis, J.N., “Introduction to Linear Optimization”, Athena Scientific Series in Optimization and Neural Computation, Massachusetts, 1997
Bazaraa, M.S., Sherali, H.D., “Nonlinear Programming: Theory and Algorithm”, 3. Edition, Wiley, New Jersey, 2006
Wolsey, L.A., “Integer Programming”, Wiley, New Jersey, 1998
GAMS Manual, downloadable from http://www.gams.com/

Weekly Contents

Theory Topics
Week	Weekly Contents
1	Modeling of optimization problems (Bazaraa, Jarvis & Sherali, Chapter 1, Bertsimas & Tsitsiklis, Chapter 1)
2	Modeling of optimization problems (Bazaraa & Sherali, Chapter 1, Wolsey, Chapter 1) and solution through GAMS and MATLAB+CPLEX
3	Basic concepts in linear algebra (Bazaraa, Jarvis & Sherali, Chapter 2)
4	Basic concepts in convex analysis (Bazaraa, Jarvis & Sherali, Chapter 2)
5	The simplex and big-M algorithms (Bazaraa, Jarvis & Sherali, Chapter 3)
6	The two-phase algorithm, degeneration, cycling, and cycling prevention rules (Bazaraa, Jarvis & Sherali, Chapter 4)
7	Farkas’ lemma, Karush-Kuhn-Tucker optimality conditions (Bazaraa, Jarvis & Sherali, Chapter 5)
8	Midterm I
9	Duality and sensitivity analysis (Bazaraa, Jarvis & Sherali, Chapter 6, Bertsimas & Tsitsiklis, Chapter 4)
10	Parametric analysis, the revised simplex algorithm (Bazaraa, Jarvis & Sherali, Chapter 6, Bertsimas & Tsitsiklis, Chapter 5)
11	The dual simplex and the primal-dual algorithms (Bazaraa, Jarvis & Sherali, Chapter 6)
12	Dantzig-Wolfe decomposition (Bazaraa, Jarvis & Sherali, Chapter 7, Bertsimas & Tsitsiklis, Chapter 6)
13	Programming the Dantzig-Wolfe decomposition in MATLAB+CPLEX
14	Midterm II

Assessment System

Contribution to Overall Grade
Activities	Number	Contribution
Contribution of in-term studies to overall grade	7	60
Contribution of final exam to overall grade	1	40
Total	8	100

In-Term Studies
Activities	Number	Contribution
Assignments	5	15
Presentation	0	0
Midterm Examinations (including preparation)	2	45
Project	0	0
Laboratory	0	0
Other Applications	0	0
Quiz	0	0
Term Paper/ Project	0	0
Portfolio Study	0	0
Reports	0	0
Learning Diary	0	0
Thesis/ Project	0	0
Seminar	0	0
Other	0	0
Total	7	60

Relation of Proficiency

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1						X
2					X
3
4					X
5						X
6					X
7						X
8
9			X
10		X
11				X
12

ECTS

Activities	Number	Period	Total Workload
Class Hours	14	3	42
Working Hours out of Class	12	3	36
Assignments	5	10	50
Midterm Examinations (including preparation)	2	10	20
Other Applications	1	17	17
Total Workload			165
Total Workload / 25			6.60
Credits ECTS			7