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Linear Optimization

Objectives

At the end of this course the student will have acquired knowledge and skills that will enable him (i) to model; and (ii) to solve and assess the obtained solutions of linear, integer and multi-objective linear programming problems.

General characterization

Code

12145

Credits

6.0

Responsible teacher

Isabel Cristina Silva Correia

Hours

Weekly - 4

Total - 70

Teaching language

Português

Prerequisites

Students should have knowledge in Linear Algebra, Calculus, and have some skills on algorithms.

Bibliography

A First Course in Linear Optimization, Jon Lee, Reex Press, 4th edition, 2013-2021 https://github.com/jon77lee/JLee_LinearOptimizationBook/blob/master/JLee.4.01.pdf

Linear Programming: Foundations and Extensions, R.J. Vanderbei, Springer Int. Series in Oper. Res. & Manag. Science, 2014. 

Integer Programming, M. Conforti, G. Cornuejols, G. Zambelli, Springer Graduate Texts in Mathematics, 2014. 

Multiobjective Linear and Integer Programming, C.H. Antunes, M.J. Alves, J. Clímaco, Springer EURO Advanced Tutorials on Oper. Res., 2016. 

Operations Research: Applications and Algorithms, W.L. Winston, Wadsworth, Belmont, CA, 1994

Teaching method

Problem-solving sessions with oral presentation of concepts, methodologies, and examples, complemented with problem solving. Specific student difficulties will be addressed during classes or in individual sessions scheduled with the teacher.

Continuous evaluation is based on two tests. If a student does not obtain approval through continuous evaluation he can try it in an additional examination.

Evaluation method

Only students with frequency will receive a final grade in this course unit.

 

Frequency:

Frequency is granted to any student who attends at least 2/3 of the classes taught 

Rules of evaluation:

1) There will be two evaluation tests during the semester. Let CT1 and CT2 be the scores in the first and second test respectively, in the scale 0-10. The student will pass the course if CT1+CT2 >= 9.5.

2) Students who have failed in the continuous evaluation may take the final exam covering all the topics taught. Let CE be the score in the exam, in the scale 0-20. The student will pass the course if CE >=  9.5.

3) Students who have already passed the course are eligible for course grade improvement via the final exam. In this case students must sign up beforehand in the "Divisão Académica".

4)  Students with a grade greater than 17 can choose between getting a final grade of 17 or taking a complementary examination to defend the grade.

Subject matter

1. Linear programming (LP): problem formulation, LP geometry, the simplex algorithm, duality. 

2. Integer linear programming (IP): problem formulation, LP vs IP, relaxations, the branch and bound method, heuristics.

3. Multiobjective programming (MOP): problem formulation, solution approaches.