Operations Research

Basic knowledge of Linear Algebra is recommended.

The theoretical classes tend to be expository, but they promote the active participation of students, either by asking questions or by solving exercises to apply the topics covered.

In theoretical-practical and practical classes, the knowledge acquired in theoretical classes is applied by solving exercises, and in practical classes, whenever possible, computational tools are used.

In order to attend this course, students must: 1 – Be able to translate simple optimization and decision problems into mathematical models of linear programming (LP); 2 – Know how to apply LP algorithms suitable for solving this type of problems; 3 – Be able to interpret the solutions obtained as a result of applying these algorithms to mathematical models; 4 – Be able to computationally solve LP algorithms.

Introduction to Operations Research

• Origins and evolution
• Methodological approach
• Linear programming branch
• Application cases

Linear Programming Problems

• Examples of linear programming problems
• Mathematical formulation of the model
• Graphic resolution
• Particular cases of the model

Simplex Method

• Fundamental concepts
• Simplex algorithm in tabular form
• Particular cases of the Simplex method

Duality

• Formulation of the dual problem
• Fundamental properties of duality
• Dual Simplex algorithm

Particular Problems of Linear Programming

• Transportation problems
• Assignment problems

NAO

Recommended:

• Documentation that supports classes (available on Moodle)
• Hillier, FS; Lieberman, GJ (1995) – Introduction to Operations Research (6th ed.). New York: McGraw-Hill (available at the ISEC’s Library:3-9-31 (ISEC) – 08145; The 10th edition (2015) of this book is available for download in: https://pt1lib.org/book/3426899/3de006)

Additional:

• Ravindran, A.; Phillips, D. T.; Solberg, J. J. (1987) – Operations Research: Principles and Practice. (2nd ed.). New York: John Wiley (disponível na Biblioteca do ISEC: 3-9-57 (ISEC) – 09253)
• Taha, H. A. (1995) – Operations research: an introduction (5th ed.). London: Prentice-Hall (available at ISEC’s Library: 3-9-29 (ISEC) – 07857)
• Murthy, P. R. (2007) – Operations Research (2nd ed.). New Delhi: New Age International Publishers (The PDF version is available for download in: https://easyengineering.net/operations-research-p-ramamurthy/)