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

The assessment will include two components:

• Final exam covering all course material - 18 points
• Set of activities to be undertaken throughout the semester - 2 points

Remarks:

• For the exam, the student may bring one reference sheet corresponding to an A4 page, prepared by themselves, with free content, either handwritten or created in a text editor;
• During the exam, the student may use a non-graphing calculator;
• The activities must be completed individually;
• The deadlines / dates for the activities will be announced at the beginning of the semester;
• If the submission deadlines / activity dates are not met, there will be no opportunity to redo that activity and the student will receive zero points for it;
• There will be no minimum grade requirement for the activities;
• The total grade obtained from the activities will be valid for all assessment periods;
• If the student attends, at least, 9 practical classes (preferably in the class they are enrolled in), they will receive a bonus of 1 point, valid for all assessment periods:
• If the student’s final grade (exam + activities + bonus) exceeds 20 points, the grade to be recorded in the register will be 20 points.

NAO