Modelling and Optimization


Optimization techniques are based on quantitative methods, and the general goal is to find the optimal way of designing and operating a system, usually under conditions of scarcity.
This course is an introduction to linear optimization and its extensions, and will be taught by example, solving real world problems from the main functional areas of business (finance, operations, resource economics and marketing) with computer software, optimization formulations and algorithms. Modeling problems from these areas will require students to think about what they are trying to achieve, what the constraints are, what the decision variables are, and how the decision variables relate to both constraints and problem objectives. Student’s ability to structure complex problems and to derive solutions that can improve their insights and ability to make good management decisions are the main skills to be developed during the course.
The course will start by emphasizing model formulation and model building as well as the interpretation of software outputs. Special emphasis will be given to the Solver tool in Excel®.

General characterization





Responsible teacher

Paulo Bárcia


Weekly - Available soon

Total - Available soon

Teaching language



Mandatory Precedence:

- 1303. Linear Algebra


Winston W. (2004). Operations Research, Applications and Algorithms 4th ed; International student edition. South-Western, Cengage Learning. ISBN: 978-0-534- 42362-9.

Luenberger D. and Ye Y. (2008). Linear and Nonlinear Programming. Springer ISBN: 978- 3-319-18841-6.



Teaching method

Evaluation method

•    Regular exam period:

There will be a final exam worth 40% of your final grade. The remaining part of your grade will be allocated to two Team Projects (20%), a midterm exam (30%) and evaluation of practical classes (10%).

Individual Assignments: there will be one midterm exam on the date tba and a final exam on the date tba. A minimum grade of 45% in the individual component is required to pass the course.

Team Assignments: to carry out the group assignments, each student must work in a team of 5/6 students. The first assignment is due on date tba and the second assignment is due on   the date tba (all files must be uploaded in moodle). Late assignments are not accepted.

Practical classes: the evaluation of practical classes will be based on participation in class (including attendance) and problems sets that students are supposed to deliver.

•    Suppl./Special Resit exame period:

There will be only a final exam, on date tba, worth 100% of your final grade.

Subject matter

1. Introducing Operations Research

2. Linear Programming

3. Duality and Sensitivity Analysis

4. Transportation Problems

5. Integer Programming

6. Network Models


Programs where the course is taught: