- Course: Optimization and Operational Research
- Semester: Fall
- ECTS credits: 3
- Duration: 22.5 hours
- Language of instruction: English
- Instructors: Jordi Villà-Freixa / Jing Yang
- Course Description
- Prerequisites
- Learning outcomes
- Method of presentation
- Contents
- Requirements to pass the course. Exam retake
In this course we will deal with Operations Research (OR), a scientific discipline at the interface of Applied Mathematics, Computer Science and Engineering, defined as the use of quantitative methods to assist analysts and decision-makers in designing, analyzing, and improving the performance or operation of systems. OR can be used in financial systems, scientific or engineering systems, or industrial systems. Its aim is to rationalize, simulate, optimize, model and plan the architecture and operation of complex systems that are increasingly present in industry and large organizations. We will focus on the optimization problem, and we will be following a fully practical approach, using Python/iPython, Colab and libraries like google OR, among others, as our main tools during the course to demonstrate and test what we learn from the theoretical sessions.
Linear algebra, matrix analysis, basic numerical analysis, differential, and integral calculus. Basic knowledge of Python programming and jupyter notebook.
By the end of the course, students should be able to:
- identify specific problems of linear programming;
- identify and use techniques to solve an optimization or linear programming problem;
- implement specific OR algorithms.
Lectures and practical training:
- Short lectures with appropriate visual support provide the theoretical content of the sessions.
- Practical training will present specific problems to be solved using computational tools and algorithms in and out of the class. Required work and assessment methods
- Introduction to systems modelling; optimality and practicality
- Introduction to the Python/colab environment; GitHub
- Concepts and algorithms in non-linear optimization
- Unconstrained optimization
- Constrained optimization (Lagrange multiplier theorem, Kuhn-Tucker multiplier theorem)
- Fundamental principles of linear programming
- Geometric resolution
- Basic mathematics tools
- Standard form,
- Deviation variables
- Basic feasible solutions
- Artificial variables
- Primal and dual problems, economic interpretation, conditions of optimality, resolution of the dual by the primal and penalty method
Sensitivity Analysis
- Sensitivity analysis: the effect of modifying the objective function or the constraints
- Graphs and Networks
- Maximum flow / minimal cost
- Network connectivity
- Shortest path problems
- Dynamic programming
- Project management
- Branch and bound
- Cutting planes
- Cover inequalities
- Lagrangian relaxation
- Column generation
To pass the course, students should obtain at least an overall average grade of 5 out 10. The grade is obtained in three tasks:
-
TESTS (E1-10): At least an average grade of 4 out 10 in tests. No delay is allowed for tests.
-
PROGRAMMING EXERCISES (P1-4): At least a grade of 5 out of 10 in programming exercises. If delivery is delayed for a particular programming exercise, the grade for such exercise will be penalized with a maximum score of 60%.
-
FINAL EXAM: A minimum grade of 5 in necessary to pass the exam.
-
RETAKE EXAM: If the global OR the final exams grades are less than 5, a retake exam will take place, but it will only account for the 30% of the final grade.
Recommended reading
- “Operations research. A practical Introduction (2nd Ed)” by Michael W. Carter, Camile C. Price and Ghaith Rabadi. CRC Press