NMAK19001U Applied Operations Research
MSc Programme in Mathematics-Economics
Operations Research, and particularly Mathematical Programming, is a widely used methodology for optimization and decision-making. It is of central importance in the industry, with applications ranging from logistics to finance, from production planning to energy. It is also of vital importance in emerging areas such as machine learning and for addressing current societal issues such as the green transition.
The course will introduce the students to the practical aspects of Operations Research. The objective is to provide the competencies necessary to work on Operations Research projects in practice. The course will go through the OR scientist's "toolbox", that is, a minimal set of mathematical and software tools required for developing OR solutions. In addition, it provides significant hands-on experience by means of several exercises and project work on real-world applications.
The course will cover the following content:
- A. Using mathematical programming to model real-life decision problems: Given a description of a real-world optimization problem, the course will discuss how to formulate an appropriate mathematical programming problem and what are the issues involved in this phase.
- B. Using general-purpose programming languages for advanced interaction with optimization solvers: The course will introduce the students to the usage of one or more general-purpose programming languages (e.g., Java, Python, C++) for advanced interaction with state-of-the-art solvers (e.g., Cplex, Gurobi).
- B. Decomposition techniques for mathematical programming problems: Very often, industrial optimization problems are challenging due to, e.g., complicating mathematical structures or very large-scale decisions (i.e., an extremely large number of interrelated elementary decisions). The course will discuss how to handle such challenging optimization problems using decomposition techniques that break them down into smaller and easier to treat problems.
- E. Implementation of advanced solution methods: The course will teach the students how to implement decomposition techniques using the software introduced during the course.
- F.Introduction to heuristics: The course introduces heuristic methods, that is, techniques for finding quick solutions to complex optimization problems, though without guarantee of optimality.
- G. Project work: The students will apply their competencies in project work describing real-world optimization tasks from, e.g., logistics, finance, energy, as well as in several practical exercises.
At the end of the course the student should have:
- gained knowledge
- of common usage of continuous and integer variables for translating real-world decision problems into mathematical programming problems
- of advanced solution methods for probles with complicating structures
- of the features of state-of-the-art optimization software
- of the concepts used in heuristic methods
- acquired skills to:
- translate the description of real-life optimization problems into suitable mathematical programming problems
- assess the quality of a mathematical formulation
- select a suitable solution method for a given mathematical problem
- implement solution methods by means of a general-purpose programming language and/or state-of-the-art solvers
- obtained the competences necessary to
- structure a real-world optimization problem and provide a suitable mathematical description
- select a suitable approach to solve a mathematical problem and justify the choice
- make the choice of software necessary for a given optimization task
- develop software products capable of handling an optimization task, possibly by implementing advanced solution methods.
Lecture notes and tutorials provided by the teacher.
Introduction to Numerical Analysis (NumIntro).
It is also advised, but not necessary, to take this course before other advanced Operations Research courses. Academic qualifications equivalent to a BSc degree is recommended.
- Practical exercises
- Practical Training
- Project work
- Exam Preparation
Lecturer's oral or written feedback on assignments. Lecturer's feedback on final exam.
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- 7,5 ECTS
- Type of assessment
- Oral examination, 30 minutes
- Type of assessment details
- 30 minutes oral examination with 30 minutes preparation time.
- Exam registration requirements
The students must hand in a project report that must be approved in order to qualify for the oral exam.
- Only certain aids allowed
During the preparation time all written aid is allowed.
During the examination no written aid is allowed.
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Several internal examiners.
As the ordinary exam, conditional on the approval of the project work. If the project was not approved before the ordinary exam it must be resubmitted at the latest three weeks before the beginning of the re-exam week.
Criteria for exam assesment
The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.
- Course code
- 7,5 ECTS
- Full Degree Master
- 1 block
- Block 1
- Course capacity
- No limit
The number of seats may be reduced in the late registration period
- Study Board of Mathematics and Computer Science
- Department of Mathematical Sciences
- Faculty of Science
- Giovanni Pantuso (2-6a73437064776b316e7831676e)