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Applied Operations Research
Provider: Faculty of Science

Activity no.: 5554-22-07-31 
Enrollment deadline: 05/09/2022
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time05.09.2022, at: 08:00 - 11.11.2022, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserGiovanni Pantuso    E-mail address: gp@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 1
Scheme groupC
Exam requirementsThe students must hand in a project report that must be approved in order to qualify for the oral exam.
Exam formOral examination, 30 minutes
Exam form30 minutes preparation, 30 minutes oral examination including grade determination
Grading scalePassed / Not passed
Course workload
Course workload categoryHours
Lectures14.00
Preparation25.00
Practical exercises14.00
E-learning40.00
Practical Training12.00
Project work40.00
Eksamensforberedelse60.00
Exam1.00
Sum206.00
Content
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 the green transition and machine learning.

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 (mainly 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).

C. 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.

D. Implementation of advanced solution methods: The course will teach the students how to implement decomposition techniques using the software introduced during the course.

E.Introduction to heuristics: The course introduces heuristic methods, that is, techniques for finding quick solutions to complex optimization problems, though without guaranteeing the optimal solution.

F. 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.

Learning outcome
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 to 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 probgramming 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.

Literature
Lecture notes and tutorials provided by the teacher.

Teaching and learning methods
2 x 2 hours of lectures or tutorials and 2 hours of exercises or project work supervision per week for 7 weeks.

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