NMAK19001U Applied Operations Research

Volume 2020/2021

MSc Programme in Mathematics-Economics



The course will introduce the students to 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 "toolbox", that is, a minimal set of (mainly software) tools required for developing OR solutions.

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. Decomposition techniques mathematical programming problems: the course will illustrate central decomposition techniques for mathematical programs with complicating structures or large-scale problems
  • C. Using optimization software to solve mathematical programming problems: Introduction to state-of-the-art Algebraic Modeling Languages (e.g., one or more among GAMS, AMPL, or the like)
  • D. Using general-purpose programming languages for advanced interaction with solvers: Introduction to 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)
  • E. Implementation of advanced solution methods: Implementation of advanced solution methods using the software introduced during the course
  • F. Project work: Given a description of a real-life problem formulate a suitable mathematical programming problem and solve the problem. Implementation of a solution method using selected optimization software.
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


  • acquired skills to:
    • translate the description of real-life optimization problems to suitable mathematical programming problems
    • assess the quality of a mathematical formulation
    • use Algebraic Modeling Languages to solve a mathematical program
    • select a suitable solution method for a given mathematical problem
    • implement solution methods by means of 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.
Operations Research 1 (OR1) or similar is strongly recommended. 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.
5 hours of lectures and 2 hours of exercises per week for 7 weeks in addition to project work.
  • Category
  • Hours
  • Lectures
  • 35
  • Preparation
  • 50
  • Practical exercises
  • 14
  • Project work
  • 106
  • Exam
  • 1
  • Total
  • 206
Feedback by final exam (In addition to the grade)

Lecturer's oral or written feedback on assignments. Lecturer's feedback on final exam.

7,5 ECTS
Type of assessment
Oral examination, 30 minutes
30 minutes oral examination with 30 minutes preparation time.
Exam registration requirements

The students must hand in two project reports 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 projects were not approved before the ordinary exam they must be resubmitted at the latest three weeks before the beginning of the re-exam week.

Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.