Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

Operations Research 2: Advanced Operations Research (OR2)

Practical information
Study year 2016/2017
Block 1
Programme level Full Degree Master
Course responsible
  • Trine Krogh Boomsma (5-76746b7067426f63766a306d7730666d)
Phone +45 35 32 07 33, room 04.3.02, mail trine@math.ku.dk
  • Department of Mathematical Sciences
Course number: NMAA09044U

Course content

A. Problem formulation and modeling:

  • A1. Formulate mathematical optimization models for well-known problems.
  • A2. Linearization of non-linear constraints.
  • A3. Quality of different model formulations.
  • A4. Modeling complex problems.


B. Integer Programming:

  • B1. Integer Programs (IP), Binary Integer Programs (BIP), and Mixed Integer Programs (MIP).
  • B2. Properties of Integer Programs.
  • B3. Examples of Integer and Mixed-Integer Programs.


C. Solution methods for Integer Programming Problems:

  • C1. Relaxation and duality.
  • C2. Decomposition.
  • C3. Branch and bound.
  • C4. Dynamic programming.
  • C5. Cutting planes.
  • C6. Column generation.


D. Practical aspects:

  • D1. External talks: Relation between academia and practice.
  • D2. Case studies: Energy planning/Vehicle routing/Travelling salesman.
  • D3. Implementation of a given problem in GAMS.
  • D4. Implementation of a solution method for a given problem in GAMS.

Learning outcome


  • Mathematical optimization problems, including LP, IP, BIP and MIP; well-known problems such as Travelling salesman, Knapsack and Network Flow problems.
  • Properties of Integer Programming problems
  • Solution methods for Integer Programming Problems



  • Characterize different classes of mathematical optimization problems, including LP, IP, BIP and MIP problems
  • Formulate models for LP, IP, BIP and MIP problems
  • Implement a given problem in GAMS
  • Apply the solutions methods presented in the course
  • Implement a solution method for a given problem in GAMS (in a simplified fashion)
  • Understand and reproduce the proofs presented in the course



  • Evaluate the quality of different model formulations
  • Discuss the challenges of solving IP problems
  • Explain how to exploit the properties of a given class of IP problems in the design of a solution method
  • Adapt a solution method to a given class of IP problems
  • Describe similarities and differences between solution methods
  • Discuss the challenges of modeling and solving practical problems
  • Formulate, implement and solve a practical problem and justify the choice of model formulation and solution method

Recommended prerequisites

Operations Research 1 (OR1) or similar is required.
Recommended but not required: Modelling and GAMS, Optimization and Convexity

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MSc Programme in Mathematic-Economics


Study Board of Mathematics and Computer Science

Course type

Single subject courses (day)


Trine Krogh Boomsma


1 block


---- SKEMA LINK ----

Teaching and learning methods

2 x 2 hours of lectures and 2 x 2 hours exercises/project work per week for 7 weeks


No limit




Category Hours
Lectures 28
Theory exercises 28
Project work 30
Exam 50
Preparation 70
English 206


Type of assessment

Oral examination, 30 min
30 minutes oral examination with 30 minutes preparation time.


Written aids allowed

Marking scale

7-point grading scale

Criteria for exam assessment

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


Censorship form

No external censorship
Several internal examiners


Same as ordinary exam. If the required project reports were not approved before the ordinary exam they must be resubmittet no later than two weeks before the beginning of the re-exam week.

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