NMAA09044U  Operations Research 2: Advanced Operations Research (OR2)

Volume 2017/2018

MSc Programme in Mathematic-Economics


A. Problem formulation and modeling:

  • A1. Formulate mathematical optimization models for classical OR problems.
  • A2. Linearization of non-linear constraints.
  • A3. Quality of different model formulations.
  • A4. Modeling practical OR 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; classical 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
Operations Research 1 (OR1) or similar is required.
Recommended but not required: Modelling and Implementation
2 x 2 hours of lectures and 2 x 2 hours exercises/project work per week for 7 weeks
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
30 minutes oral examination with 30 minutes preparation time.
Exam registration requirements

Approval of two project reports is a prerequisite for enrolling for examination.

Written aids allowed
Marking scale
7-point grading scale
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.

Criteria for exam assesment

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


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