Operations Research 2: Advanced Operations Research (OR2)

Course content

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.
Education

MSc Programme in Mathematic-Economics

Learning outcome

Knowledge:

  • 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

 

Skills:

  • 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

 

Competences:

  • 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

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

Operations Research 1 (OR1) or similar is required.
Recommended but not required: Modelling and Implementation

ECTS
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
30 minutes oral examination with 30 minutes preparation time.
Aid
Written aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners
Criteria for exam assessment

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

 

Single subject courses (day)

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