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.
MSc Programme in Mathematic-Economics
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
Previous years, the textbook L. A. Wolsey: Integer Programming, 1998, John Wiley & Sons, Inc. was used.
Operations Research 1 (OR1) or similar is required.
Recommended but not required: Applied Operations Research
Academic qualifications equivalent to a BSc degree is
recommended.
Individual written feedback will be given on mandatory assignments in order for students to improve subsequent submissions and resubmissions of assignments.
Collective oral feedback will be given on students’ presentations in class.
- ECTS
- 7,5 ECTS
- Type of assessment
-
Oral examination, 30 minutes30 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 outcomes.
Single subject courses (day)
- Category
- Hours
- Lectures
- 28
- Preparation
- 70
- Theory exercises
- 28
- Project work
- 30
- Exam
- 50
- English
- 206
Kursusinformation
- Language
- English
- Course number
- NMAA09044U
- ECTS
- 7,5 ECTS
- Programme level
- Full Degree Master
- Duration
-
1 block
- Schedulegroup
-
C
- Capacity
- No limit
- Studyboard
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinator
- Trine Krogh Boomsma (5-78766d7269447165786c326f7932686f)
Teacher
Trine Krogh Boomsma
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