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Operations Research 2: Advanced Operations Research (OR2)
Provider: Faculty of Science

Activity no.: 5563-19-07-31 
Enrollment deadline: 18/11/2019
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time18.11.2019, at: 09:00 - 26.01.2020, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserTrine Krogh Boomsma    E-mail address: trine@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 2
Scheme groupC
Exam formOral examination, 30 minutes
Exam formOral examination
Exam aidsWriten aids allowed
Course workload
Course workload categoryHours
Lectures28.00
Project work30.00
Theory exercises28.00
Exam50.00
Preparation70.00

Sum206.00


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.

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

Literature
Previous years, the textbook L. A. Wolsey: Integer Programming, 1998, John Wiley & Sons, Inc. was used.

Teaching and learning methods
2 x 2 hours of lectures and 2 x 2 hours exercises/project work per week for 7 weeks.

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