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

Activity no.: 5563-18-07-31 
Enrollment deadline: 19/11/2018
Tilmelding : Operations Research 2: Advanced Operations Research (OR2)
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time19.11.2018, at: 09:00 -
26.01.2019, at: 16:00
 
Tilmelding : Operations Research 2: Advanced Operations Research (OR2)
ECTS credits7.50
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time19.11.2018, at: 09:00 -
27.01.2019, 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
Teaching languageEnglish partially in English
Semester/BlockBlock 2
Scheme groupC
Exam formOral examination, 30 minutes
Exam formOral examination
Exam details30 minutes oral examination with 30 minutes preparation time. Approval of two project reports is a prerequisite for enrolling for examination. Written aids allowed.
Course workload
Course workload categoryHours
Lectures28.00
Theory exercises28.00
Project work30.00
Exam50.00
Preparation70.00

Sum206.00


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

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.

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