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Advanced Operations Research: Stochastic Programming
Provider: Faculty of Science

Activity no.: 5635-20-07-31 
Enrollment deadline: 15/04/2020
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time20.04.2020, at: 09:00 - 19.06.2020, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserGiovanni Pantuso    E-mail address: gp@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 4
Scheme groupA (Tues 8-12 + Thurs 8-17)
Exam formOral examination, 30 minutes
Exam form30 minutes preparation, 30 minutes oral examination including grade determination
Exam details Approval of two project reports is a prerequisite for enrolling for examination (failed project reports can be resubmitted) Aid Written aids allowed
Exam aidsOnly certain aids allowed
Course workload
Course workload categoryHours
Lectures28.00
Theoretical exercises14.00
Project work40.00
Exam1.00
Preparation123.00
Sum206.00
Content
This course introduces the students to optimization under uncertainty by means of stochastic programming. In many real-life problems input data is often uncertain, noisy, imprecise. For these problems, the course illustrates different problem formulations, discusses how uncertain parameters can be transfortmed into "scenarios", discusses specific properties of stochastic programs, and shows how to exploit these properties in various solution methods. Furthermore, the students of this course will independently handle practical problems in project work. The content can be summarized as follows.

A. Stochastic programming problems:
A1. Formulations of stochastic programming problems.
A2. Examples.
A3. Implementation and solution of mathematical programming problems using state-of-the-art optimization software (e.g., GAMS, AMPL, Cplex or the like).
A4. Analysis of the solution.

B. Scenario generation:
B1. Moment matching.
B2. Sampling.
B3. Scenario tree construction.
B4. The quality of scenario generation methods.

C. Properties of stochastic programming problems:
C1. The value of stochastic programming: EVPI and EEV.
C2. Structural properties of stochastic programs.

D. Solution methods:
D1. L-shaped decomposition.
D2. Integer L-shaped decomposition.
D3. Dual decomposition.

E. Practical aspects and applications:
E1. Implementation of a real-life problem using optimization software.
E2. Implementation of a solution method using optimization software.
E3. Case studies from e.g., Energy planning, Finance, Transportation.

Formel requirements
Operations Research 1 (OR1) or similar is required.
Recommended but not required: One or more between Applied Operations Research and Operations Research 2 (OR2)

Learning outcome
Knowledge:
- Formulations of stochastic programming problems
- Scenario generation methods
- Properties of stochastic programming problems
- Solution methods

Skills:
- Formulate different types of stochastic programming problems
- Implement and solve a stochastic programming problem using suitable software
- Apply selected methods to describe the uncertainty of the problem (so-called "scenario generation" methods)
- Apply the solution methods presented in the course
- Implement a (simplified version of a) solution method using optimization software
- Understand and reproduce the proofs presented in the course

Compentences:
- Work out simple proofs using the same techniques as in the course
- Discuss the challenges of solving stochastic programming problems
- Explain how to exploit the properties of a given class of stochastic programs in the design of a solution method
- Adapt a solution method to a given class of stochastic programming problems, and make small changes to and extensions of the method
- Evaluate the quality of scenario trees
- Formulate, implement and solve a practical problem and justify the choice of model formulation, scenario generation method and solution method

Literature
See Absalon.

Teaching and learning methods
2x2 hours of lectures per week, 2 hours of exercise sessions per week, and project work for 7 weeks.

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