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Advanced Operations Research: Stochastic Programming
Provider: Faculty of Science

Activity no.: 5635-19-07-31 
Enrollment deadline: 18/04/2019
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time23.04.2019, at: 09:00 - 23.06.2019, 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
Teaching languageEnglish partially in English
Semester/BlockBlock 4
Scheme groupA (Tues 8-12 + Thurs 8-17)
Exam formWritten assignment
Exam formWritten assignment
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 aidsAll aids allowed
Course workload
Course workload categoryHours
Lectures28.00
Theoretical exercises14.00
Project work44.00
Exam50.00
Preparation70.00

Sum206.00


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

Skills:
• Formulate two-stage and multi-stage recourse problems
• Implement and solve a stochastic programming problem in GAMS or other 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 solution method using software such as GAMS (in a simplified fashion).
• 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 SP problems
• Explain how to exploit the properties of a given class of SP problems in the design of a solution method
• Adapt a solution method to a given class of SP problems, and make small changes to and extensions of the method
• Evaluate the quality of scenario trees
• Discuss the challenges of modeling and solving practical problems
• Formulate, implement and solve a practical problem and justify the choice of model formulation, scenario generation method and solution method

Literature
See Absalon.

Target group
Knowledge:
• Formulations of stochastic programming problems.
• Scenario generation methods.
• Properties of stochastic programming problems.
• Solution methods.

Skills:
• Formulate two-stage and multi-stage recourse problems
• Implement and solve a stochastic programming problem in GAMS or other 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 solution method using software such as GAMS (in a simplified fashion).
• 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 SP problems
• Explain how to exploit the properties of a given class of SP problems in the design of a solution method
• Adapt a solution method to a given class of SP problems, and make small changes to and extensions of the method
• Evaluate the quality of scenario trees
• Discuss the challenges of modeling and solving practical problems
• Formulate, implement and solve a practical problem and justify the choice of model formulation, scenario generation method and solution method

Teaching and learning methods
2 x 2 hours of lectures and 1 x 2 hours exercises/project work per week for 7 weeks

Content
This course is about optimization under uncertainty by means of stochastic programming. Special emphasis is placed on different problem formulations and selected scenario generation methods as well as to understand specific properties of stochastic programming problems and how to exploit these properties in various solution methods. Furthermore, the students of this course will independently handle more practical problems by stochastic programming.

A. Stochastic programming problems:
A1. Formulation of two-stage and multi-stage recourse problems, simple recourse, linear and integer problems, chance constrained problems.
A2. Examples.
A3. Implementation and solution of problems in GAMS or other suitable software.
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: Continuity and convexity.

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 software such as GAMS.
E2. Implementation of a solution method using software such as GAMS.
E3. Case studies from Energy planning, Finance, Transportation.

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