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Advanced Operations Research: Stochastic Programming
Provider: Faculty of Science

Activity no.: 5635-21-07-31 
Enrollment deadline: 26/04/2021
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time26.04.2021, at: 08:00 - 25.06.2021, 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 languageDanish
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 aidsWriten aids allowed
Course workload
Course workload categoryHours
Lectures42.00
Theoretical exercises6.00
Project work55.00
Exam1.00
Preparation94.00
Guidance8.00
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 uncertain, noisy, imprecise. Examples are investments in assets with uncertain returns or production of goods with uncertain demand. For these problems, the course presents different mathematical formulations, illustrates the corresponding properties, shows how to exploit these properties in various solution methods, and discusses how uncertain parameters can be transfortmed into input data (scenarios). 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. Decision making under uncertainty.
A2. Formulations of stochastic programming problems.


B. Approximations and scenario generation:
B1. Monte Carlo techniques.
B2. Property matching.
B3. The quality of scenario generation methods.


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


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


E. Practical aspects and applications:
E1. Solution of case studies from e.g., Energy planning, Finance, Transportation, using optimization software such as GAMS, Cplex or Gurobi

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
- Recognize and prove properties of stochastic programs
- Represent/approximate the uncertain data by means of scenarios
- Evaluate the added value of stochastic programming
- Apply the solution methods presented in the course to solve stochastic programs
- Implement a (simplified version of a) solution method using optimization software

Compentences:
- Recognize and structure a decision problem affected by uncertainty and propose a suitable mathematical formulation
- Design a solution method for a stochastic program based on an analysis of its properties and justify the choice
- Identify a suitable way of representing the uncertain data of the problem, and its effect on the solutions obtained
- Quantify the benefit of using stochastic programming in a particular decision making problem

Literature
See Absalon.

Target group

Teaching and learning methods
2x3 hours of lectures per week, 2 hours of classroom exercises or project work supervision. Individual or group-based project work throughout the course.

Content

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