# NMAK15004U Advanced Operations Research: Stochastic Programming

Volume 2020/2021
Education

MSc Programme in Mathematics-Economics

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

See Absalon for a list of course litterature.

Operations Research 1 (OR1) or similar is required.
Recommended but not required: Applied Operations Research and/or Operations Research 2 (OR2)

Academic qualifications equivalent to a BSc degree is recommended.
2x3 hours of lectures per week, 2 hours of classroom exercises or project work supervision. Individual or group-based project work throughout the course.
• Category
• Hours
• Lectures
• 42
• Preparation
• 14
• Theory exercises
• 6
• Project work
• 55
• Guidance
• 8
• Exam Preparation
• 80
• Exam
• 1
• Total
• 206
Oral

Lecturer's oral or written feedback (collective and/or individual) on the project work.

Credit
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
30 minutes oral examination with 30 minutes preparation time.
Exam registration requirements

Approval of one project report is a prerequisite for enrolling for examination.

Aid
Only certain aids allowed

All aid can be used during the preparation time.

No aid can be used during the exam.

Marking scale