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.