Advanced Operations Research: Stochastic Programming

In countless real-life situations, decision makers are required to make decisions under uncertainty, that is while relevant information is uncertain, noisy, imprecise. Examples are investments in assets or projects with uncertain returns, scheduling of taks with uncertain duration, or production of goods with uncertain demand. Decision problems with these features are central in the modern finance, energy, and logistics sector, to name a few.

This course introduces the students to optimization in conditions of uncertainty by means of stochastic programming. The course presents different mathematical formulations, illustrates the corresponding mathematical properties, shows how to exploit these properties in various solution methods, and discusses how uncertain parameters can be transfortmed into sound input data (scenarios). The students of this course will independently handle practical problems in project work and exercises, hereby gaining the practical experience necessary to work on complex decision problems under uncertainty. 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. Assessing the quality of a solution.

C. Properties of stochastic programming problems:

• C1. Structural mathematical properties of stochastic programs.
• C2. The value of stochastic programming and the value of information.

D. Solution methods:

• D1. Decomposition techniques for two-stage stochastic programs (e.g., L-shaped decomposition).
• D3. Decomposition techniques for multistage stochastic programs (e.g., Dual decomposition or Stochastic Dual Dynamic Programming).

E. Practical applications:

• E1. Solution of case studies from e.g., the energy, finance, or logistics sector, using optimization software such as GAMS, Cplex or Gurobi.
• E2. Solution of several practical exercises.