Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, November 29, 2005, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Rüdiger Schultz (Univ. Duisburg)

Risk Aversion in Stochastic Integer Programming: Models and Algorithms

Stochastic programming models aim at optimizing nonanticipative decisions in the presence of uncertainty. Traditional models are risk neutral, meaning that expected values of relevant decision dependent random variables constitute the objectives. In a risk averse setting these expected values are replaced or supplemented by statistical dispersion parameters. Examples for the latter are (semi-)variance, central or semi-deviation, expected excess, value-at-risk, or conditional value-at-risk. Incorporating these parameters into stochastic programs has structural and algorithmic consequences. With emphasis on stochastic integer programs we will discuss these consequences.

In particular, we will analyze the block structures that arise in the equivalent mixed-integer linear programs if the underlying probability distributions are discrete. We will discuss decomposition and approximation approaches for solving these problems, including illustrations at practical examples from the chemical process and power industries. Most of the talk will be in a two-stage setting where a first-stage decision is followed by an observation of the uncertain data and a second-stage recourse action. We will conclude with an outlook to multi-stage models where this scheme of alternating decision and observation is expanded to a finite number of steps.

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