Deviation measures in stochastic programming with mixed-integer recourse
Stochastic programming offers a way to treat uncertainty in decision problems. In particular, it allows the minimization of risk. We consider mean-risk models involving deviation measures, as for instance the standard deviation and the semideviation, and discuss these risk measures in the framework of stochastic dominance as well as in the framework of coherent risk measures. We derive statements concerning the structure and the stability of the resulting optimization problems whereby we emphasize on models including integrality requirements on some decision variables. Then we propose decomposition algorithms for the mean-risk models under consideration and present numerical results for two stochastic programming applications.
Advisor:Prof. Dr. Rüdiger Schultz; Prof. Dr. Maarten H. van der Vlerk
School:Universität Duisburg-Essen, Standort Essen
Source Type:Master's Thesis
Keywords:mathematik universitaet duisburg essen
Date of Publication:06/09/2004