Andreas Märkert :

Deviation measures in stochastic programming with mixed-integer recourse

Dissertation angenommen durch: Universität Duisburg-Essen, Campus Duisburg, Fakultät für Naturwissenschaften, Institut für Mathematik, 2004-06-04

BetreuerIn: Prof. Dr. Rüdiger Schultz , Universität Duisburg-Essen, Campus Duisburg, Fakultät für Naturwissenschaften, Institut für Mathematik

GutachterIn: Prof. Dr. Rüdiger Schultz , Universität Duisburg-Essen, Campus Duisburg, Fakultät für Naturwissenschaften, Institut für Mathematik
GutachterIn: Prof. Dr. Maarten H. van der Vlerk , University of Groningen (NL), Department of Economics & OR

Schlüsselwörter in Englisch: Stochastic integer programming, risk measures, decomposition algorithms

  
   
 Klassifikation     
    MSC Primary: 90C15
MSC Secondary: 90C11
Sachgruppe der DNB: 510 Mathematik
  
   
 Abstrakt     
   

Abstrakt in Englisch

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.