Risk Management in Stochastic Integer Programming: With Application to Dispersed Power Generation - Softcover

Neise, Frederike

Softcover

ISBN 10: 3834805475 ISBN 13: 9783834805478

Publisher: Vieweg+Teubner Verlag, 2008

Synopsis

I am deeply grateful to my advisor Prof. Dr. Rüdiger Schultz for his untiring - couragement. Moreover, I would like to express my gratitude to Prof. Dr. -Ing. - mund Handschin and Dr. -Ing. Hendrik Neumann from the University of Dortmund for inspiration and support. I would like to thank PD Dr. René Henrion from the Weierstrass Institute for Applied Analysis and Stochastics in Berlin for reviewing this thesis. Cordial thanks to my colleagues at the University of Duisburg-Essen for motivating and fruitful discussions as well as a pleasurable cooperation. Contents 1 Introduction 1 1. 1 Stochastic Optimization. . . . . . . . . . . . . . . . . . . . . . . 3 1. 1. 1 The two-stage stochastic optimization problem . . . . . . 3 1. 1. 2 Expectation-based formulation. . . . . . . . . . . . . . . 5 1. 2 Content and Structure. . . . . . . . . . . . . . . . . . . . . . . . 6 2 RiskMeasuresinTwo-StageStochasticPrograms 9 2. 1 Risk Measures. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2. 1. 1 Deviation measures. . . . . . . . . . . . . . . . . . . . . 10 2. 1. 2 Quantile-based risk measures . . . . . . . . . . . . . . . 11 2. 2 Mean-Risk Models . . . . . . . . . . . . . . . . . . . . . . . . . 12 2. 2. 1 Results concerning structure and stability . . . . . . . . . 13 2. 2. 2 Deterministic equivalents. . . . . . . . . . . . . . . . . . 22 2. 2. 3 Algorithmic issues – dual decomposition method . . . . . 26 3 StochasticDominanceConstraints 33 3. 1 Introduction to Stochastic Dominance . . . . . . . . . . . . . . . 33 3. 1. 1 Stochastic orders for the preference of higher outcomes . . 34 3. 1. 2 Stochastic orders for the preference of smaller outcomes . 38 3. 2 Stochastic Dominance Constraints . . . . . . . . . . . . . . . . . 42 3. 2. 1 First order stochastic dominanceconstraints. . . . . . . . 43 3. 2. 2 Results concerning structure and stability . . . . . . . . . 44 3. 2. 3 Deterministic equivalents. . . . . . . . . . . . . . . . . . 51 3. 2. 4 Algorithmic issues . . . . . . . . . . . . . . . . . . . . .

About this title

About the Author

Dr. Frederike Neise gained a PhD in Mathematics from the University of Duisburg-Essen studying two-stage stochastic programming and its application to the optimal management of dispersed generation systems. She currently works as a gas market analyst with E.ON Ruhrgas AG.

From the Back Cover

Two-stage stochastic optimization is a useful tool for making optimal decisions under uncertainty. Frederike Neise describes two concepts to handle the classic linear mixed-integer two-stage stochastic optimization problem: The well-known mean-risk modeling, which aims at finding a best solution in terms of expected costs and risk measures, and stochastic programming with first order dominance constraints that heads towards a decision dominating a given cost benchmark and optimizing an additional objective. For this new class of stochastic optimization problems results on structure and stability are proven. Moreover, the author develops equivalent deterministic formulations of the problem, which are efficiently solved by the presented dual decomposition method based on Lagrangian relaxation and branch-and-bound techniques. Finally, both approaches – mean-risk optimization and dominance constrained programming – are applied to find an optimal operation schedule for a dispersed generation system, a problem from energy industry that is substantially influenced by uncertainty.

Edition details

• Publisher: Vieweg+Teubner Verlag
• Publication date: 2008
• Language: English
• ISBN 10: 3834805475
• ISBN 13: 9783834805478
• Binding: Paperback
• Number of pages: 115