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

✍ Scribed by Frederike Neise (auth.)

• Publisher: Vieweg+Teubner Verlag
• Year: 2008
• Tongue: English
• Leaves: 107
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-VIII
Introduction....Pages 1-7
Risk Measures in Two-Stage Stochastic Programs....Pages 9-32
Stochastic Dominance Constraints induced by Mixed-Integer Linear Recourse....Pages 33-67
Application: Optimal Operation of a Dispersed Generation System....Pages 69-89
Conclusion and Perspective....Pages 91-92
Back Matter....Pages 93-105

✦ Subjects

Mathematics, general