Safe Approximations of Chance Constraints Using Historical Data
AbstractThis paper proposes a new way to construct uncertainty sets for robust optimization. Our approach uses the available historical data for the uncertain parameters and is based on goodness-of-fit statistics. It guarantees that the probability that the uncertain constraint holds is at least the prescribed value. Compared to existing safe approximation methods for chance constraints, our approach directly uses the historical-data information and leads to tighter uncertainty sets and therefore to better objective values. This improvement is significant especially when the number of uncertain parameters is low. Other advantages of our approach are that it can handle joint chance constraints easily, it can deal with uncertain parameters that are dependent, and it can be extended to nonlinear inequalities. Several numerical examples illustrate the validity of our approach.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2011-137.
Date of creation: 2011
Date of revision:
Contact details of provider:
Web page: http://center.uvt.nl
robust optimization; chance constraint; phi-divergence; goodness-of-fit statistics;
Find related papers by JEL classification:
- C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-12-19 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- A. Charnes & W. W. Cooper & G. H. Symonds, 1958. "Cost Horizons and Certainty Equivalents: An Approach to Stochastic Programming of Heating Oil," Management Science, INFORMS, vol. 4(3), pages 235-263, April.
- den Hertog, Dick & Stehouwer, Peter, 2002. "Optimizing color picture tubes by high-cost nonlinear programming," European Journal of Operational Research, Elsevier, vol. 140(2), pages 197-211, July.
- Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
- A. Charnes & W. W. Cooper, 1959. "Chance-Constrained Programming," Management Science, INFORMS, vol. 6(1), pages 73-79, October.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Richard Broekman).
If references are entirely missing, you can add them using this form.