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An empirical analysis of scenario generation methods for stochastic optimization

Löhndorf, Nils (2016) An empirical analysis of scenario generation methods for stochastic optimization. European Journal of Operational Research, 255 (1). pp. 121-132. ISSN 0377-2217

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Abstract

This work presents an empirical analysis of popular scenario generation methods for stochastic optimization, including quasi-Monte Carlo, moment matching, and methods based on probability metrics, as well as a new method referred to as Voronoi cell sampling. Solution quality is assessed by measuring the error that arises from using scenarios to solve a multi-dimensional newsvendor problem, for which analytical solutions are available. In addition to the expected value, the work also studies scenario quality when minimizing the expected shortfall using the conditional value-at-risk. To quickly solve problems with millions of random parameters, a reformulation of the risk-averse newsvendor problem is proposed which can be solved via Benders decomposition. The empirical analysis identifies Voronoi cell sampling as the method that provides the lowest errors, with particularly good results for heavy-tailed distributions. A controversial finding concerns evidence for the ineffectiveness of widely used methods based on minimizing probability metrics under high-dimensional randomness.

Item Type: Article
Additional Information: The author would like to thank Lena Silbermayr for a fruitful discussion on risk-averse newsvendors as well as the three anonymous referees for their helpful comments and suggestions which helped to significantly improve the paper.
Keywords: stochastic optimization / sample average approximation / scenario generation / vector quantization / probability metrics / moment matching / Monte Carlo methods / conditional value-at-risk
Divisions: Departments > Informationsverarbeitung u Prozessmanag. > Produktionsmanagement > Taudes
Version of the Document: Accepted for Publication
Variance from Published Version: Typographical
Depositing User: Elena Simukovic
Date Deposited: 13 Jun 2017 13:10
Last Modified: 13 Jun 2017 14:18
Related URLs:
FIDES Link: https://bach.wu.ac.at/d/research/results/71943/
URI: http://epub.wu.ac.at/id/eprint/5594

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