Universität zu Köln

Mosler, Karl and Bazovkin, Pavel (2014). Stochastic linear programming with a distortion risk constraint. OR Spectrum, 36 (4). S. 949 - 970. NEW YORK: SPRINGER. ISSN 1436-6304

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Abstract

Coherent distortion risk measures are applied to capture the possible violation of a restriction in linear optimization problems whose parameters are uncertain. Each risk constraint induces an uncertainty set of coefficients, which is proved to be a weighted-mean trimmed region. Thus, given a sample of the coefficients, an uncertainty set is a convex polytope that can be exactly calculated. We construct an efficient geometrical algorithm to solve stochastic linear programs that have a single distortion risk constraint. The algorithm is available as an R-package. The algorithm's asymptotic behavior is also investigated, when the sample is i.i.d. from a general probability distribution. Finally, we present some computational experience.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Mosler, Karl UNSPECIFIED UNSPECIFIED UNSPECIFIED Bazovkin, Pavel UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-427732
DOI:	10.1007/s00291-014-0372-9
Journal or Publication Title:	OR Spectrum
Volume:	36
Number:	4
Page Range:	S. 949 - 970
Date:	2014
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	1436-6304
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language ROBUST OPTIMIZATION Multiple languages Operations Research & Management Science Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/42773