Exact Robust Counterparts of Ambiguous Stochastic Constraints Under Mean and Dispersion Information

CentER Discussion Paper Series No. 2015-030

36 Pages Posted: 7 Jun 2015 Last revised: 18 Jun 2015

See all articles by Krzysztof Postek

Krzysztof Postek

Tilburg University - Center for Economic Research (CentER)

Aharon Ben-Tal

Technion-Israel Institute of Technology

Dick den Hertog

Tilburg University - Department of Econometrics & Operations Research

Bertrand Melenberg

Tilburg University - Center for Economic Research (CentER)

Date Written: June 5, 2015

Abstract

In this paper we consider ambiguous stochastic constraints under partial information consisting of means and dispersion measures of the underlying random parameters. Whereas the past literature used the variance as the dispersion measure, here we use the mean absolute deviation from the mean (MAD). This makes it possible to use the old result of Ben-Tal and Hochman (1972) in which tight upper and lower bounds on the expectation of a convex function of a random variable are given. We use these bounds to derive exact robust counterparts of expected feasibility of convex constraints and to construct new safe tractable approximations of chance constraints. Numerical examples show our method to be applicable to numerous applications of Robust Optimization, e.g., where implementation error or linear decision rules are present. Also, we show that the methodology can be used for optimization the average-case performance of worst-case optimal Robust Optimization solutions.

Keywords: robust optimization; ambiguity; stochastic programming; chance constraints

JEL Classification: C61

Suggested Citation

Postek, Krzysztof and Ben-Tal, Aharon and den Hertog, Dick and Melenberg, Bertrand, Exact Robust Counterparts of Ambiguous Stochastic Constraints Under Mean and Dispersion Information (June 5, 2015). CentER Discussion Paper Series No. 2015-030. Available at SSRN: https://ssrn.com/abstract=2614985 or http://dx.doi.org/10.2139/ssrn.2614985

Krzysztof Postek (Contact Author)

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Aharon Ben-Tal

Technion-Israel Institute of Technology ( email )

Technion City
Haifa 32000, Haifa 32000
Israel

Dick Den Hertog

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

Bertrand Melenberg

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 466 2730 (Phone)

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