Efficient Methods for Several Classes of Ambiguous Stochastic Programming Problems Under Mean-MAD Information

CentER Discussion Paper Series No. 2016-039

48 Pages Posted: 29 Sep 2016

See all articles by Krzysztof Postek

Krzysztof Postek

Tilburg University - Center for Economic Research (CentER)

Ward Romeijnders

University of Groningen

Dick den Hertog

Tilburg University - Department of Econometrics & Operations Research

Maarten H. Vlerk

University of Groningen

Date Written: September 22, 2016

Abstract

We consider decision making problems under uncertainty, assuming that only partial distributional information is available - as is often the case in practice. In such problems, the goal is to determine here-and-now decisions, which optimally balance deterministic immediate costs and worst-case expected future costs. These problems are challenging, since the worst-case distribution needs to be determined while the underlying problem is already a difficult multistage recourse problem. Moreover, as found in many applications, the model may contain integer variables in some or all stages. Applying a well-known result by Ben-Tal and Hochman (1972), we are able to efficiently solve such problems without integer variables, assuming only readily available distributional information on means and mean-absolute deviations. Moreover, we extend the result to the non-convex integer setting by means of convex approximations (see Romeijnders et al. (2016a)), proving corresponding performance bounds. Our approach is straightforward to implement using of-the-shelf software as illustrated in our numerical experiments.

Keywords: robust, ambiguous, integer, recourse, stochastic, multi-stage

JEL Classification: C61

Suggested Citation

Postek, Krzysztof and Romeijnders, Ward and den Hertog, Dick and Vlerk, Maarten H., Efficient Methods for Several Classes of Ambiguous Stochastic Programming Problems Under Mean-MAD Information (September 22, 2016). CentER Discussion Paper Series No. 2016-039. Available at SSRN: https://ssrn.com/abstract=2845229 or http://dx.doi.org/10.2139/ssrn.2845229

Krzysztof Postek (Contact Author)

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

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Ward Romeijnders

University of Groningen ( email )

P.O. Box 800
9700 AH Groningen, Groningen 9700 AV
Netherlands

Dick Den Hertog

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

Tilburg, 5000 LE
Netherlands

Maarten H. Vlerk

University of Groningen ( email )

P.O. Box 800
9700 AH Groningen, Groningen 9700 AV
Netherlands

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