### 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.

Our approach is straightforward to implement using of-the-shelf software as illustrated in our numerical experiments.

Original language | English |
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Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 48 |

Volume | 2016-039 |

Publication status | Published - 22 Sep 2016 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2016-039 |

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### Keywords

- robust
- ambiguous
- integer
- recourse
- stochastic
- multi-stage

### Cite this

Postek, K., Romeijnders, W., den Hertog, D., & van der Vlerk, M. H. (2016).

*Efficient Methods for Several Classes of Ambiguous Stochastic Programming Problems under Mean-MAD Information*. (CentER Discussion Paper; Vol. 2016-039). Tilburg: Operations research.