### Abstract

Original language | English |
---|---|

Pages (from-to) | 30-43 |

Journal | European Journal of Operational Research |

Volume | 227 |

Issue number | 1 |

Publication status | Published - 2013 |

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### Cite this

*European Journal of Operational Research*,

*227*(1), 30-43.

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*European Journal of Operational Research*, vol. 227, no. 1, pp. 30-43.

**Robust counterparts of inequalities containing sums of maxima of linear functions.** / Gorissen, B.L.; den Hertog, D.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Robust counterparts of inequalities containing sums of maxima of linear functions

AU - Gorissen, B.L.

AU - den Hertog, D.

PY - 2013

Y1 - 2013

N2 - This paper addresses the robust counterparts of optimization problems containing sums of maxima of linear functions. These problems include many practical problems, e.g.~problems with sums of absolute values, and arise when taking the robust counterpart of a linear inequality that is affine in the decision variables, affine in a parameter with box uncertainty, and affine in a parameter with general uncertainty. In the literature, often the reformulation is used that is exact when there is no uncertainty. However, in robust optimization this reformulation gives an inferior solution and provides a pessimistic view. We observe that in many papers this conservatism is not mentioned. Some papers have recognized this problem, but existing solutions are either conservative or their performance for different uncertainty regions is not known, a comparison between them is not available, and they are restricted to specific problems. We describe techniques for general problems and compare them with numerical examples in inventory management, regression and brachytherapy. Based on these examples, we give recommendations for reducing the conservatism.

AB - This paper addresses the robust counterparts of optimization problems containing sums of maxima of linear functions. These problems include many practical problems, e.g.~problems with sums of absolute values, and arise when taking the robust counterpart of a linear inequality that is affine in the decision variables, affine in a parameter with box uncertainty, and affine in a parameter with general uncertainty. In the literature, often the reformulation is used that is exact when there is no uncertainty. However, in robust optimization this reformulation gives an inferior solution and provides a pessimistic view. We observe that in many papers this conservatism is not mentioned. Some papers have recognized this problem, but existing solutions are either conservative or their performance for different uncertainty regions is not known, a comparison between them is not available, and they are restricted to specific problems. We describe techniques for general problems and compare them with numerical examples in inventory management, regression and brachytherapy. Based on these examples, we give recommendations for reducing the conservatism.

M3 - Article

VL - 227

SP - 30

EP - 43

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 1

ER -