Robust counterparts of inequalities containing sums of maxima of linear functions

B.L. Gorissen, D. den Hertog

Research output: Contribution to journalArticleScientificpeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)30-43
JournalEuropean Journal of Operational Research
Volume227
Issue number1
Publication statusPublished - 2013

Fingerprint

Linear Function
Uncertainty
Reformulation
Inventory Management
Robust Optimization
Absolute value
Linear Inequalities
Recommendations
Regression
Optimization Problem
Numerical Examples
Conservatism

Cite this

@article{20e7dc586a7449429454c1039f9a5fea,
title = "Robust counterparts of inequalities containing sums of maxima of linear functions",
abstract = "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.",
author = "B.L. Gorissen and {den Hertog}, D.",
year = "2013",
language = "English",
volume = "227",
pages = "30--43",
journal = "European Journal of Operational Research",
issn = "0377-2217",
publisher = "Elsevier Science BV",
number = "1",

}

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

In: European Journal of Operational Research, Vol. 227, No. 1, 2013, p. 30-43.

Research output: Contribution to journalArticleScientificpeer-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 -