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Robust Optimization under Multi-band Uncertainty - Part I: Theory

Christina Büsing (buesing***at***or.rwth-aachen.de)
Fabio D'Andreagiovanni (d.andreagiovanni***at***zib.de)

Abstract: The classical single-band uncertainty model introduced by Bertsimas and Sim has represented a breakthrough in the development of tractable robust counterparts of Linear Programs. However, adopting a single deviation band may be too limitative in practice: in many real-world problems, observed deviations indeed present asymmetric distributions over asymmetric ranges, so that getting a higher modeling resolution by partitioning the band into multiple sub-bands is advisable. The critical aim of our work is to close the knowledge gap on the adoption of multi-band uncertainty in Robust Optimization: a general definition and intensive theoretical study of a multi-band model are actually still missing. Our new developments have been also strongly inspired and encouraged by our industrial partners, interested in getting a better modeling of arbitrary shaped distributions, built on historical data about the uncertainty affecting the considered real-world problems.

Keywords: Robust Optimization, Multi-band Uncertainty, Compact Robust Counterpart, Cutting Planes, Probabilistic Bound

Category 1: Robust Optimization

Category 2: Integer Programming ((Mixed) Integer Linear Programming )

Category 3: Combinatorial Optimization (Polyhedra )

Citation: Submitted (2012)

Download: [PDF]

Entry Submitted: 01/31/2013
Entry Accepted: 01/31/2013
Entry Last Modified: 03/14/2013

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