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Robust location transportation problems under uncertain demands

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Date
2014
Dewey
Recher opérationnelle
Sujet
Robust optimization; Location transportation problem; Mixed integer linear programming; Interval uncertainty; Convex optimization
Journal issue
Discrete Applied Mathematics
Volume
146
Number
part 1
Publication date
2014
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.dam.2011.09.015
URI
https://basepub.dauphine.fr/handle/123456789/9344
Collections
  • LAMSADE : Publications
Metadata
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Author
Gabrel, Virginie
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Lacroix, Mathieu
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Murat, Cécile
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Remli, Nabila
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Type
Article accepté pour publication ou publié
Abstract (EN)
In robust optimization, the multi-stage context (or dynamic decision-making) assumes that the information is revealed in stages. So, part of the decisions must be taken before knowing the real values of the uncertain parameters, and another part, called recourse decisions, is taken when the information is known. In this paper, we are interested in a robust version of the locationtransportationproblem with an uncertaindemand using a 2-stage formulation. The obtained robust formulation is a convex (not linear) program, and we apply a cutting plane algorithm to exactly solve the problem. At each iteration, we have to solve an NP-hard recourse problem in an exact way, which is time-consuming. Here, we go further in the analysis of the recourse problem of the locationtransportationproblem. In particular, we propose a mixed integer program formulation to solve the quadratic recourse problem and we define a tight bound for this reformulation. We present an extensive computation analysis of the 2-stage robustlocationtransportationproblem. The proposed tight bound allows us to solve large size instances.

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