2-Stage Robust MILP with continuous recourse variables

Alain Billionnet, Marie-Christine Costa and Pierre-Louis Poirion

2014

Publication type:

Paper in peer-reviewed journals

Journal:

Discrete Applied Mathematics, vol. 170, pp. 21-32

Conference:

Présenté à EURO-INFORMS International Conference on Operational research, Roma, 2013.

DOI:

10.1016/j.dam.2014.01.017

HAL:

hal-00968777

Keywords :

Mixed integer linear programming, robust optimization

Abstract:

We solve a linear robust problem with mixed-integer first-stage variables and continuous second stage variables. We consider column wise uncertainty. We first focus on a problem with right hand-side uncertainty which satisfies a “full recourse property” and a specific definition of the uncertainty. We propose a solution based on a generation constraint algorithm. Then we give some generalizations of the approach: for left-hand side uncertainty and for uncertainty sets defined by a polytope. Finally we solve the problem when the “full recourse property” is not satisfied. http://cedric.cnam.fr/fichiers/art_2683.pdf

BibTeX:

@article{Bil-Cos-Poi-2014,
    author={Alain Billionnet and Marie-Christine Costa and Pierre-Louis 
           Poirion },
    title={2-Stage Robust MILP with continuous recourse variables },
    doi={10.1016/j.dam.2014.01.017 },
    journal={Discrete Applied Mathematics },
    year={2014 },
    volume={170 },
    pages={21--32},
}