Linear Programming with interval right handsides

Virginie Gabrel (1) , Cecile Murat (1) , Nadila Remli (1)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

In this paper, we study general linear programs in which right handsides are interval numbers. This model is relevant when uncer- tain and inaccurate factors make di±cult the assignment of a single value to each right handside. When objective function coe±cients are interval numbers in a linear program, it is used to determine optimal solutions according to classical criteria coming from decision theory (like the worst case criterion). When the feasible solutions set is uncer- tain, another approach consists in determining the worst and best op- timum solutions. We study the complexity of these two optimization problems when each right handside is an interval number. Moreover, we analysis the relationship between these two problems and the clas- sical approach coming from decision theory. We exhibit some duality relation between the worst optimum solution problem and the best optimum solution problem in the dual. This study highlights some duality property in robustness analysis.

Mots clés: linear programming; interval right handside; robustness analy- sis; worst case criteria; maximum regret criteria; complexity theory

Domaines: Complexité [cs.CC]

Virginie Gabrel, Cecile Murat, Nadila Remli. Linear Programming with interval right handsides. 2007. ⟨hal-00178102⟩