Linear Programming with interval right hand sides
Gabrel, Virginie; Murat, Cécile; Remli, Nabila (2010), Linear Programming with interval right hand sides, International Transactions in Operational Research, 17, 3, p. 397-408. http://dx.doi.org/10.1111/j.1475-3995.2009.00737.x
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00178102/en/
Journal nameInternational Transactions in Operational Research
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Abstract (EN)In this paper, we study general linear programs in which right handsides are interval numbers. This model is relevant when uncertain and inaccurate factors make di±cult the assignment of a single value to each right handside. When objective function coefficients 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 optimum 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 classical 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.
Subjects / Keywordsmaximum regret criteria; robustness analysis; interval right handside; linear programming
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