Details

Autor(en) / Beteiligte

• Calvete, Herminia I.
• Galé, Carmen

Titel

Linear bilevel programming with interval coefficients

Ist Teil von

• Journal of computational and applied mathematics, 2012-09, Vol.236 (15), p.3751-3762

Ort / Verlag

Elsevier B.V

Erscheinungsjahr

2012

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this paper, we address linear bilevel programs when the coefficients of both objective functions are interval numbers. The focus is on the optimal value range problem which consists of computing the best and worst optimal objective function values and determining the settings of the interval coefficients which provide these values. We prove by examples that, in general, there is no precise way of systematizing the specific values of the interval coefficients that can be used to compute the best and worst possible optimal solutions. Taking into account the properties of linear bilevel problems, we prove that these two optimal solutions occur at extreme points of the polyhedron defined by the common constraints. Moreover, we develop two algorithms based on ranking extreme points that allow us to compute them as well as determining settings of the interval coefficients which provide the optimal value range.