Robust aspects of solutions in deterministic multiple objective linear programming

► We give conditions for efficiency under some alterations of the objective matrix. ► We establish necessary and sufficient conditions for robust efficient solutions. ► We provide a formula to compute the robustness radius. We study questions of robustness of linear multiple objective problems in th...

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Vydáno v:European journal of operational research Ročník 229; číslo 1; s. 29 - 36
Hlavní autoři: Georgiev, Pando Gr, Luc, Dinh The, Pardalos, Panos M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 16.08.2013
Elsevier
Elsevier Sequoia S.A
Témata:
Criteria
Linear programming
Mathematical problems
Mathematics
Matrix
Multiple objective linear problem
Radius of robustness
Robust efficient solutions
Studies
Multiple objective linear problem
Robust efficient solutions
Radius of robustness
ISSN:0377-2217, 1872-6860
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Shrnutí:► We give conditions for efficiency under some alterations of the objective matrix. ► We establish necessary and sufficient conditions for robust efficient solutions. ► We provide a formula to compute the robustness radius. We study questions of robustness of linear multiple objective problems in the sense of post-optimal analysis, that is, we study conditions under which a given efficient solution remains efficient when the criteria/objective matrix undergoes some alterations. We consider addition or removal of certain criteria, convex combination with another criteria matrix, or small perturbations of its entries. We provide a necessary and sufficient condition for robustness in a verifiable form and give two formulae to compute the radius of robustness.
Bibliografie:SourceType-Scholarly Journals-1
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2013.02.037