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A dual simplex method for grey linear programming problems based on duality results

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Publié dans:Grey Systems vol. 10, no. 2 (2020), p. 145-157
Auteur principal: Davood Darvishi Salookolaei
Autres auteurs: Seyed Hadi Nasseri
Publié:
Emerald Group Publishing Limited
Sujets:
Linear programming
Theorems
Simplex method
Decision making
Optimization
System theory
Accès en ligne:Citation/Abstract
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Résumé:PurposeFor extending the common definitions and concepts of grey system theory to the optimization subject, a dual problem is proposed for the primal grey linear programming problem.Design/methodology/approachThe authors discuss the solution concepts of primal and dual of grey linear programming problems without converting them to classical linear programming problems. A numerical example is provided to illustrate the theory developed.FindingsBy using arithmetic operations between interval grey numbers, the authors prove the complementary slackness theorem for grey linear programming problem and the associated dual problem.Originality/valueComplementary slackness theorem for grey linear programming is first presented and proven. After that, a dual simplex method in grey environment is introduced and then some useful concepts are presented.
ISSN:2043-9377
2043-9385
DOI:10.1108/GS-10-2019-0044
Source:ABI/INFORM Global