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

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Pubblicato in:Grey Systems vol. 10, no. 2 (2020), p. 145-157
Autore principale: Davood Darvishi Salookolaei
Altri autori: Seyed Hadi Nasseri
Pubblicazione:
Emerald Group Publishing Limited
Soggetti:
Linear programming
Theorems
Simplex method
Decision making
Optimization
System theory
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Abstract: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
Fonte:ABI/INFORM Global