A dual simplex method for grey linear programming problems based on duality results. Issue 2 (30th April 2020)

• Record Type: Journal Article
• Authors: Darvishi Salookolaei, Davood; Nasseri, Seyed Hadi
• Is Part Of: Grey systems. Volume 10:Issue 2(2020)
• Page Start: 145
• Page End: 157
• Publication Date: 2020-04-30
• Subjects: Duality results -- Dual simplex method -- Grey system -- Grey number -- Grey linear programming; Cybernetics -- Periodicals; Systems engineering -- Periodicals; 003.5
• DOI: 10.1108/GS-10-2019-0044
• Languages: English
• ISSNs: 2043-9377

Abstract

Abstract : Purpose: For 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/approach: The 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. Findings: By 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/value: Complementary 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.