A PRIMAL SIMPLEX ALGORITHM FOR SOLVING LINEAR PROGRAMMING PROBLEM WITH GREY COST COEFFICIENTS

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NASSERI S.H.; YAZDANI A.; DARVISHI SALOKOLAEI D.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2016 | Volume:1 | Issue:4 Page(s): 115-135

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Title

A PRIMAL SIMPLEX ALGORITHM FOR SOLVING LINEAR PROGRAMMING PROBLEM WITH GREY COST COEFFICIENTS

Author(s)

NASSERI S.H. | YAZDANI A. | DARVISHI SALOKOLAEI D. | Issue Writer Certificate

Keywords

GREY LINEAR PROGRAMMING

GREY SYSTEM THEORY

INTERVAL GREY NUMBER

PRIMAL SIMPLEX ALGORITHM

UNCERTAINTY

Abstract

in this paper, a linear programming problem is considered involving INTERVAL GREY NUMBERs as an extension of the classical linear programming problem to an inexact environment as well as fuzzy and stochastic environment. Hence, here a new approach for solving INTERVAL GREY NUMBER linear programming problems is introduced without converting them to classical linear programming problems. The proposed method is established based on the PRIMAL SIMPLEX ALGORITHM where the cost coefficient row includes grey numbers. As an essential tool in the solving process, a theoretical discussion on grey arithmetic and in particular an ordering role for grey numbers is necessary to evaluate the optimality conditions of a candidate feasible solution. It is also emphasized that the discussed model and the solution process is useful for real situations and practical cases, when a kind of the grey number linear programming is appeared, such as Water Resource Management and Planning, Economics, etc. Finally, the proposed approach is illustrated by a numerical example.

Cites

REVISIT ORDERING ON L-R FUZZY NUMBERS AND ITS APPLICATION IN FUZZY MATHEMATICAL PROGRAMMING

References

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APA: Copy

NASSERI, S.H., YAZDANI, A., & DARVISHI SALOKOLAEI, D.. (2016). A PRIMAL SIMPLEX ALGORITHM FOR SOLVING LINEAR PROGRAMMING PROBLEM WITH GREY COST COEFFICIENTS. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 1(4), 115-135. SID. https://sid.ir/paper/686639/en

Vancouver: Copy

NASSERI S.H., YAZDANI A., DARVISHI SALOKOLAEI D.. A PRIMAL SIMPLEX ALGORITHM FOR SOLVING LINEAR PROGRAMMING PROBLEM WITH GREY COST COEFFICIENTS. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2016;1(4):115-135. Available from: https://sid.ir/paper/686639/en

IEEE: Copy

S.H. NASSERI, A. YAZDANI, and D. DARVISHI SALOKOLAEI, “A PRIMAL SIMPLEX ALGORITHM FOR SOLVING LINEAR PROGRAMMING PROBLEM WITH GREY COST COEFFICIENTS,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 1, no. 4, pp. 115–135, 2016, [Online]. Available: https://sid.ir/paper/686639/en

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