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Grey linear programming: a survey on solving approaches and applications

Davood Darvishi (Department of Mathematics, Payame Noor University, Tehran, Iran)
Sifeng Liu (Institute for Grey Systems Studies, Nanjing University of Aeronautics and Astronautics, Nanjing, China)
Jeffrey Yi-Lin Forrest (Department of Accounting Economics Finance, Slippery Rock University, Slippery Rock, Pennsylvania, USA)

Grey Systems: Theory and Application

ISSN: 2043-9377

Article publication date: 17 June 2020

Issue publication date: 13 January 2021

Abstract

Purpose

The purpose of this paper is to survey and express the advantages and disadvantages of the existing approaches for solving grey linear programming in decision-making problems.

Design/methodology/approach

After presenting the concepts of grey systems and grey numbers, this paper surveys existing approaches for solving grey linear programming problems and applications. Also, methods and approaches for solving grey linear programming are classified, and its advantages and disadvantages are expressed.

Findings

The progress of grey programming has been expressed from past to present. The main methods for solving the grey linear programming problem can be categorized as Best-Worst model, Confidence degree, Whitening parameters, Prediction model, Positioned solution, Genetic algorithm, Covered solution, Multi-objective, Simplex and dual theory methods. This survey investigates the developments of various solving grey programming methods and its applications.

Originality/value

Different methods for solving grey linear programming problems are presented, where each of them has disadvantages and advantages in providing results of grey linear programming problems. This study attempted to review papers published during 35 years (1985–2020) about grey linear programming solving and applications. The review also helps clarify the important advantages, disadvantages and distinctions between different approaches and algorithms such as weakness of solving linear programming with grey numbers in constraints, inappropriate results with the lower bound is greater than upper bound, out of feasible region solutions and so on.

Keywords

Acknowledgements

This work was partially supported by Institute for Grey System Studies, Nanjing University of Aeronautics and Astronautics, Nanjing, P.R. China.

Citation

Darvishi, D., Liu, S. and Yi-Lin Forrest, J. (2021), "Grey linear programming: a survey on solving approaches and applications", Grey Systems: Theory and Application, Vol. 11 No. 1, pp. 110-135. https://doi.org/10.1108/GS-04-2020-0043

Publisher

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Emerald Publishing Limited

Copyright © 2020, Emerald Publishing Limited