Grey linear programming: a survey on solving approaches and applications
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
:Emerald Publishing Limited
Copyright © 2020, Emerald Publishing Limited