Grey linear programming: a survey on solving approaches and applications

PurposeThe 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/approachAfter presenting the concepts of grey systems and grey numbers, this paper surveys existing...

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Vydáno v:Grey systems Ročník 11; číslo 1; s. 110 - 135
Hlavní autoři: Darvishi, Davood, Liu, Sifeng, Yi-Lin Forrest, Jeffrey
Médium: Journal Article
Jazyk:angličtina
Vydáno: Bingley Emerald Publishing Limited 13.01.2021
Emerald Group Publishing Limited
Témata:
Algorithms
Decision making
Fuzzy sets
Games
Genetic algorithms
Integer programming
Linear programming
Lower bounds
Mathematical programming
Optimization
Prediction models
Simplex method
System theory
Systems analysis
Upper bounds
Variables
Optimization with uncertainty
Grey linear programming
Grey systems theory
Grey number
Decision making
ISSN:2043-9377, 2043-9385
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Shrnutí:PurposeThe 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/approachAfter 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.FindingsThe 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/valueDifferent 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.
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ISSN:2043-9377
2043-9385
DOI:10.1108/GS-04-2020-0043