Affiliations: [a]
Department of Industrial Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Iran
| [b]
College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, P.R. China | [c]
Institute for Grey Systems and Decision Sciences, GreySys Foundation, Lahore, Pakistan
Abstract: Linear programming is being widely applied in various fields e.g., management sciences, operations research, economics and engineering. In real-world settings, the input data of linear programming models entail many uncertainties. Overlooking these uncertainties may lead to erroneous decision making. In the problems surrounding uncertainty and incomplete/partially known data, Grey System Theory (GST) is a suitable approach for data analysis. Accordingly, the current study is an attempt to propose a new method for solving grey linear programming problems. The grey linear programing methods proposed to date suffer from numerous drawbacks 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. To counter these drawbacks, the current study proposes a novel method of linear programming with grey parameters. Later, its solutions are compared with that of other alternative methods. Comparative analyses of the methods revealed the superiority of the proposed method over other methods in terms of quality of optimal solution and computational steps. As opposed to the other existing methods that usually comprise several stages, the proposed method has only three stages for solving grey linear programming problems and is therefore simple to work with.
Keywords: Grey linear programming, grey system theory, novel method, grey parameters, uncertainty data.
