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Pourofoghi F. Simultaneous and Continuous Analysis of Changes in the Grey Linear Programming Model: Grey Parametric Programming. jor 2026; 23 (1)
URL: http://jamlu.lahijan.iau.ir/article-1-2295-en.html
URL: http://jamlu.lahijan.iau.ir/article-1-2295-en.html
Department of Applied Mathematics, Payame Noor University, Tehran, Iran. , f_pourofoghi@pnu.ac.ir
Abstract: (76 Views)
In many real-world problems, available data and information are often incomplete or imprecise; therefore, the use of grey system theory and, in particular, grey linear programming as an effective tool for modeling such conditions is of special importance. Post-optimal analysis of the model’s behavior, known as sensitivity (post-optimal) analysis, makes it possible to understand the model’s sensitivity to changes in parameters. When model parameters change continuously and simultaneously due to temporal or economic factors, dynamic examination of the optimal solution using grey parametric programming is necessary. In this research, the concept of traditional parametric programming, which analyzes parameter variations within a defined range, has been extended to the grey domain, enabling the analysis of parameters that are represented by intervals rather than point estimates. Three types of grey parametric programming are examined: continuous changes in the coefficients of decision variables, changes in the right-hand side values of constraints, and simultaneous changes in both parts. The proposed method allows analysis of the effects of these changes across the entire parameter range and illustrates the trend of changes in the optimal solution under different conditions. Finally, a numerical example is provided for each case to demonstrate the effectiveness of the proposed approach.
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