Volume 21, Issue 1 (3-2024)                   jor 2024, 21(1): 93-106 | Back to browse issues page

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Pourofoghi F, Darvishi Salokolaei D. A New Approach to Solving Grey Assignment Problems Using the Concept of Operators and Ranking of Grey Numbers. jor 2024; 21 (1) :93-106
URL: http://jamlu.liau.ac.ir/article-1-2135-en.html
A New Approach to Solving Grey Assignment Problems Using the Concept of Operators and Ranking of Grey Numbers
F. Pourofoghi * , D. Darvishi Salokolaei
Department of Mathematics, Payame Noor University, Tehran, Iran , f_pourofoghi@pnu.ac.ir
Abstract:   (1096 Views)
One of the most important applied models in linear programming problems is the linear assignment problem. Due to the uncertainty in the data and information of real world problems, accurate data cannot always be used in the cost matrix of the linear assignment problem. Therefore, sometimes in practical situations, the theory of grey systems (grey numbers) is used to represent the imprecise data of the cost matrix of the assignment problem. One of the usual methods to solve the assignment problem with grey parameters is to whiten the grey numbers. Because the whitening technique only provides a clear equivalent model. Therefore, the answer obtained by this method cannot maintain the features of uncertainty. For these shortcomings, in this paper, a direct approach (without whitening) is introduced to solve the assignment problem in the grey environment. For this purpose, a ranking method and a new difference method for interval grey numbers have been presented, which improves the answer and reduces the amount of calculations. In the end, an example is presented to show the effectiveness of the proposed method. It is emphasized, whenever a linear programming model is formulated in the grey environment, the proposed approach can be used.
 
Keywords: Assignment, Grey Number, Linear Programming, Cost Matrix, Grey Ranking
Full-Text [PDF 749 kb]   (233 Downloads)    
Type of Study: Applicable | Subject: Special
Received: 2023/09/6 | Accepted: 2024/01/11 | Published: 2024/03/20
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