Solving the Problem of Linear Programming with Cost Coefficients and Grey Resources Using the Primal Simplex Algorithm
In most real-world issues, we are dealing with situations where accurate data and complete information are not available. One way to deal with these uncertainties in real life is to use Grey System Theory (GST). In this paper, a linear programing problem in a grey environment with interval Grey Numb...
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REA Press
2022-06-01
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| Series: | Big Data and Computing Visions |
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| Online Access: | https://www.bidacv.com/article_153167_5ccfdc1662cc2874f339a074f77a3cee.pdf |
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| author | Farid Pourofoghi |
| author_facet | Farid Pourofoghi |
| author_sort | Farid Pourofoghi |
| collection | DOAJ |
| description | In most real-world issues, we are dealing with situations where accurate data and complete information are not available. One way to deal with these uncertainties in real life is to use Grey System Theory (GST). In this paper, a linear programing problem in a grey environment with interval Grey Numbers (GN) is considered. Most of the proposed methods for solving grey linear programing problems are done by using GN whitening and turning the problem into a common linear programing problem. However, in this paper we seek to solve the grey linear programing problem directly without turning it into a regular linear programing problem in order to maintain uncertainty in the original problem data in the final answer. For this purpose, by proving the desired theorems, we propose a method based on the initial simplex algorithm to solve grey linear programing problems. This method is simpler than the previous methods. We emphasize that the proposed concept is useful for real and practical situations. To illustrate the efficiency of the method, we solve an example of Grey Linear Programming (GLP). |
| format | Article |
| id | doaj-art-45d4bc21a63544e2843fbb4107759492 |
| institution | Kabale University |
| issn | 2783-4956 2821-014X |
| language | English |
| publishDate | 2022-06-01 |
| publisher | REA Press |
| record_format | Article |
| series | Big Data and Computing Visions |
| spelling | doaj-art-45d4bc21a63544e2843fbb41077594922025-01-30T12:21:49ZengREA PressBig Data and Computing Visions2783-49562821-014X2022-06-0122808910.22105/bdcv.2022.350381.1082153167Solving the Problem of Linear Programming with Cost Coefficients and Grey Resources Using the Primal Simplex AlgorithmFarid Pourofoghi0Department of Mathematics, Payame Noor University, Tehran, iran.In most real-world issues, we are dealing with situations where accurate data and complete information are not available. One way to deal with these uncertainties in real life is to use Grey System Theory (GST). In this paper, a linear programing problem in a grey environment with interval Grey Numbers (GN) is considered. Most of the proposed methods for solving grey linear programing problems are done by using GN whitening and turning the problem into a common linear programing problem. However, in this paper we seek to solve the grey linear programing problem directly without turning it into a regular linear programing problem in order to maintain uncertainty in the original problem data in the final answer. For this purpose, by proving the desired theorems, we propose a method based on the initial simplex algorithm to solve grey linear programing problems. This method is simpler than the previous methods. We emphasize that the proposed concept is useful for real and practical situations. To illustrate the efficiency of the method, we solve an example of Grey Linear Programming (GLP).https://www.bidacv.com/article_153167_5ccfdc1662cc2874f339a074f77a3cee.pdfuncertaintygrey interval numbersgrey linear programming |
| spellingShingle | Farid Pourofoghi Solving the Problem of Linear Programming with Cost Coefficients and Grey Resources Using the Primal Simplex Algorithm Big Data and Computing Visions uncertainty grey interval numbers grey linear programming |
| title | Solving the Problem of Linear Programming with Cost Coefficients and Grey Resources Using the Primal Simplex Algorithm |
| title_full | Solving the Problem of Linear Programming with Cost Coefficients and Grey Resources Using the Primal Simplex Algorithm |
| title_fullStr | Solving the Problem of Linear Programming with Cost Coefficients and Grey Resources Using the Primal Simplex Algorithm |
| title_full_unstemmed | Solving the Problem of Linear Programming with Cost Coefficients and Grey Resources Using the Primal Simplex Algorithm |
| title_short | Solving the Problem of Linear Programming with Cost Coefficients and Grey Resources Using the Primal Simplex Algorithm |
| title_sort | solving the problem of linear programming with cost coefficients and grey resources using the primal simplex algorithm |
| topic | uncertainty grey interval numbers grey linear programming |
| url | https://www.bidacv.com/article_153167_5ccfdc1662cc2874f339a074f77a3cee.pdf |
| work_keys_str_mv | AT faridpourofoghi solvingtheproblemoflinearprogrammingwithcostcoefficientsandgreyresourcesusingtheprimalsimplexalgorithm |