The solution of the transport problem by the method of the smallest element based on the use of complex numbers in the algorithm
To determine whether a transport problem has a solution , you can use the Lagrange multiplier method . To do this, it is advisable to replace variables so that the objective function is a sum of exponentials. The peculiarity of the sum of exponents is that the principal diagonal minors of the Hessia...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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EDP Sciences
2023-01-01
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| Series: | E3S Web of Conferences |
| Online Access: | https://www.e3s-conferences.org/articles/e3sconf/pdf/2023/39/e3sconf_transsiberia2023_03045.pdf |
| _version_ | 1797775786989584384 |
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| author | Yekimov Sergey Salkova Daniela Belyaev Vladislav Kucherenko Dmitriy Klyukanov Aleksey Shmoilov Andrey |
| author_facet | Yekimov Sergey Salkova Daniela Belyaev Vladislav Kucherenko Dmitriy Klyukanov Aleksey Shmoilov Andrey |
| author_sort | Yekimov Sergey |
| collection | DOAJ |
| description | To determine whether a transport problem has a solution , you can use the Lagrange multiplier method . To do this, it is advisable to replace variables so that the objective function is a sum of exponentials. The peculiarity of the sum of exponents is that the principal diagonal minors of the Hessian of the sum of exponents are positive quantities , and therefore the sum of exponents has an extremum and this extremum is the minimum. Solutions of large - dimensional transport tasks are of great practical importance for optimizing transportation schedules by transport enterprises . There are several algorithms for solving this problem, but the development of other methods for solving the transport problem that would use computing power more efficiently deserves attention. The method proposed in this paper for solving the transport problem based on the use of complex numbers in the algorithm makes it simpler and more visual for practical application. |
| first_indexed | 2024-03-12T22:40:41Z |
| format | Article |
| id | doaj.art-c6359401dd81494ab3d5a84ce23a653d |
| institution | Directory Open Access Journal |
| issn | 2267-1242 |
| language | English |
| last_indexed | 2024-03-12T22:40:41Z |
| publishDate | 2023-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | E3S Web of Conferences |
| spelling | doaj.art-c6359401dd81494ab3d5a84ce23a653d2023-07-21T09:41:05ZengEDP SciencesE3S Web of Conferences2267-12422023-01-014020304510.1051/e3sconf/202340203045e3sconf_transsiberia2023_03045The solution of the transport problem by the method of the smallest element based on the use of complex numbers in the algorithmYekimov Sergey0Salkova Daniela1Belyaev Vladislav2Kucherenko Dmitriy3Klyukanov Aleksey4Shmoilov Andrey5Department of Trade and Finance, Faculty of Economics and Management, Czech University of Life Sciences PragueDepartment of Trade and Finance, Faculty of Economics and Management, Czech University of Life Sciences PragueTula Branch of Plekhanov Russian University of EconomicsKuban State Agrarian University named after I.T. TrubilinSamara State University of Railway TransportSamara State University of Railway TransportTo determine whether a transport problem has a solution , you can use the Lagrange multiplier method . To do this, it is advisable to replace variables so that the objective function is a sum of exponentials. The peculiarity of the sum of exponents is that the principal diagonal minors of the Hessian of the sum of exponents are positive quantities , and therefore the sum of exponents has an extremum and this extremum is the minimum. Solutions of large - dimensional transport tasks are of great practical importance for optimizing transportation schedules by transport enterprises . There are several algorithms for solving this problem, but the development of other methods for solving the transport problem that would use computing power more efficiently deserves attention. The method proposed in this paper for solving the transport problem based on the use of complex numbers in the algorithm makes it simpler and more visual for practical application.https://www.e3s-conferences.org/articles/e3sconf/pdf/2023/39/e3sconf_transsiberia2023_03045.pdf |
| spellingShingle | Yekimov Sergey Salkova Daniela Belyaev Vladislav Kucherenko Dmitriy Klyukanov Aleksey Shmoilov Andrey The solution of the transport problem by the method of the smallest element based on the use of complex numbers in the algorithm E3S Web of Conferences |
| title | The solution of the transport problem by the method of the smallest element based on the use of complex numbers in the algorithm |
| title_full | The solution of the transport problem by the method of the smallest element based on the use of complex numbers in the algorithm |
| title_fullStr | The solution of the transport problem by the method of the smallest element based on the use of complex numbers in the algorithm |
| title_full_unstemmed | The solution of the transport problem by the method of the smallest element based on the use of complex numbers in the algorithm |
| title_short | The solution of the transport problem by the method of the smallest element based on the use of complex numbers in the algorithm |
| title_sort | solution of the transport problem by the method of the smallest element based on the use of complex numbers in the algorithm |
| url | https://www.e3s-conferences.org/articles/e3sconf/pdf/2023/39/e3sconf_transsiberia2023_03045.pdf |
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