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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">veststu</journal-id><journal-title-group><journal-title xml:lang="ru">Вестник Сибирского государственного университета путей сообщения</journal-title><trans-title-group xml:lang="en"><trans-title>Bulletin of Siberian State University of Transport</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1815-9265</issn><publisher><publisher-name>Сибирский государственный университет путей сообщения</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.52170/1815-9265_2026_79_13</article-id><article-id custom-type="elpub" pub-id-type="custom">veststu-266</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ТРАНСПОРТ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>TRANSPORT</subject></subj-group></article-categories><title-group><article-title>Оптимизация маршрутов топливозаправщиков методом Кларка - Райта при эксплуатации путевых машин</article-title><trans-title-group xml:lang="en"><trans-title>Route optimization for fuel delivery to railway transport using the Clarke - Wright method</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Оленберг</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Olenberg</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Артур Андреевич Оленберг - аспирант кафедры «Технология транспортного машиностроения и эксплуатация машин»</p><p>Новосибирск</p></bio><bio xml:lang="en"><p>Artur A. Olenberg - Postgraduate of the Transport Engineering Technology and Machine Operation Departmen</p><p>Novosibirsk</p></bio><email xlink:type="simple">snipe54@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кочергин</surname><given-names>В. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Kochergin</surname><given-names>V. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Виктор Иванович Кочергин - доктор технических наук, профессор, заведующий кафедрой «Технология транспортного машиностроения и эксплуатация машин»</p><p>Новосибирск</p></bio><bio xml:lang="en"><p>Viktor I. Kochergin - Doctor of Engineering, Professor, Head of the Transport Engineering Technology and Machine Operation Department</p><p>Novosibirsk</p></bio><email xlink:type="simple">vkplus2011@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Корягин</surname><given-names>М. Е.</given-names></name><name name-style="western" xml:lang="en"><surname>Koryagin</surname><given-names>M. E.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Марк Евгеньевич Корягин - доктор технических наук, профессор, заведующий кафедрой «Высшая математика»</p><p>Новосибирск</p></bio><bio xml:lang="en"><p>Mark E. Koryagin - Doctor of Engineering, Professor, Head of the Higher Mathematics Department</p><p>Novosibirsk</p></bio><email xlink:type="simple">math@stu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Сибирский государственный университет путей сообщения</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Siberian Transport University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>20</day><month>07</month><year>2026</year></pub-date><volume>0</volume><issue>2</issue><fpage>13</fpage><lpage>22</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Оленберг А.А., Кочергин В.И., Корягин М.Е., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Оленберг А.А., Кочергин В.И., Корягин М.Е.</copyright-holder><copyright-holder xml:lang="en">Olenberg A.A., Kochergin V.I., Koryagin M.E.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.vestnikstu.ru/jour/article/view/266">https://www.vestnikstu.ru/jour/article/view/266</self-uri><abstract><p>В статье рассматривается задача оптимизации маршрутов доставки топливно-смазочных материалов специальному подвижному составу железных дорог с использованием метода Кларка Райта. Актуальность исследования определяется необходимостью решения проблемы совмещения подвижных средств обслуживания (топливозаправщиков) с местами обслуживания (топливными базами) при минимизации логистических издержек.</p><p>На основе реальных данных участка Западно-Сибирской железной дороги построена матрица кратчайших расстояний между пятью станциями по автомобильным дорогам. Применен классический алгоритм Кларка Райта (Clark Wright Savings Algorithm), как один из наиболее эффективных методов для решения задачи маршрутизации транспорта с ограничениями вместимости. Алгоритм реализован на Python с пошаговой визуализацией процесса объединения маршрутов.</p><p>Метод Кларка Райта позволил сократить количество топливозаправщиков с пяти (при индивидуальной доставке каждому клиенту) до двух, при общей протяженности маршрутов 86,9 км. Экономия количества транспортных средств составила 60 %, что приводит к значительному сокращению операционных расходов на содержание автопарка, оплату труда водителей и топливо.</p><p>Научная новизна работы состоит в применении классического алгоритма Кларка Райта к специфической задаче оптимизации топливоснабжения специального подвижного состава железных дорог с подробной пошаговой реализацией и анализом результатов. Полученные результаты демонстрируют практическую эффективность метода и его применимость для железнодорожного транспорта. Предложенный подход может быть распространен на другие участки сети и модифицирован для учета динамических ограничений (временные окна, переменные объемы спроса).</p></abstract><trans-abstract xml:lang="en"><p>This paper addresses the optimization of fuel and lubricating materials (FSM) delivery routes to special rolling stock on railways using the Clarke-Wright algorithm. The relevance of the study is determined by the need to solve the problem of combining mobile service vehicles (fuel tankers) with service locations (fuel depots) while minimizing logistics costs.</p><p>Based on real data from the West Siberian Railway section, a shortest distance matrix between five stations along road networks was constructed. The classical Clarke-Wright Savings Algorithm was applied one of the most effective methods for solving vehicle routing problems with capacity constraints. The algorithm was implemented in Python with step-by-step visualization of the route merging process.</p><p>The Clarke-Wright method reduced the number of fuel tankers from five (individual delivery to each client) to two, with a total route length of 86,9 km. The savings in transport vehicles was 60 %, resulting in significant reductions in operating expenses for fleet maintenance, driver wages, and fuel consumption.</p><p>The scientific novelty of the work lies in applying the classical Clarke-Wright algorithm to the specific task of optimizing fuel supply to special rolling stock on railways with detailed step-by-step implementation and result analysis. The obtained results demonstrate the practical effectiveness of the method and its applicability to railway transport. The proposed approach can be extended to other network sections and modified to account for dynamic constraints (time windows, variable demand volumes).</p></trans-abstract><kwd-group xml:lang="ru"><kwd>оптимизация маршрутов</kwd><kwd>метод Кларка Райта</kwd><kwd>Vehicle Routing Problem</kwd><kwd>топливозаправщики</kwd><kwd>железнодорожный транспорт</kwd><kwd>логистика</kwd><kwd>экономия ресурсов</kwd></kwd-group><kwd-group xml:lang="en"><kwd>route optimization</kwd><kwd>Clarke Wright algorithm</kwd><kwd>Vehicle Routing Problem</kwd><kwd>fuel trackers</kwd><kwd>railway transport</kwd><kwd>logistics</kwd><kwd>resource savings</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Оленберг А. А., Кочергин В. И. Интегрированное оптимизационное моделирование логистики топливо-заправщиков в транспортных и транспортно-технологических системах // Фундаментальные и прикладные во-просы транспорта. 2025. № 2 (17). С. 59–65. DOI 10.52170/2712-9195_2025_2_59. EDN HBILZZ.</mixed-citation><mixed-citation xml:lang="en">Olenberg A. A., Kochergin, V. I. Integrated optimization modeling of fuel tanker logistics in transport and transport-technological systems. Fundamental and Applied Transport Issues. 2025;(17):59–65. (In Russ.). DOI 10.52170/2712-9195_2025_2_59 EDN HBILZZ.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Оленберг А. А., Кочергин В. И. Использование ГИС карт для создания имитационной модели // Фунда-ментальные и прикладные вопросы транспорта. 2024. № 3 (14). С. 56–61. DOI 10.52170/2712-9195_2024_3_56. EDN BYVGVU.</mixed-citation><mixed-citation xml:lang="en">Olenberg A. A., Kochergin V. I. Use of GIS maps to create a simulation model. Fundamental and Applied Transport Issues. 2024;(14):56–61. DOI 10.52170/2712-9195_2024_3_56 EDN BYVGVU. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Clarke G., Wright W. Scheduling of vehicles from a central depot to a number of delivery points // Operations Research. 1964. No. 12 (4). P. 568–581. DOI 10.1287/opre.12.4.568.</mixed-citation><mixed-citation xml:lang="en">Clarke G., Wright W. Scheduling of vehicles from a central depot to a number of delivery points. Operations Research. 1964;12(4):568–581. DOI 10.1287/opre.12.4.568.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Laporte G. The vehicle routing problem: An overview of exact and approximate algorithms // European Journal of Operational Research. 1992. No. 59 (3). P. 345–358. DOI 10.1016/0377-2217(92)90192-C.</mixed-citation><mixed-citation xml:lang="en">Laporte G. The vehicle routing problem: An overview of exact and approximate algorithms. European Journal of Operational Research. 1992;59(3):345–358. DOI 10.1016/0377-2217(92)90192-C.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Dantzig G. B., Ramser J. H. The truck dispatching problem // Management Science. 1959. No. 6 (1). P. 80–91. DOI 10.1287/mnsc.6.1.80.</mixed-citation><mixed-citation xml:lang="en">Dantzig G. B., Ramser J. H. The truck dispatching problem. Management Science. 1959; 6(1):80–91. DOI 10.1287/mnsc.6.1.80.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Toth P., Vigo D. The vehicle routing problem. SIAM, 2002. 367 p. DOI 10.1137/1.9780898718515.</mixed-citation><mixed-citation xml:lang="en">Toth P., Vigo D. The vehicle routing problem. SIAM; 2002. 367 p. DOI 10.1137/1.9780898718515.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Baldacci R., Mingozzi A., Roberti R. Recent exact algorithms for solving the vehicle routing problem under capacity and time window constraints // European Journal of Operational Research. 2012. No. 218 (1). P. 1–6. DOI 10.1016/j.ejor.2011.07.037.</mixed-citation><mixed-citation xml:lang="en">Baldacci R., Mingozzi A., Roberti R. Recent exact algorithms for solving the vehicle routing problem under capacity and time window constraints. European Journal of Operational Research. 2012;218(1):1–6. DOI 10.1016/j.ejor.2011.07.037.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Guerriero F., Saccomanno F. P. A Parallel implementation of the Clarke-Wright algorithm on GPUS // 14th International Conference on Operations Research and Enterprise Systems. 2025. No. 1. P. 100–111. DOI 10.5220/0013138100003893.</mixed-citation><mixed-citation xml:lang="en">Guerriero F., Saccomanno F. P. A Parallel implementation of the Clarke-Wright algorithm on GPUs. Conference: 14th International Conference on Operations Research and Enterprise Systems. 2025;(1):100–111. DOI 10.5220/0013138100003893.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Garside A. K., Erlinda L., Amallynda I. Solving heterogeneous fleet vehicle routing problem with Clarke Wright saving heuristic and genetic algorithm // Proceedings of the 4th International Conference on Green Civil and Environmental Engineering (GCEE) 2023. 2024. No. 2927. Р. 050002. DOI 10.1063/5.0192216.</mixed-citation><mixed-citation xml:lang="en">Garside A. K., Erlinda L., Amallynda I. Solving heterogeneous fleet vehicle routing problem with Clarke Wright saving heuristic and genetic algorithm. Proceedings of the 4th international Conference on green Civil and environmental Engineering (GCEE) 2023. 2024;(2927):050002. DOI 10.1063/5.0192216.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Fikejz J., Brázdová M., Jánošíková L. Modification of the Clarke and Wright algorithm with a dynamic savings matrix // Journal of Advanced Transportation. 2024. No. 2024 (1). P. 1–15. DOI 10.1155/2024/8753106.</mixed-citation><mixed-citation xml:lang="en">Fikejz J., Brázdová M., Jánošíková L. Modification of the Clarke and Wright algorithm with a dynamic savings matrix. Journal of Advanced Transportation. 2024;(1):1–15. DOI 10.1155/2024/8753106.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Selecting fast algorithms for the capacitated vehicle routing problem with machine learning techniques / R. Asín-Achá, A. Espinoza, O. Goldschmidt [et al.] // Networks. 2024. No. 84 (4). P. 465–480. DOI 10.1002/net.22244.</mixed-citation><mixed-citation xml:lang="en">Asín-Achá R., Espinoza A., Goldschmidt O., Hochbaum D.S., Huerta I.I. Selecting fast algorithms for the capacitated vehicle routing problem with machine learning techniques. Networks. 2024;84(4):465–480. DOI 10.1002/net.22244.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Segerstedt A. A simple heuristic for vehicle routing – A variant of Clarke and Wright's saving method // International Journal of Production Economics. 2014. No. 157. P. 74–79. DOI 10.1016/j.ijpe.2013.09.017.</mixed-citation><mixed-citation xml:lang="en">Segerstedt A. A simple heuristic for vehicle routing – A variant of Clarke and Wright's saving method. International Journal of Production Economics. 2014;(157):74–79. DOI 10.1016/j.ijpe.2013.09.017.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Heuristics for vehicle routing problem: A survey and recent advances / F. Liu, C. Lu, L. Gui [et al.] // Artificial Intelligence. 2023. DOI 10.48550/arXiv.2303.04147.</mixed-citation><mixed-citation xml:lang="en">Liu F., Lu C., Gui L. [et al.]. Heuristics for vehicle routing problem: A survey and recent advances. Artificial Intelligence. 2023. DOI 10.48550/arXiv.2303.04147.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">CAMP: Collaborative attention model with profiles for vehicle routing problems / C. Hua, F. Berto, J. Son [et al.] // Multiagent Systems. 2025. DOI 10.48550/arXiv.2501.02977.</mixed-citation><mixed-citation xml:lang="en">Hua C., Berto F., Son J. [et al.]. CAMP: Collaborative attention model with profiles for vehicle routing problems. Multiagent Systems. 2025. DOI 10.48550/arXiv.2501.02977.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Nurcahyo R., Irawan D. A., Kristanti F. The Effectiveness of the Clarke &amp; Wright savings algorithm in determining logistics distribution routes (case study PT.XYZ) // E3S Web of Conferences. 2023. No. 426 (01107). DOI 10.1051/e3sconf/202342601107.</mixed-citation><mixed-citation xml:lang="en">Nurcahyo R., Irawan D. A., Kristanti F. The effectiveness of the Clarke &amp; Wright savings algorithm in determining logistics distribution routes (case study PT.XYZ). E3S Web of Conferences. 2023;426(01107). DOI 10.1051/e3sconf/202342601107.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Nugroho J. A. Penentuan Rute Pengambilan Sampah Dengan Menggunakan Metode Clarke &amp; Wright Algorithm Saving Heuristic Di Perusahaan Daerah Kebersihan Untuk Wilayah Bandung Timur // Journal Pendidikan Sains Dan Teknologi. 2024. No. 3 (3). P. 569–573. DOI 10.47233/jpst.v3i3.1984.</mixed-citation><mixed-citation xml:lang="en">Nugroho J. A. Penentuan Rute Pengambilan Sampah Dengan Menggunakan Metode Clarke &amp; Wright Algorithm Saving Heuristic Di Perusahaan Daerah Kebersihan Untuk Wilayah Bandung Timur. Journal Pendidikan Sains Dan Teknologi. 2024;3(3):569–573. DOI 10.47233/jpst.v3i3.1984.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Vehicle routing problems with multiple commodities: A survey / W. Gu, C. Archetti, D. Cattaruzza [et al.] // European Journal of Operational Research. 2024. No. 317 (1). P. 1–15. DOI 10.1016/j.ejor.2023.11.032.</mixed-citation><mixed-citation xml:lang="en">Gu W., Archetti C., Cattaruzza D. [et al.]. Vehicle routing problems with multiple commodities: A survey. European Journal of Operational Research. 2024;317(1):1–15. DOI 10.1016/j.ejor.2023.11.032.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">A machine learning optimization approach for last-mile delivery and third-party logistics / M. E. Bruni, E. Fadda, S. Fedorov, G. Perboli // Computers &amp; Operations Research. 2023. No. 157 (20). DOI 10.1016/j.cor.2023.106262.</mixed-citation><mixed-citation xml:lang="en">Bruni M. E., Fadda E., Fedorov S., Perboli G. A machine learning optimization approach for last-mile delivery and third-party logistics. Computers &amp; Operations Research. 2023;157(20). DOI 10.1016/j.cor.2023.106262.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Analysis and optimization of transportation logistics for supply chain management of perishable goods using Monte Carlo Simulation / S. M. Pol, A. Rayte, B. T. Patil, K. N. Joshi // E3S Web of Conferences. 2024. No. 559 (04004). DOI 10.1051/e3sconf/202455904004.</mixed-citation><mixed-citation xml:lang="en">Pol S. M., Rayte A., Patil B. T., Joshi K. N. Analysis and optimization of transportation logistics for supply chain management of perishable goods using monte carlo simulation. E3S Web of Conferences. 2024;559(04004). DOI 10.1051/e3sconf/202455904004.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Vehicle routing problem approach for improving fuel delivery scheduling to austere test sites / S. Allen, J. Heller, G. Lamb [et al.] // A Regional Conference of the Society for Industrial and Systems Engineering. 2024. No. 12 (2). P. 109–114. DOI 10.37266/ISER.2025v12i2.pp109-114.</mixed-citation><mixed-citation xml:lang="en">Allen S., Heller J., Lamb G. [et al.]. Vehicle routing problem approach for improving fuel delivery scheduling to austere test sites. A Regional Conference of the Society for Industrial and Systems Engineering. 2024;12(2):109–114. DOI 10.37266/ISER.2025v12i2.pp109-114.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Kaczor G., Szkoda M. The application of a simulation method in the evaluation of the reliability of transport systems // Czasopismo Techniczne. 2018. No. 6 (115). P. 167–178. DOI 10.4467/2353737XCT.18.096.8701.</mixed-citation><mixed-citation xml:lang="en">Kaczor G., Szkoda M. The application of a simulation method in the evaluation of the reliability of transport systems. Czasopismo Techniczne. 2018;6(115):167–178. DOI 10.4467/2353737XCT.18.096.8701.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Qu P. Design of supply chain logistics intelligent management information system based on GIS optimization model // Procedia Computer Science. 2024. No. 243. P. 396–405. DOI 10.1016/j.procs.2024.09.049.</mixed-citation><mixed-citation xml:lang="en">Qu P. Design of supply chain logistics intelligent management information system based on GIS optimization model. Procedia Computer Science. 2024;243:396–405. DOI 10.1016/j.procs.2024.09.049.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Яндекс Карты : [поисково-информационная картографическая служба]. URL: https://yandex.ru/maps (дата обращения: 01.02.2026).</mixed-citation><mixed-citation xml:lang="en">Search and information cartographic service Yandex Maps. URL: https://yandex.ru/maps..</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">MATLAB : платформа для программирования и численных вычислений. URL: https://www.math-works.com/products/matlab.html (дата обращения: 01.02.2026).</mixed-citation><mixed-citation xml:lang="en">MATLAB programming and numerical computing platform. URL: https://www.mathworks.com/products/matlab.html.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Wang R. Research on cold chain logistics distribution path optimization based on improved ant colony algorithm // 2023 IEEE 3rd International Conference on Power, Electronics and Computer Applications (ICPECA). 2023. DOI 10.1109/ICPECA56706.2023.10075989.</mixed-citation><mixed-citation xml:lang="en">Wang R. Research on cold chain logistics distribution path optimization based on improved ant colony algorithm. 2023 IEEE 3rd International Conference on Power, Electronics and Computer Applications (ICPECA). 2023. DOI 10.1109/ICPECA56706.2023.10075989.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Li Y., Zhang Z. Research on the site selection of fresh agricultural products distribution center based on logistics cost and its MATLAB implementation // AICI 25: Proceedings of the 2025 International Conference on Artificial Intelligence and Computational Intelligence. 2025. P. 293–297. DOI doi.org/10.1145/3730436.3730485.</mixed-citation><mixed-citation xml:lang="en">Li Y., Zhang Z. Research on the site selection of fresh agricultural products distribution center based on logistics cost and its MATLAB implementation. AICI '25: Proceedings of the 2025 International Conference on Artificial Intelligence and Computational Intelligence. 2025:293–297. DOI doi.org/10.1145/3730436.3730485.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang W., Xu M., Wang S. Joint location and pricing optimization of self-service in urban logistics considering customers’ choice behavior // Transportation Research. Part E. Logistics and Transportation Review. 2023. No. 174. DOI 10.1016/j.tre.2023.103128.</mixed-citation><mixed-citation xml:lang="en">Zhang W., Xu M., Wang S. Joint location and pricing optimization of self-service in urban logistics considering customers’ choice behavior. Transportation Research Part E: Logistics and Transportation Review. 2023;174. DOI 10.1016/j.tre.2023.103128.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
