<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<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">managementscience</journal-id><journal-title-group><journal-title xml:lang="ru">Управленческие науки / Management Sciences</journal-title><trans-title-group xml:lang="en"><trans-title>Management Sciences</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2304-022X</issn><issn pub-type="epub">2618-9941</issn><publisher><publisher-name>Financial University under The Government of Russian Federation</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.26794/2304-022X-2023-13-4-22-33</article-id><article-id custom-type="elpub" pub-id-type="custom">managementscience-500</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>МАТЕМАТИЧЕСКИЕ МЕТОДЫ И МОДЕЛИ В УПРАВЛЕНИИ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>MATHEMATICAL METHODS AND MODELS IN MANAGEMENT</subject></subj-group></article-categories><title-group><article-title>Математическая модель поиска оптимального решения задачи по формированию цепочек поставок сырья лесопромышленных предприятий в условиях неопределенности</article-title><trans-title-group xml:lang="en"><trans-title>Mathematical Model for Searching for an Optimal Solution to the Problem of Forming Supply Chains for Raw Materials of Forestry Enterprises under Conditions of Uncertainty</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-3235-6429</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Рогулин</surname><given-names>Р. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Rogulin</surname><given-names>R. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Родион Сергеевич Рогулин – кандидат экономических наук, доцент кафедры «Математики и моделирования»</p><p>Владивосток</p></bio><bio xml:lang="en"><p>Rodion S. Rogulin – Cand. Sci. (Econ.), Associated Professor at the Department of Mathematics and Modeling</p><p>Vladivostok</p></bio><email xlink:type="simple">rafassiaofusa@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Владивостокский государственный университет экономики и сервиса</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Vladivostok State University of Economics and Service</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2023</year></pub-date><pub-date pub-type="epub"><day>03</day><month>02</month><year>2024</year></pub-date><volume>13</volume><issue>4</issue><fpage>22</fpage><lpage>33</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Рогулин Р.С., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Рогулин Р.С.</copyright-holder><copyright-holder xml:lang="en">Rogulin R.S.</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://managementscience.fa.ru/jour/article/view/500">https://managementscience.fa.ru/jour/article/view/500</self-uri><abstract><p>В данной работе рассматриваются важные аспекты, связанные с проблемами формирования цепочек поставок и объемов производства на лесоперерабатывающих предприятиях. Основной акцент делается на вопросах оценки оптимальности принятых решений. Исследование фокусируется на предприятиях, не имеющих собственных источников сырья и стремящихся найти наиболее приемлемое решение, исходя из горизонта планирования на основе данных о сделках, реализованных на товарно-сырьевой бирже. Цель исследования заключается в создании математической модели, которая позволяет установить оптимальный объем производства товаров на базе формируемых цепочек поставок сырья с товарно-сырьевой биржи с учетом доли его полезного объема, времени нахождения лотов в пути и неопределенности, связанной с предложением и логистикой. В работе были использованы математическое моделирование, теория и методы оптимизации. Тестирование модели с помощью данных Санкт-Петербургской биржи и предприятий Приморского края позволило определить оптимальные траектории прибыли, объема производства и другие важные показатели. В работе также поднимаются вопросы планирования цепочек поставок и объемов производства, анализируются регионы – источники сырья и приводятся преимущества и недостатки представленной математической модели. Полученные результаты представляют интерес для топ-менеджмента лесопромышленных предприятий, стремящихся повысить эффективность своей деятельности, и могут явиться основой для оценки рациональности сырьевых сделок на товарно-сырьевой бирже России.</p></abstract><trans-abstract xml:lang="en"><p>This paper examines important aspects related to the problems of forming supply chains and production volumes at forest processing enterprises. The main emphasis is on assessing the optimality of decisions made. The study focuses on enterprises that do not have their own sources of raw materials and that are seeking to find the most appropriate solution based on the planning horizon based on data on transactions carried out on the commodity exchange. The purpose of the study is to create a mathematical model that allows us to establish the optimal volume of production of goods based on the formed supply chains of raw materials from the commodity exchange, considering the share of its useful volume, the time the lots are in transit and the uncertainty associated with supply and logistics. The following research methods were proposed: mathematical modeling, theory and optimization methods. Testing the model using data from the St. Petersburg Stock Exchange and enterprises of the Primorsky Territory made it possible to determine the optimal trajectories of profit, production volume and other important indicators. The work also raises issues of planning supply chains and production volumes, analyzes regions – sources of raw materials and presents the advantages and disadvantages of the presented mathematical model. The results obtained are of interest to the top management of forestry enterprises seeking to improve the efficiency of their activities and can be the basis for assessing the rationality of commodity transactions on the Russian Commodity and Raw Materials Exchange.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>формирование цепочек поставок</kwd><kwd>объемы производства</kwd><kwd>лесоперерабатывающие предприятия</kwd><kwd>оптимальность решений</kwd><kwd>математическая модель</kwd><kwd>товарно-сырьевая биржа</kwd><kwd>доля полезного объема сырья</kwd><kwd>время лотов в пути</kwd><kwd>рациональные сырьевые сделки</kwd><kwd>повышение эффективности</kwd></kwd-group><kwd-group xml:lang="en"><kwd>formation of supply chains</kwd><kwd>production volumes</kwd><kwd>timber processing enterprises</kwd><kwd>optimality of decisions</kwd><kwd>mathematical model</kwd><kwd>commodity and raw material exchange</kwd><kwd>share of useful volume of raw materials</kwd><kwd>time of lots in transit</kwd><kwd>rational raw material transactions</kwd><kwd>efficiency improvement</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">Tsay A. A., Agrawal N. Channel dynamics under price and service competition. Manufacturing &amp; Service Operations Management. 2000;2(4):372–391. DOI: 10.1287/msom.2.4.372.12342</mixed-citation><mixed-citation xml:lang="en">Tsay A. A., Agrawal N. Channel dynamics under price and service competition. Manufacturing &amp; Service Operations Management. 2000;2(4):372–391. DOI: 10.1287/msom.2.4.372.12342</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Tsay A. A., Agrawal N. Channel conflict and coordination in the e-commerce age. Production and Operations Management. 2004;13(1):93–110. DOI: 10.1111/j.1937–5956.2004.tb00147.x</mixed-citation><mixed-citation xml:lang="en">Tsay A. A., Agrawal N. Channel conflict and coordination in the e-commerce age. Production and Operations Management. 2004;13(1):93–110. DOI: 10.1111/j.1937–5956.2004.tb00147.x</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Bernstein F., Federgruen A. A general equilibrium model for industries with price and service competition. Operations Research. 2004;52(6):868–886. DOI: 10.1287/opre.1040.0149</mixed-citation><mixed-citation xml:lang="en">Bernstein F., Federgruen A. A general equilibrium model for industries with price and service competition. Operations Research. 2004;52(6):868–886. DOI: 10.1287/opre.1040.0149</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Yao D.-Q., Yue X., Liu J. Vertical cost information sharing in a supply chain with value-adding retailers. Omega. 2008;36(5):838–851. DOI: 10.1016/j.omega.2006.04.003</mixed-citation><mixed-citation xml:lang="en">Yao D.-Q., Yue X., Liu J. Vertical cost information sharing in a supply chain with value-adding retailers. Omega. 2008;36(5):838–851. DOI: 10.1016/j.omega.2006.04.003</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Xiao T., Yang D. Price and service competition of supply chains with risk-averse retailers under demand uncertainty. International Journal of Production Economics. 2008;114(1):187–200. DOI: 10.1016/j.ijpe.2008.01.006</mixed-citation><mixed-citation xml:lang="en">Xiao T., Yang D. Price and service competition of supply chains with risk-averse retailers under demand uncertainty. International Journal of Production Economics. 2008;114(1):187–200. DOI: 10.1016/j.ijpe.2008.01.006</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Wu D. Joint pricing-servicing decision and channel strategies in the supply chain. Central European Journal of Operations Research. 2011;19(1):99–137. DOI: 10.1007/s10100–009–0133-z</mixed-citation><mixed-citation xml:lang="en">Wu D. Joint pricing-servicing decision and channel strategies in the supply chain. Central European Journal of Operations Research. 2011;19(1):99–137. DOI: 10.1007/s10100–009–0133-z</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Wu C.-H. Price and service competition between new and remanufactured products in a two-echelon supply chain. International Journal of Production Economics. 2012;140(1):496–507. DOI: 10.1016/j.ijpe.2012.06.034</mixed-citation><mixed-citation xml:lang="en">Wu C.-H. Price and service competition between new and remanufactured products in a two-echelon supply chain. International Journal of Production Economics. 2012;140(1):496–507. DOI: 10.1016/j.ijpe.2012.06.034</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Rezapour S., Farahani R. Z. Supply chain network design under oligopolistic price and service level competition with foresight. Computers &amp; Industrial Engineering. 2014;72:129–142. DOI: 10.1016/j.cie.2014.03.005</mixed-citation><mixed-citation xml:lang="en">Rezapour S., Farahani R. Z. Supply chain network design under oligopolistic price and service level competition with foresight. Computers &amp; Industrial Engineering. 2014;72:129–142. DOI: 10.1016/j.cie.2014.03.005</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Ali S. M., Rahman M. H., Tumpa T. J., Rifat A. A.M., Paul S. K. Examining price and service competition among retailers in a supply chain under potential demand disruption. Journal of Retailing and Consumer Services. 2018;40:40–47. DOI: 10.1016/j.jretconser.2017.08.025</mixed-citation><mixed-citation xml:lang="en">Ali S. M., Rahman M. H., Tumpa T. J., Rifat A. A.M., Paul S. K. Examining price and service competition among retailers in a supply chain under potential demand disruption. Journal of Retailing and Consumer Services. 2018;40:40–47. DOI: 10.1016/j.jretconser.2017.08.025</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Pi Z., Fang W., Zhang B. Service and pricing strategies with competition and cooperation in a dualchannel supply chain with demand disruption. Computers &amp; Industrial Engineering. 2019;138:106130. DOI: 10.1016/j.cie.2019.106130</mixed-citation><mixed-citation xml:lang="en">Pi Z., Fang W., Zhang B. Service and pricing strategies with competition and cooperation in a dualchannel supply chain with demand disruption. Computers &amp; Industrial Engineering. 2019;138:106130. DOI: 10.1016/j.cie.2019.106130</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Bernstein F., Federgruen A. Pricing and replenishment strategies in a distribution system with competing retailers. Operations Research. 2003;51(3):409–426. DOI: 10.1287/opre.51.3.409.14957</mixed-citation><mixed-citation xml:lang="en">Bernstein F., Federgruen A. Pricing and replenishment strategies in a distribution system with competing retailers. Operations Research. 2003;51(3):409–426. DOI: 10.1287/opre.51.3.409.14957</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Bernstein F., Federgruen A. Decentralized supply chains with competing retailers under demand uncertainty. Management Science. 2005;51(1):18–29. DOI: 10.1287/mnsc.1040.0218</mixed-citation><mixed-citation xml:lang="en">Bernstein F., Federgruen A. Decentralized supply chains with competing retailers under demand uncertainty. Management Science. 2005;51(1):18–29. DOI: 10.1287/mnsc.1040.0218</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Chen K., Xiao T. Pricing and replenishment policies in a supply chain with competing retailers under different retail behaviors. Computers &amp; Industrial Engineering. 2017;103:145–157. DOI: 10.1016/j.cie.2016.11.018</mixed-citation><mixed-citation xml:lang="en">Chen K., Xiao T. Pricing and replenishment policies in a supply chain with competing retailers under different retail behaviors. Computers &amp; Industrial Engineering. 2017;103:145–157. DOI: 10.1016/j.cie.2016.11.018</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Cachon G. P. Stock wars: Inventory competition in a two-echelon supply chain with multiple retailers. Operations Research. 2001;49(5):658–674. DOI: 10.1287/opre.49.5.658.10611</mixed-citation><mixed-citation xml:lang="en">Cachon G. P. Stock wars: Inventory competition in a two-echelon supply chain with multiple retailers. Operations Research. 2001;49(5):658–674. DOI: 10.1287/opre.49.5.658.10611</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Anderson E. J., Bao Y. Price competition with integrated and decentralized supply chains. European Journal of Operational Research. 2010;200(1):227–234. DOI: 10.1016/j.ejor.2008.11.049</mixed-citation><mixed-citation xml:lang="en">Anderson E. J., Bao Y. Price competition with integrated and decentralized supply chains. European Journal of Operational Research. 2010;200(1):227–234. DOI: 10.1016/j.ejor.2008.11.049</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">David A., Adida E. Competition and coordination in a two-channel supply chain. Production and Operations Management. 2015;24(8):1358–1370. DOI: 10.1111/poms.12327</mixed-citation><mixed-citation xml:lang="en">David A., Adida E. Competition and coordination in a two-channel supply chain. Production and Operations Management. 2015;24(8):1358–1370. DOI: 10.1111/poms.12327</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Adida E., DeMiguel V. Supply chain competition with multiple manufacturers and retailers. Operations Research. 2011;59(1):156–172. DOI: 10.1287/opre.1100.0863</mixed-citation><mixed-citation xml:lang="en">Adida E., DeMiguel V. Supply chain competition with multiple manufacturers and retailers. Operations Research. 2011;59(1):156–172. DOI: 10.1287/opre.1100.0863</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Konur D., Geunes J. Supplier wholesale pricing for a retail chain: implications of centralized vs. decentralized retailing and procurement under quantity competition. Omega. 2016;65:98–110. DOI: 10.1016/j.omega.2016.01.002</mixed-citation><mixed-citation xml:lang="en">Konur D., Geunes J. Supplier wholesale pricing for a retail chain: implications of centralized vs. decentralized retailing and procurement under quantity competition. Omega. 2016;65:98–110. DOI: 10.1016/j.omega.2016.01.002</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Shenoy P. P. Competitive inventory models. RAIRO — Operations Research. 1987;21(1):1–19. URL: http://www.numdam.org/article/RO_1987__21_1_1_0.pdf</mixed-citation><mixed-citation xml:lang="en">Shenoy P. P. Competitive inventory models. RAIRO — Operations Research. 1987;21(1):1–19. URL: http://www.numdam.org/article/RO_1987__21_1_1_0.pdf</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Yang S.-L., Zhou Y.-W. Two-echelon supply chain models: Considering duopolistic retailers’ different competitive behaviors. International Journal of Production Economics. 2006;103(1):104–116. DOI: 10.1016/j.ijpe.2005.06.001</mixed-citation><mixed-citation xml:lang="en">Yang S.-L., Zhou Y.-W. Two-echelon supply chain models: Considering duopolistic retailers’ different competitive behaviors. International Journal of Production Economics. 2006;103(1):104–116. DOI: 10.1016/j.ijpe.2005.06.001</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang P., He Y., Shi C. V. Transshipment and coordination in a two-echelon supply chain. RAIRO — Operations Research. 2017;51(3):729–747. DOI: 10.1051/ro/2016052</mixed-citation><mixed-citation xml:lang="en">Zhang P., He Y., Shi C. V. Transshipment and coordination in a two-echelon supply chain. RAIRO — Operations Research. 2017;51(3):729–747. DOI: 10.1051/ro/2016052</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Yan X., Zhao H. Inventory sharing and coordination among n independent retailers. European Journal of Operational Research. 2015;243(2):576–587. DOI: 10.1016/j.ejor.2014.12.033</mixed-citation><mixed-citation xml:lang="en">Yan X., Zhao H. Inventory sharing and coordination among n independent retailers. European Journal of Operational Research. 2015;243(2):576–587. DOI: 10.1016/j.ejor.2014.12.033</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Рогулин Р. С., Мазелис Л. С. Алгоритм и математическая модель формирования устойчивых цепочек поставок древесного сырья из регионов России: сравнение и анализ. Вестник Пермского университета. Серия: Экономика. 2020;15(3):385–404. DOI: 10.17072/1994–9960–2020–3–385–404</mixed-citation><mixed-citation xml:lang="en">Rogulin R. S., Mazelis L. S. Algorithm and mathematical model of supply chain management for raw wood from the regions in Russia: Comparison and analysis. Vestnik Permskogo universiteta. Seriya: Ekonomika = Perm University Herald. Economy. 2020;15(3):385–404. (In Russ.). DOI: 10.17072/1994–9960–2020–3–385–404</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Рогулин Р. С. Моделирование перспектив взаимодействия предприятия лесопромышленного комплекса и товарно-сырьевой биржи России. Journal of Applied Economic Research. 2020;19(4):489–511. DOI: 10.15826/vestnik.2020.19.4.023</mixed-citation><mixed-citation xml:lang="en">Rogulin R. S. Modeling of promising interaction between a timber industry enterprise and a commodity exchange in Russia. Journal of Applied Economic Research. 2020;19(4):489–511. (In Russ.). DOI: 10.15826/vestnik.2020.19.4.023</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Рогулин Р. С. Модель оптимизации плана закупок сырья из регионов России лесоперерабатывающим комплексом. Бизнес-информатика. 2020;14(4):19–35. DOI: 10.17323/2587–814X.2020.4.19.35</mixed-citation><mixed-citation xml:lang="en">Rogulin R. S. A model for optimizing plans for procurement of raw materials from regions of Russia in a timber-processing enterprise. Business Informatics. 2020;14(4):19–35. DOI: 10.17323/2587–814X.2020.4.19.35 (In Russ.: Biznes-informatika. 2020;14(4):19–35. DOI: 10.17323/2587–814X.2020.4.19.35).</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Рогулин Р. С. Место ИКТ и предпринимательства в формировании устойчивых цепочек поставок. Экономическая политика. 2021;16(4):84–103. DOI: 10.18288/1994–5124–2021–4–84–103</mixed-citation><mixed-citation xml:lang="en">Rogulin R. S. The place of ICT and entrepreneurship in forming sustainable supply chains. Ekonomicheskaya politika = Economic Policy. 2021;16(4):84–103. (In Russ.). DOI: 10.18288/1994–5124–2021–4–84–103</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Рогулин Р. С. Математическая модель формирования ценовой политики и плана производственно-транспортной системы лесопромышленного предприятия. Бизнес-информатика. 2021;15(3):60–77. DOI: 10.17323/2587–814X.2021.3.60.77</mixed-citation><mixed-citation xml:lang="en">Rogulin R. S. A mathematical model for the formation of the pricing policy and the plan of the production and transport system in a timber-processing enterprise. Business Informatics. 2021;15(3):60–77. (In Russ.: Biznes-informatika. 2021;15(3):60–77. DOI: 10.17323/2587–814X.2021.3.60.77).</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Рогулин Р. С. Роль информационно-коммуникационных технологий в формировании устойчивых цепочек поставок до и после пандемии COVID-19. Journal of Applied Economic Research. 2021;20(3):461–488. DOI: 10.15826/vestnik.2021.20.3.019</mixed-citation><mixed-citation xml:lang="en">Rogulin R. S. The role of ICT and entrepreneurship in forming sustainable supply chains: Before and after the COVID-19 pandemic. Journal of Applied Economic Research. 2021;20(3):461–488. (In Russ.). DOI: 10.15826/vestnik.2021.20.3.019</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Mazelis L., Rogulin R. Devising a method for the formation of sustainable chains of supply of raw materials from mercantile exchange to a timber processing enterprise considering uncertainties and risks. Eastern-European Journal of Enterprise Technologies. 2021;5(3–113):6–18. DOI: 10.15587/1729–4061.2021.242960</mixed-citation><mixed-citation xml:lang="en">Mazelis L., Rogulin R. Devising a method for the formation of sustainable chains of supply of raw materials from mercantile exchange to a timber processing enterprise considering uncertainties and risks. Eastern-European Journal of Enterprise Technologies. 2021;5(3–113):6–18. DOI: 10.15587/1729–4061.2021.242960</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Тарасов В. Б. От многоагентных систем к интеллектуальным организациям: философия, психология, информатика. М.: Эдиториал УРСС; 2002. 352 с.</mixed-citation><mixed-citation xml:lang="en">Tarasov V. B. From multi-agent systems to intelligent organizations: Philosophy, psychology, computer science. Moscow: Editorial URSS; 2002. 352 p. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Канторович Л. В. Математические методы организации и планирования производства. Л.: ЛГУ; 1939. 96 с.</mixed-citation><mixed-citation xml:lang="en">Kantorovich L. V. Mathematical methods of organizing and planning production. Leningrad: Leningrad State University; 1939. 96 p. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Shao J., Krishnan H., McCormick S. T. Incentives for transshipment in a supply chain with decentralized retailers. Manufacturing &amp; Service Operations Management. 2011;13(3):361–372. DOI: 10.1287/msom.1110.0326</mixed-citation><mixed-citation xml:lang="en">Shao J., Krishnan H., McCormick S. T. Incentives for transshipment in a supply chain with decentralized retailers. Manufacturing &amp; Service Operations Management. 2011;13(3):361–372. DOI: 10.1287/msom.1110.0326</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Huang H., Ke H., Wang L. Equilibrium analysis of pricing competition and cooperation in supply chain with one common manufacturer and duopoly retailers. International Journal of Production Economics. 2016;178:12–21. DOI: 10.1016/j.ijpe.2016.04.022</mixed-citation><mixed-citation xml:lang="en">Huang H., Ke H., Wang L. Equilibrium analysis of pricing competition and cooperation in supply chain with one common manufacturer and duopoly retailers. International Journal of Production Economics. 2016;178:12–21. DOI: 10.1016/j.ijpe.2016.04.022</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Glock C. H., Kim T. The effect of forward integration on a single-vendor-multi-retailer supply chain under retailer competition. International Journal of Production Economics. 2015;164:179–192. DOI: 10.1016/j.ijpe.2015.03.009</mixed-citation><mixed-citation xml:lang="en">Glock C. H., Kim T. The effect of forward integration on a single-vendor-multi-retailer supply chain under retailer competition. International Journal of Production Economics. 2015;164:179–192. DOI: 10.1016/j.ijpe.2015.03.009</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Chen K., Xiao T. Pricing and replenishment policies in a supply chain with competing retailers under different retail behaviors. Computers &amp; Industrial Engineering. 2017;103:145–157. DOI: 10.1016/j.cie.2016.11.018</mixed-citation><mixed-citation xml:lang="en">Chen K., Xiao T. Pricing and replenishment policies in a supply chain with competing retailers under different retail behaviors. Computers &amp; Industrial Engineering. 2017;103:145–157. DOI: 10.1016/j.cie.2016.11.018</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Karimi M., Khademi-Zare H., Zare-Mehrjerdi Y., Fakhrzad M. B. Optimizing service level, price, and inventory decisions for a supply chain with retailers’ competition and cooperation under VMI strategy. RAIRO — Operations Research. 2022;56(2):1051–1078. DOI: 10.1051/ro/2022039</mixed-citation><mixed-citation xml:lang="en">Karimi M., Khademi-Zare H., Zare-Mehrjerdi Y., Fakhrzad M. B. Optimizing service level, price, and inventory decisions for a supply chain with retailers’ competition and cooperation under VMI strategy. RAIRO — Operations Research. 2022;56(2):1051–1078. DOI: 10.1051/ro/2022039</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>
