MATHEMATICAL METHODS IN LOGISTICS: ANALYSIS, CLASSIFICATION, APPLIED MODELS
Abstract
The relevance of structuring economic and mathematical models in logistics lies in the need for systematic information about mathematical methods and models with examples of their application in logistics to facilitate the selection of optimal approaches to managing logistics business processes in practice. Modern logistics faces many challenges, including the efficient allocation of financial resources, cost reduction, and increased staff productivity, which requires mathematical tools to make informed decisions. Due to rapidly changing market conditions and increasing demands of logistics business customers, as well as economic instability, entrepreneurs and companies are forced to adapt their logistics strategies using integrated approaches to big data analysis. The purpose of the study is a theoretical analysis of economic and mathematical models used in logistics, their typology and classification, examples of application, and an assessment of the possibilities of using them to improve and optimise logistics business processes. The methodology of the study is based on the use of economic and mathematical modelling methods to formalise business processes in logistics, methods of analysis and synthesis to study the use of mathematical models in logistics and their application, and methods of generalisation and systematisation to structure these models and build their classification table. The scientific novelty and results consist in the original classification of economic and mathematical methods and models in logistics, which allows to quickly identify appropriate tools for solving specific practical problems that arise in the logistics business and provides a better understanding of the relationship between different methods, models and their application in practice. The considered models cover a wide range of directions and tasks in logistics, from the optimisation of operations of transport hubs to designing the supply chains. The usage of mathematical models allows to make reasoned decisions focused on increasing the efficiency of the logistics operations, reducing the costs and improving the level of customer service.
References
1. Babich M. I., Biloshytskyi V. V. (2019) Rozrobka ta doslidzhennia modeli prohnozuvannia popytu dlia efektyvnoi roboty rozpodilnoi lohistyky na pidpryiemstvi [Development and research of a demand forecasting model for effective distribution logistics in an enterprise]. Informatsiini tekhnolohii i avtomatyzatsiia – 2019: XII Mizhnarodnoi naukovo-praktychnoi konferentsii, (Odesa, October 17th–18th, 2019). Odesa: ONATHT, pp. 40–42. Available at: https://card-file.ontu.edu.ua/server/api/core/bitstreams/bacd6327-5079-46f8-a3a1-e8e8a71b1137/ (in Ukrainian)
2. Dziuba S., Koriashkina L., Stanina O., Lubenets D. (2023) Matematychni modeli optymizatsiinykh zadach chastkovo-dvoetapnoi evakuatsii naselennia iz zonuvanniam rehionu [Mathematical models of optimization problems for partially two-stage population evacuation with region zoning]. Information Technology: Computer Science, Software Engineering and Cyber Security, no. 3, pp. 13–21. DOI: https://doi.org/10.32782/IT/2023-3-2
3. Bakayev O. O. (2009) Ekonomichna kibernetyka [Economic Cybernetics]. Entsyklopediia Suchasnoi Ukrainy [Electronic resource], Natsionalna akademiia nauk Ukrainy, NTSh. Kyiv: Instytut entsyklopedychnykh doslidzhen NAN Ukrainy. Available at: https://esu.com.ua/article-18775
4. Kovalchuk M., Bondarenko S. (2024) Modeliuvannia funktsionuvannia lohistychnykh protsesiv za dopomohoiu matematychnykh ta kompiuternykh pidkhodiv [Modeling the functioning of logistics processes using mathematical and computer approaches]. Visnyk Khmelnytskoho natsionalnoho universytetu, no. 4 (339), pp. 165–168. DOI: https://doi.org/10.31891/2307-5732-2024-339-4-27
5. Kozar K. P. Typolohiia ekonomiko-matematychnykh modelei u lohistytsi [Typology of economic-mathematical models in logistics]. Available at: http://repository.hneu.edu.ua
6. Kozachenko D. M., Hermaniuk Yu. M. (2013) Matematychna model dlia doslidzhennia perevezennia vantazhiv u mizhnarodnomu spoluchenni [Mathematical model for studying cargo transportation in international communication]. Transportni systemy ta tekhnolohii perevezen, no. 5, pp. 28–32. DOI: https://doi.org/10.15802/tstt2013/19273
7. Kozachok L. M., Kozachok A. Ye. (2021) Pobudova matematychnoi modeli protsesiv roboty transportnykh system z vykorystanniam metodiv nechitkoi lohiky [Construction of a mathematical model of the transport systems’ operation processes using fuzzy logic methods]. Socio-economic research bulletin, no. 3-4 (78-79), pp. 98–106. DOI: https://doi.org/10.33987/vsed.3-4(78-79).2021.98-106
8. Koriashkina L. S., Lubenets D. Ye. (2024) Systemnyi analiz ta matematychne modeliuvannia chastkovo-dvoetapnykh protsesiv rozpodilu materialnykh potokiv [System analysis and mathematical modeling of partially two-stage material flow distribution processes]. System technologies, no. 1 (150), pp. 86–99. DOI: https://doi.org/10.34185/1562-9945-1-150-2024-08
9. Lavrov Ye. A., Perkhun L. P., Shendryk V. V. (2017) Matematychni metody doslidzhennia operatsii [Mathematical methods of operations research]. Sumy: Sumskyi derzhavnyi universytet, 212 p. (in Ukrainian)
10. Mykolenko R. O., Zhebka V. V., Koretska V. O. (2022) Optymizatsiia matematychnoi modeli lohistychnykh potokiv torhovelnoi merezhi [Optimization of the mathematical model of logistics flows in a trade network]. Telekomunikatsiini ta informatsiini tekhnolohii, no. 2 (75), pp. 23–31. DOI: https://doi.org/10.31673/2412-4338.2022.022330
11. Nuzhna S., Karimov G., Karimov I. (2023) Ekonomiko-matematychne modeliuvannia v lohistychnii diialnosti ahrarnykh pidpryiemstv [Economic-mathematical modeling in the logistics activities of agricultural enterprises]. Ekonomichnyi analiz, vol. 33, no. 1, pp. 258–269. DOI: https://doi.org/10.35774/econa2023.01.258
12. Prodashchuk S. M., Rakhmatuloieva T. M., Kukharchyk Yu. I. (2013) Matematychna model vzaiemodii avtomobilnoho i zaliznychnoho transportu pry pererobtsi konteineriv [Mathematical model of interaction between road and rail transport in container processing]. Zbirnyk naukovykh prats UkrDAZT, vol. 137, pp. 61–67. DOI: https://doi.org/10.18664/1994-7852.137.2013.102721
13. Romanych I. (2024) Ekonomiko-matematychna model zadachi upravlinnia rozpodilom poshtovykh vidpravlen [Economic-mathematical model of the postal distribution management problem]. Zbirnyk naukovykh prats Derzhavnoho podatkovoho universytetu, vol. 1, pp. 59–64. DOI: https://doi.org/10.32782/2617-5940.1.2024.9
14. Serhiiev O., Us S. (2023) Analiz suchasnykh pidkhodiv do rozviazannia dyskretnykh ta neperervnykh bahatoetapnykh zadach rozmishchennia [Analysis of modern approaches to solving discrete and continuous multistage location problems]. Information Technology: Computer Science, Software Engineering and Cyber Security, no. 2, pp. 59–70. DOI: https://doi.org/10.32782/IT/2023-2-7
15. Skakalina E. (2021) Intelektualne upravlinnia lohistychnymy protsesamy z vykorystanniam henetychnykh alhorytmiv [Intelligent management of logistics processes using genetic algorithms]. Systemy upravlinnia, navihahtsii ta zviazku: Zbirnyk naukovykh prats, vol. 1 (63), pp. 111–114. DOI: https://doi.org/10.26906/SUNZ.2021.1.111
16. Azizi V., Hu G. (2021) Multi-Stage Stochastic Programming Model for the Multi-Echelon Multi-Period Reverse Logistics Problem. Sustainability, no. 13 (24). DOI: https://doi.org/10.3390/su132413596
17. Econometrics. Encyclopedia of Mathematics. Available at: http://encyclopediaofmath.org/index.php?title=Econometrics&oldid=46790
18. Koriashkina L. S., Dziuba S. W., Us S. A., Stanina O. D., Odnovol M. M. (2024) Two-stage problems of optimal location and distribution of the humanitarian logistics system’s structural subdivisions. Naukovyi visnyk Natsionalnoho hirnychoho universytetu, no. 1, pp. 130–139. DOI: https://doi.org/10.33271/nvngu/2024-1/130
19. Medio A. (2020) Mathematical Models in Economics. Mathematical Models, vol. III. Available at: https://www.eolss.net/Sample-Chapters/C02/E6-03B-09-02.pdf
