Harmonic analysis in inventory management in logistics and supply chains

The article examines the possibilities of using harmonic analysis apparatus while planning the need in stocks of various categories. The issues of improving material planning (forecasting) are currently quite relevant applied tasks in business, and are also of interest in terms of developing the theory of logistics and supply chain management. Among the approaches to planning the need for inventory, a wide range of statistical theory methods are used in practice, among which two large groups can be distinguished, such as one-parameter time series analysis models for goods of stable and relatively stable demand, as well as correlation and regression models for chaotic consumption stocks. Most of the goods sold to end consumers have a seasonal component, which may not always be explicitly expressed in statistics. However, due to change of seasons, regular fluctuations in the values of consumption from the warehouse, around the average chronological or trend, may necessitate regular recalculation of the main parameters of inventory management models, such as maximum, insurance, threshold inventory levels, etc. In addition, sales statistics may contain fluctuations of a higher order if the stocks sold have life cycles of interest in goods on the market, which can also be attributed to periodic or quasi-periodic processes. One of the methods to formalize such cyclic processes can be trigonometric approximation or harmonic analysis, when the values of a time series are represented as terms of a Fourier series (harmonics) having corresponding amplitudes and phases. The article compares the effectiveness (accuracy) of forecasts of inventory requirements made using harmonic analysis and traditional time series extrapolation methods.

1. Baturov, A. V., & Drobnaya, E. N. (2019). The economic role of inventory in the production process. Economic growth as a basis for sustainable development of Russia, 78–83.

2. Chashchina, D. A., & Onokhina, E. A. (2020). Using the Wilson model to ensure the competitiveness of the enterprise. Modern Science, 3-1, 154–162.

3. Dybskaya, V. V. (2023). Designing a distribution system in logistics: a monograph. M.: NIC INFRA-M. https://doi.org/10.12737/24760

4. Dybskaya, V. V., & Sergeev, V. I. (2023). Logistics in 2 hours: textbook for bachelor’s and master’s degrees. М.: Yurayt Publishing House.

5. Eliseeva, I. I. (ed.). (2023). Business statistics: textbook and workshop for universities. 2nd ed. M.: Yurayt Publishing House.

6. George, L. M. (2017). Lean manufacturing + six sigma in the service sector. How the speed of lean manufacturing and the quality of six sigma help business improvement. М.: Mann, Ivanov and Ferber.

7. Glebkova, I. Yu., & Churilova, E. Yu. (2023). Socio-economic statistics: textbook. M.: Knorus.

8. Golov, V. A., & Ryumkin, V. I. (2018). Optimization of the inventory management system for stationary random demand. Modern trends in the development of management, economics and education, 78–82.

9. Lukinsky, V. S. (ed.). (2023). Inventory management in supply chains in 2 hours: textbook and workshop for universities. M.: Yurayt Publishing House.

10. Markina, S. A., & Kharina, N. L. (2018). Management of current assets of trading organizations using optimization models in order to ensure economic security. Proceedings of the Southwestern State University. Series: Economics. Sociology. Management, 8, 4(29), 223–234.

11. Mishchenko, A. V., & Mikheeva, E. V. (2019). Methods of assessing the effectiveness of the management of production and financial activities of the enterprise. Monograph. M.: NIC INFRA-M. www.dx.doi.org/10.12737/monography_5d1ae60d82d6d9.87533425

12. Mishchenko, A. V., & Pilyugina, A. V. (2023). Methods of financial planning and evaluation of the effectiveness of management of production and financial activities of the enterprise: monograph. M.: NIC INFRA-M. https://doi.org/10.12737/1875454

13. Moiseeva, N. K., & Oleinik, S. P. (2022). Economic fundamentals of logistics: textbook. 2nd ed. M.: NIC INFRA-M. https://doi.org/10.12737/1439631

14. Portal eRUDA.ru — rating of gold mining companies of the Russian Federation (n.d.). Leading coal mining companies of the Russian Federation — 2022. Retrieved April 22, 2023, from http://www.eruda.ru/gdp/top_50_vedushchikh_ugledobyvayushchikh_kompaniy_rf_reyting.htm

15. Salin, V. N., & Shpakovskaya, E. P. (ed.). (2023). Statistics. (Socio-economic statistics): textbook.M.: Knorus.

16. Sergeev, V. I. (2023). Supply chain Management: Textbook for universities. M.: Yurayt Publishing House. https://doi.org/10.12737/1844337

17. Sergeev, V. I. (ed.). (2023). Corporate logistics in questions and answers: a monograph. 2nd ed. M.: NIC INFRA-M. https://doi.org/10.12737/2373

18. Sergeev, V. I., & Elyashevich, I. P. (2023). Logistics of supply: textbook for universities. 5th ed. M.: Yurayt Publishing House.

19. Sergeev, V. I., & Elyashevich, I. P. (2023). Procurement and inventory management in supply chains: Textbook. M.: NIC INFRA-M. https://doi.org/10.12737/1844337

20. Sterligova, A. N. (2022). Inventory management in Supply chains: A textbook. M.: SIC INFRA-M.

21. Sterligova, A. N., & Fel, A. V. (2022). Operational (production) management: A textbook. M.: NIC INFRA-M.

22. Tinkoff Bank (n.d.). Accounting statements of counterparties for 2022. Retrieved April 22, 2023, from https://www.tinkoff.ru/business/contractor/legal/1034205040935/financialstatements/

23. Tsarkova, E. V. (2020). Inventory management models under uncertainty. Transformation of the National socio-economic system of Russia, 506–514.

24. Turchenko, A. A. (2021). Explicit and opportunity costs as a tool for studying possible transaction costs of an entity within the framework of logistics outsourcing. Actual problems of accounting, economic analysis and financial and economic control of the organization’s activities, 187–190.

25. Vlasova, Yu. E., Malich, A. V., & Zakrevskaya, E. A. (2016). Sales forecasting by harmonic analysis methods. International Student Scientific Bulletin, 2, 102.

26. Yurov, V. M. (2018). The technology of forecasting periodic economic processes based on harmonic analysis methods in MS Excel. Bulletin of the Moscow State Regional University. Series: Economics, 3, 19–28. https://doi.org/10.18384/2310-6646-2018-3-19-28

27. Zaitseva, I. V., Malafeev, O. A., Rezenkov, D. N., Ryzhov A. V., & Pozhidaev, S. V. (2021). Economic and mathematical modeling of minimizing total costs in inventory management. Fundamental Research, 2, 18–22. https://doi.org/10.17513/fr.42960