Mathematical model of transport and warehouse processes in retail sales systems evolving traditional and online technologies

Introduction. The article is devoted to increasing the productivity of transport and warehouse processes with an emphasis on the analysis of operations performed in the warehouse. Household appliances and electronics retailers have been taken as an example for solving the problem, but the results of the study can be extended to retail systems based on traditional and online technologies.
The productivity of integral parts of transportation and warehousing for the stores under investigation, such as vehicles for delivering goods and warehouse workers, has been given a differentiated assessment. The problems associated with unbalanced warehouse operation during peak sales periods are considered. The relevance of the study refers to statistical data confirming the growth of sales in this market segment. The purpose of the study is to develop a mathematical model that determines the relationship between the output of a warehouse of household appliances and electronics stores and the output of vehicles transporting goods.
Materials and methods. The method of optimization of technological processes was used to develop the mathematical model. The solution of the problem is achieved through using the search method for output physical indicator with the adopted restrictions taken into account. Elements of transport and warehouse processes for mathematical description include the output per each warehouse worker performing a specific operation; the output of each vehicle performing a specific task in the warehouse. Planning is considered on daily basis for the specific month of the year.
Results and conclusions. The developed mathematical model defines that the output of all workers and rolling stock units ensures the necessary operations for processing the goods received at the warehouse. The mathematical model prescribes the required number of warehouse workers and vehicles, taking into account the output of the entire work according to the efficiency criterion – profit. Directions for further research on practical implementation of the mathematical model include determining the probabilistic parameters of the model – output of warehouse workers and vehicles, time for processing an order by groups.

1. Boysen N., René de Koster, Füßler D., The forgotten sons: Warehousing systems for brick-andmortar retail chains. European Journal of Operational Research. 2021; Vol. 288, Is. 2: 361–381, DOI: https:// doi.org/10.1016/j.ejor.2020.04.058.

2. Guzenko A.V., Guzenko N.V. Diversified approach to organizing multichannel sales of federal food chain. Vestnik of Rostov state university of economics (RINH). 2022; 3(79): 10–18. DOI: https:// doi.org/10.54220/v.rsue.1991-0533.2022.79.3.001.(in Russ.)

3. Pavlov K.V., Zenkova I.V., Nikiforov S.A. Evaluation of the effective use of logistics centers in the transportation of meat and dairy products from the Vitebsk region of Belarus to foreign markets. Corporate Governance and Innovative Economic Development of the North: Bulletin of the Research Center of Corporate Law, Management and Venture Investment of Syktyvkar State University. 2022; Vol. 2, issue 4: 397–408. DOI: https://doi.org/10.34130/2070-4992-2022-2-4-397. (in Russ.)

4. Pavlov K.V., Zenkova I.V., Nikiforov S.A. Effective use of logistics centers in transportation of meat and dairy products from of belarus to foreign markets. Economy and Finance (Uzbekistan). 2023; 3: 38–48. DOI: https://doi.org/10.34920/EIF/VOL_2023_ISSUE_3_6. (in Russ.)

5. Živičnjak M., Rogić K., Bajor I., Case-study analysis of warehouse process optimization. Transportation Research Procedia. 2022; Vol. 64: 215–223. DOI: https://doi.org/10.1016/j.trpro.2022.09.026.

6. Burganova N., Grznar P., Gregor M., Mozol Š. Optimalisation of Internal Logistics. Transport Time Through Warehouse Management: Case Study,Transportation Research Procedia. 2021; Vol. 55: 553-560. DOI: https://doi.org/10.1016/j.trpro.2021.07.021.

7. Santos O.M., Hernández-González J.C., Román-del-Valle M.A. Application of Simulation in the Management of the Operational Warehouse, A Systematic Literature Review Hernández. Saudi Journal of Engineering and Technology Abbreviated Key Title: Saudi J Eng Technol. 2024. DOI: https://doi.org/10.36348/sjet.2024.v09i10.003

8. Abideen A., Fazeeda B. M. Improving the performance of a Malaysian pharmaceutical warehouse supply chain by integrating value stream mapping and discrete event simulation. Journal of Modelling in Management , 2021: 70–102. DOI: https://doi.org/10.1108/JM2-07-2019-0159.

9. Moreno R.P.R., Lopes R.B., Ferreira J.V., Ramos A.L., Correia D.A Study of the Main Mathematical Models Used in Mobility. Storage, Pickup and Delivery in Urban Logistics. A Systematic Review. Systems 2024; 12: 374. DOI: https://doi.org/10.3390/systems12090374

10. Murav`eva N.A. Approach to the classification of technological processes in transportation and warehousing logistics systems. Vestnik of Saratov State Technical University. 2013; 2, no 2(71): 316–318. (in Russ.)

11. Protopopov N.D. Optimization solution for automotive component logistics. Vestnik Rossijskogo novogo universiteta. Seriya: Slozhny`e sistemy`: modeli, analiz i upravlenie. 2021; 2: 45–55. DOI 10.255. (in Russ.)

12. Xoruzhenko E.S., Mochalin S.M. Planning of transport and warehouse costs when organizing deliveries by machine shipments. Omsk Scientific Bulletin. 2015; 3(139): 258–261. (in Russ.)

13. Levina A.B., Yakunina Yu.S., Trofimenko E.Yu. Assessment of the Level of Logistisation of Trade Enterprises. Vestnik Volgogradskogo gosudarstvennogo universiteta. Ekonomika. Journal of Volgograd State University. Economics. 2024; vol. 26, no. 3: 134–148. (in Russ.) DOI: https://doi.org/10.15688/ek.jvolsu.2024.3.11

14. Aravindaraj K., Rajan Chinna P. A systematic literature review of integration of industry 4.0 and warehouse management to achieve Sustainable Development Goals (SDGs). Cleaner Logistics and Supply Chain, 2022; vol. 5: 100072. DOI: https://doi.org/10.1016/j.clscn.2022.100072.

15. Leon J.F., Li Y., Martin X.A., Calvet L., Panadero J., Juan A.A. A Hybrid Simulation and Reinforcement Learning Algorithm for Enhancing Efficiency in Warehouse Operations. Algorithms. 2023; 16: 408. https://doi.org/10.3390/a16090408.

16. Razumovsky A.V., Saramud M.V., Pikalov Y.Y. The algorithms for managing a matrix-based warehouse utilizing standardized transport and storage cells. Vestnik NSU. Series: Information Technologies. 2023; vol. 21, no. 4: 54–70. (in Russ.) DOI: https://doi.org/10.25205/1818-7900-2023-21-4-54-70

17. Zeng Y.Q., Li W.B., Li C.H. A dynamic simulation framework based on hybrid modeling paradigm for parallel scheduling systems in warehouses,Simulation. Modelling Practice and Theory. 2024; vol. 133: 102921. DOI: https://doi.org/10.1016/j.simpat.2024.102921.

18. Trofimova L.S. The methodology of the current planning of a motor transport enterprise operation for the transportation of goods in the city. The Russian Automobile and Highway Industry Journal. 2020; 17(2): 234–247. (In Russ.) DOI: https://doi.org/10.26518/2071-7296-2020-17-2-234-247

19. Trofimova L.S., Pevnev N.G. Struktura metodologii tekushhego planirovaniya raboty` gruzovogo avtotransportnogo predpriyatiya. Vestnik SibADI. 2017; 6(58): 63–71. (in Russ.)