Methodology of Determining the Location of the Distribution Center of Material Flows in a Combined Scheme of Goods Delivery

Introduction. The research is aimed at developing a methodology for determining the optimal location of material flows’ distribution center, taking into account the formation of ring routes based on the use of the fictitious nodes and branches’ method (FNB), in order to minimize overall logistical costs. Despite the sufficient number of existing ways to solve this problem, they have some disadvantages: they are not entirely realistic and do not completely meet the requirements of logistical optimization. Namely, existing algorithms do not take into account the need to visit the branches of the transport graph several times and the curvature of the movement trajectory.

The developed technique has greater practical application because it deals with determining the optimal location of the distribution center based on the criterion of full vehicle loading, using piecewise linear approximation to account for the curvature of routes, forming delivery routes using the accurate fictitious nodes and branches’ method (FNB) to optimize transportation and minimize overall logistical costs. This technique can be used by both providers to analyze and select the location of a logistics distribution center taking into account the formation of optimal routes for the delivery of goods, and by owners of large retailers.

Materials and methods. The developed methodology includes several stages. At the first stage, the area of the most probable location of the distribution center (DC) is determined. We calculate the coordinates of cargo center of gravity using the formulas for the strength of materials. As its weight, we take the amount of cargo in receiving points. We accept the hypothesis that the placing area for distribution center is located around the cargo center of gravity. Its boundary passes through the nodes closest to it. The nodes are cargo points, road intersections and points of abrupt changes in the direction of movement. The expert can assign additional nodes to clarify the influence of geometry, length, and other parameters of the trajectory of movement. As a rule, there is no road between the center of gravity and the nodes. At the second stage, a rational location of the regional center is determined. There is no road between the center of gravity and the nodes. Therefore, ring routes are calculated that originate from nodal points using the method of fictitious nodes and branches. The routing problem is reduced to finding one ring that passes through the selected nodal point several times. The constraint is taken into account by the blocking method. At the third stage, we replace the branches of the curvilinear route of movement with piecewise linear interpolation. We determine the transport work and the coordinates of the center of gravity of the rectangular diagram on each branch of the route. We find the value of the total transport work around the coordinate axes. We calculate the coordinates of the regional center. We accept its rational coordinates according to the average values obtained for each selected node.

Result. The application of the developed methodology for the network delivering goods from the distribution center to the Public Joint Stock Company “Magnit” trading points per shift has reduced the number of routes, time on the route by 10% and the length of the route by 16%.

Conclusion. The methodology for determining the optimal location of the distribution center of material flows has been provided. The program has been developed on the basis of the proposed methodology. Results of the use of the proposed methodology have been obtained by testing on the example of Public Joint Stock Company “Magnit”.

1. Dybskaya V.V., Sverchkov P.A. An approach to designing a rational distribution network of a retail chain company. Logistics and Supply Chain Management. 2015; 1: 44–59. (in Russ.)

2. Volkhin E.T. Location models for distribution centres. Upravlenets (The Manager). 2018; T.9, 2: 54–60. (in Russ.)

3. Novikov A.N., Gestkova S.A. Methodology for designing ring routes with return cargo. World of transport and technological machines. 2024; 1-3(84): 19–27. (in Russ.)

4. Nikoline V.I., Vitvitskyi E.E., Mochalin S.M. Road freight transport: Monograph. Omsk: Edition of «Option-Siberia», 2004: 482. (in Russ.)

5. Ubozhenko E.V., Solovyova Yu.Y., Vdovin S.A. Determining the coordinates of the location of the distribution center in logistics taking into account the random component. Vestnik Altajskoj akademii jekonomiki i prava. 2024; 3-3: 499–503. (in Russ.)

6. Pugachev I.N., Burkov S.M. Practical application of the model of cluster network structures in solving problems of increasing the efficiency of urban transport and distribution systems. Bulletin of PNU. 2010; 2 (17): 121–130. (in Russ.)

7. Volodina, E.V., Studentova E.A. Practical application of the algorithm for solving the traveling salesman problem. Inzhenernyj vestnik Dona. 2015; 2, part 2: 96–97. (in Russ.)

8. Martynov A.V., Kureichik V.M. Hybrid algorithm for solving the traveling salesman problem. Izvestiya SFU. Technical sciences. 2015; 4 (165): 36–44. (in Russ.)

9. Brodetsky G. L. Application of the analytical hierarchy method to optimize the location of a regional distribution center. Logistics and Supply Chain Management. 2005; 6: 26–34. (in Russ.)

10. Gusev S. A. Problems of determining the location of a warehouse. Logistika. 2011; 2: 53–55. (in Russ.)

11. Eldestein Yu.M., Shaporova Z.E. Supply chain management in the forest complex. The Crimean Scientific Bulletin. 2016; 1 (7): 323–342. (in Russ.)

12. Konstantinov R.V. Designing an optimal warehouse network. Inzhenernyj vestnik Dona. 2011; 4: 1–8. (in Russ.)

13. Sho S., Haruna M., Yoshifumi N. Ant colony optimization using genetic information for TSP. Proceedings of the International Symposium on Nonlinear Theory and its Applications OLTA.2011. Japan: Kobe. P. 48 – 51.

14. Sedighpour M., Yousefikhoshbakht M., Narges M.D. An effective genetic algorithm for solving the multiple traveling salesman problem. Journal of Optimization in Industrial Engineering. 2012; Vol. Volume 4, no.8: 73–79.

15. Harrath Y. [et al.] A novel hybrid approach for solving the multiple traveling salesmen problem. Arab Journal of Basic and Applied Sciences. 2019; Jan. Vol. 26: 103–112.

16. Littl J.D.C., Murty K.G., Sweeney D., Karel C. An algoritm for thethe traveling salesman problem. Operations Research. 1963; Vol. 11: 972–989.