Assessment of the Structural Stability of Transport and Logistics Systems Based on Graph Models and the Percolation Coefficient

Global changes in the global economy and trade place new demands on transport and logistics systems (TLS). Increasing their resilience to disruptions and structural changes is becoming a critical task amid the growing share of logistics costs in Russia’s GDP. Existing optimization methods often do not take into account the resilience of the network structure itself to destructive influences, which creates a gap in knowledge.

The purpose of the study is to develop and test methodological tools for assessing and improving the structural stability of the TL.

The approach integrates graph-theoretical modeling, multi-criteria optimization methods, and a new indicator, the percolation coefficient, which characterizes the network’s ability to deliver goods to all destinations. The multi-criteria optimization problem of finding paths and flows is formalized. Sustainability was assessed through the coefficient of influence of structural changes on the effectiveness of solutions. A large-scale computational experiment was conducted with the generation of more than 1 million graph structures. A mathematical model of the radar has been developed based on a matrix of initial conditions, and an efficiency coefficient has been proposed for comparing alternative options. A close correlation has been established between network bandwidth, percolation coefficient, and solution efficiency. The barrier values of the coefficient of influence have been determined, which make it possible to classify the system as stable or unstable to a specific type of structural failure. The principles of building sustainable radar stations are formulated, the key of which is the availability of alternative routes with efficiency close to optimal.

The results obtained lay the foundation for the creation of intelligent radar stations that are resistant to failures and load fluctuations.

1. Costa Y., Duarte L., Pereira R. The impact of global supply chain reconfiguration on international trade patterns: A network analysis. Research in Transportation Business & Management. 2024;52:100811. DOI: 10.1016/j.rtbm.2024.100811

2. Gavish B., Graves S.C. The Travelling Salesman Problem and Related Problems. INFORMS Journal on Computing. 2023;35(2):319–335. DOI: 10.1287/ijoc.2022.0123

3. Cota P.M., de Lima F.S., de Araújo O.C.B. A two-stage integer programming model for cargo allocation with transshipment time considerations. Computers & Industrial Engineering. 2023;175:108852. DOI: 10.1016/j.cie.2023.108852

4. Roy S.K., Mula P. A stochastic transportation problem with multiple choice of cost and requirement. International Journal of Operational Research. 2022;44(3):365–382. DOI: 10.1504/IJOR.2022.120211

5. Pournader M., Kach A., Fahimnia B. A Review of Transport Network Resilience: Concepts, Models, and Future Research Directions. Transport Reviews. 2023;43(4):689–715. DOI: 10.1080/01441647.2023.2201771

6. Ivanov D., Dolgui A. Viability of intertwined supply networks: extending the supply chain resilience angles towards survivability. International Journal of Production Research. 2022;60(1):1–17. DOI: 10.1080/00207543.2020.1750727

7. Dubey R., Gunasekaran A., Bryde D.J., Dwivedi Y.K., Papadopoulos T. Blockchain technology for enhancing supply chain resilience and sustainability. International Journal of Production Research. 2023;61(7):2266– 2285. DOI: 10.1080/00207543.2022.2101771

8. Dmitriev A., Shnurkov M. Graph Theory Application in Modern Supply Chain Network Design: A Systematic Review. Transportation Research Part E: Logistics and Transportation Review. 2023;175:103–145. DOI: 10.1016/j.tre.2023.103145

9. Zhang Y., Li X., Wang Q. Modeling Multimodal Transportation Networks as Directed Hypergraphs for Enhanced Logistics Planning. Computers & Industrial Engineering. 2024;187:109821. DOI: 10.1016/j.cie.2024.109821

10. Chen, L., Pietrabissa, A. A Robust Network Flow Model for Strategic Logistics Hub Classification under Demand Uncertainty. European Journal of Operational Research. 2022;301(1):283–297. DOI: 10.1016/j.ejor.2021.09.021

11. Garcia-Herrero S., Mar-Ortiz J., & De-La-Peña J.L. An Integrated Multi-Objective Optimization Model for Green Vehicle Routing and Scheduling with Heterogeneous Fleet and Time-Dependent Capacities. Journal of Cleaner Production. 2023;414:137503. DOI: 10.1016/j.jclepro.2023.137503

12. Ivanov D., Dolgui A. A Digital Supply Chain Twin for Managing the Disruption Risks and Resilience in the Era of Industry 4.0. Production Planning & Control. 2021;32(9):775–788. DOI: 10.1080/09537287.2021.1922771

13. Newman M.E.J. A Measure of Structural Redundancy for Semantically Annotated Networks. Scientific Reports. 2022;12(1):13487. DOI: 10.1038/s41598-022-17191-81

14. Katarzyniak M., Mulawka D. Identification of Critical Nodes in Transport Networks Using Centrality Measures and Vulnerability Scenarios. IEEE Access. 2023;11:45678-45691. DOI: 10.1109/ACCESS.2023.3281171

15. Ghavamifar A., Saberi M. Robustness of Interdependent Logistics Networks: A Percolation-Based Analysis of Cascade Failures. Transportation Research Part E: Logistics and Transportation Review. 2024;181:103367. DOI: 10.1016/j.tre.2024.103367