A Comprehensive Survey of Methods and Challenges of Vehicle Routing Problem with Uncertainties

Meraliyev M. Turan C. Kadyrov S. Sadyk U.
December 2025 Multidisciplinary Digital Publishing Institute (MDPI)

Mathematics
2025 #13 Issue 23

This paper presents a comprehensive survey of the methodologies and challenges associated with the Vehicle Routing Problem (VRP), focusing on the uncertainties that impact routing decisions in real-world logistics and transportation scenarios. Traditional VRP models often assume static and deterministic conditions, which do not fully capture the complexities of actual logistics operations. This paper categorizes uncertainties into demand variability, travel-time fluctuations, and other dynamic factors, such as service-time variability and vehicle breakdowns. It reviews various approaches to addressing these uncertainties, including dynamic VRP models and the application of reinforcement learning in stochastic environments. The research methodology includes a systematic review of articles published in recent years, emphasizing influential research at the intersection of VRP and uncertainty. The findings highlight the importance of bridging theoretical advances with practical applications to enhance the robustness and adaptability of VRP solutions. The paper concludes by advocating for continued research in this area to improve operational efficiency and service reliability in logistics.

demand variability , dynamic routing , reinforcement learning , transportation management , travel time variability , uncertainty , vehicle routing problem

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Department of Computer Science, School of Information Technology and Applied Mathematics, SDU University, Abylaikhan 1/1, Almaty Region, Kaskelen, 040900, Kazakhstan
Department of General Education, New Uzbekistan University, Movarounnahra 1, Tashkent, 100125, Uzbekistan

Department of Computer Science
Department of General Education

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