Abstract
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.