<![CDATA[This research focuses ons addresses vehicle routing uncertainty in time windows and stochastic needs. The project intends to increase vehicle routing efficiency, adaptability, and robustness by developing optimization approaches. Traffic congestion, unanticipated events, and changing client expectations can greatly impact truck routing solutions. Traditional methods presume fixed time frames and deterministic needs, resulting in suboptimal or infeasible paths. This paper presents a mathematical model that includes time window uncertainty and stochastic needs into the vehicle routing issue to address these restrictions. The formulation incorporates arrival times, delivery amounts, and route decisions to minimize transportation costs and ensure timely deliveries and resource efficiency. Advanced algorithms and solvers tackle the optimization challenge. Integer programming, flow conservation constraints, and temporal window constraints are used to identify optimal or near-optimal solutions to uncertainty and dynamic changes. Numerical examples and case studies demonstrate the approach's efficacy. Numerical examples demonstrate the mathematical formulation, while the case study shows the practical consequences and benefits for a dynamic delivery service organization. The research shows that the proposed approach can handle temporal window uncertainties and stochastic demands. These innovations can optimize vehicle routing, reduce transportation costs, boost customer happiness, and increase resource utilization. Addressing time window uncertainty and stochastic demands advances vehicle routing. The proposed approach helps logistics and transportation industries overcome dynamic and uncertain operating environments, boosting operational efficiency and competitiveness.]]>
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