| Summary: | Purpose. In order to study the impact of grey delivery time uncertainty on customer satisfaction and delivery costs, a vehicle routing problem with grey delivery time windows and multiobjective constraints is defined. Method. The paper first defines the uncertainty of the delivery vehicle’s arrival time to the customer as grey uncertainty and then whitens the grey time windows; at the same time, the customer’s hard time windows is expanded into a soft time windows to measure customer satisfaction when the vehicle arrives. Experiment. In order to verify the validity of the established model, numerical experiments are carried out in two groups based on the Solomon example, and the solution is solved based on the improved quantum evolution algorithm. Analysis. Distribution cost fluctuations and customer satisfaction fluctuations with grey time windows are relatively small; under different satisfaction threshold conditions, the distribution cost is increased gently with the satisfaction threshold. Conclusion. The grey delivery time windows have certain advantages in solving the random travel time vehicle routing problem.
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