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Vehicle routing problem with time-varying speed(VRPTS)is a generalization of vehicle routing problem in which the travel speed between two locations depends on the passing areas and the time of a day.This paper proposes a simple model for estimating time-varying travel speeds in VRPTS that relieves much bur den to the data-related problems.The study further presents three heuristics(saving technique,proximity priority searching technique,and insertion technique)for VRPTS,developed by extending and modifying the existing heuristics for conventional VRP.The results of computational experiments demonstrate that the proposed estimation model performs well and the saving technique is the best among the three heuristics.