In the Vehicle Routing Problem with Time Windows, a set of customers requests service by vehicles initially located at a central depot. Each customer provides a period of time in which they must be served. The service may consist of repair work or loading/unloading of the vehicle. The objective is to find tours for the vehicles, such that each customer is served in its specified time window and the total distance traveled by the vehicles is as small as possible. In this paper, we present a new polynomial-time heuristic for a stylized version of the problem, and show it is asymptotically optimal when customer locations are independent and identically distributed in a given region. We also describe the implementation of the heuristic and present computational results.
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