Most of the models for vehicle routing reported in the literature assume constant travel times. Clearly, ignoring the fact that the travel time between two locations does not depend only on the distance traveled, but on many other factors including the time of the day, impact the application of these models to real-world problems. In this paper, we present a model based on time-dependent travel speeds which satisfies the ''first-in-first-out'' property. An experimental evaluation of the proposed model is performed in a static and a dynamic setting, using a parallel tabu search heuristic. It is shown that the time-dependent model provides substantial improvements over a model based on fixed travel times.

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An abundant literature about vehicle routing and scheduling problems is available in the scientific community. However, a large fraction of this work deals with static problems where all data are known before the routes are constructed. Recent technological advances now create environments where decisions are taken quickly, using new or updated information about the current routing situation. This paper describes such a dynamic problem, motivated from courier service applications, where customer requests with soft time windows must be dispatched in real time to a fleet of vehicles in movement. A tabu search heuristic, initially designed for the static version of the problem, has been adapted to the dynamic case and implemented on a parallel platform to increase the computational effort. Numerical results are reported using different request arrival rates, and comparisons are established with other heuristic methods.

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