A Note on the Ichoua, Gendreau, and Potvin (2003) Travel Time Model

In this paper we exploit some properties of the travel time model proposed by Ichoua, Gendreau, and Potvin [Ichoua S, Gendreau M, Potvin J-Y (2003) Vehicle dispatching with time-dependent travel times. Eur. J. Oper. Res. 144: 379-396], on which most of the current time-dependent vehicle-routing literature relies. First, we prove that any continuous piecewise-linear travel time model, satisfying the FIFO property, can be generated by an appropriate model. We also show that the model parameters can be obtained by solving a system of linear equations for each arc. Then such parameters are proved to be nonnegative, which allows us to interpret them as (dummy) speeds. Finally, we illustrate the procedure through a numerical example. As a by-product, we are able to link the travel time models of a road graph and the associated complete graph over which vehicle-routing problems are usually formulated.