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.

https://doi.org/10.1287/trsc.2013.0491

Cite as:

@article{Ghiani_2014,
	doi = {10.1287/trsc.2013.0491},
	url = {https://doi.org/10.1287%2Ftrsc.2013.0491},
	year = 2014,
	month = {aug},
	publisher = {Institute for Operations Research and the Management Sciences ({INFORMS})},
	volume = {48},
	number = {3},
	pages = {458--462},
	author = {Gianpaolo Ghiani and Emanuela Guerriero},
	title = {A Note on the Ichoua, Gendreau, and Potvin (2003) Travel Time Model},
	journal = {Transportation Science}
}