In this paper we exploit some properties of the travel time model proposed by Ichoua et al (2003), on which most of the current time-dependent vehicle routing literature relies. Firstly, we prove that any continuous piecewise lin- ear travel time model can be generated by an appropriate Ichoua et al (2003) 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 if the continuous piecewise linear travel time model satis- es the FIFO property, which allows 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.
A Note on the Ichoua et al (2003) Travel Time Model.
GUERRIERO, Emanuela;GHIANI, GIANPAOLO
2014-01-01
Abstract
In this paper we exploit some properties of the travel time model proposed by Ichoua et al (2003), on which most of the current time-dependent vehicle routing literature relies. Firstly, we prove that any continuous piecewise lin- ear travel time model can be generated by an appropriate Ichoua et al (2003) 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 if the continuous piecewise linear travel time model satis- es the FIFO property, which allows 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
