A Note on "The Latest Arrival Hub Location Problem"

Kara and Tansel (Management Science, Volume 47, 2001, 1408--1420) introduce the latest arrival hub location problem as a more realistic way of modeling cargo delivery. The key feature of the new model is that each link in the network is served by a single vehicle that makes exactly one trip. As a result, the traffic requiring a particular link may be forced to wait for all other traffic requiring the same link to arrive. Therefore, the travel time between a particular pair of nodes depends not just on travel times of the links on the path taken, but also on these forced "waiting times," which are called transient times in Kara and Tansel (2001). We show, however, that if the objective function depends only on the maximum travel time, this "new" model is essentially the same as the classical model that ignores the transient times. Our result implies that two of the three versions of the latest arrival hub location problem proposed by Kara and Tansel, including the one to which they devote most of their paper, are equivalent to their classical counterparts.