In this section, we focus on the modeling of the on-demand mode of the PRT–FRT transportation problem with the aim of
minimizing the movement of empty vehicles and the waiting time of passengers and goods requests in a dynamic context. As
underlined previously, both economic and sustainability performances are desired in city logistics contexts and thus are considered
in the model hereafter. In fact, determining which vehicle to move and where to move it is known as the empty vehicle
redistribution (EVR) problem for PRT systems (Lees-Miller, 2013). In the dynamic case, operating the PRT–FRT mode
along time can result in a high level of unused capacity because of empty vehicles moving between stations when responding
to passengers or goods demand. This issue is made more challenging in this article by considering the use of electric PRT
vehicles with limited battery capacity, which causes additional empty vehicle movements to recharge the vehicle batteries at
the network depot.
Furthermore, the PRT–FRT dynamic problem shares some characteristics with the dynamic one-to-one pickup and delivery
problem. As Berbeglia et al. (2010) suggested, the dynamic one-to-one pickup and delivery problem can be partitioned
into three subcategories:
Vehicles serving more than one request at a time create a classic dynamic pickup and delivery problem.
Transportation requests consisting of passengers, as in a bus system, create a dial-a-ride