Environmental Engineering Reference
In-Depth Information
vehicle routing optimization problems (m-VRP). Such problems have been
introduced for the first time in Laporte (
1988
) but formally presented in Gonzalez-
Feliu (
2012a
). In urban logistics, the attention is focused on the Two-Stage version
of the problem (2-VRP), a simplified version frequently arising in the context of
Two-Stage distribution systems design. This system is composed by three inter-
acting levels, linked by different vehicle fleets performing delivery operations:
• Primary facilities, also called depots: high capacitated facilities generally
located far from the urban area, where freight is loaded on first stage vehicles.
• Secondary facilities, also called satellites: low capacitated facilities devoted to
transhipment operations, in which freight arriving from primary facilities is
transferred into smaller vehicles, referred as second stage vehicles, which per-
form the distribution to the final customers.
• Customers: End points of the distribution, which must be served by at least one
second stage vehicle.
Given this structure, the 2-VRP consists in defining number and location of
primary and secondary facilities, performs the allocation operations, i.e. assign
each final customers to an open secondary facility, and each secondary facility to
an open primary facility, satisfying capacity facility constraints, and solve the
resulting routing problem, identifying how many vehicles, for each fleet, are used,
by which vehicle each customer is served, and in which order the vehicle performs
its deliveries. From a physical point of view, a General Two-Stage Capacitated
Vehicle Routing system (G 2-VRP) operates as follows (see also Fig.
1
):
• Freight arrives at an external zone, one depot, where it is consolidated into the
1st-stage vehicles, which constitute heterogeneous fleets.
• Each 1st-stage vehicle travels to a subset of satellites that will be determined by
the model and then it will return to the depot.
• At each satellite, freight is transferred from 1st-stage vehicles to smaller,
environmental
friendly
vehicles,
belonging
to
2nd-stage
fleets
(also
heterogeneous).
• Each 2nd-stage vehicle performs a route to serve the designated customers, and
then travels to a satellite (not necessarily its departure point).
The basic version of the problems is called Two-stage capacitated VRP (2-
CVRP). This is the simplest version of multi-stage VRPs. At each stage, all
vehicles belonging to that stage have the same fixed capacity. The size of the fleet
of each stage is fixed and known in advance, and there exists an upper bound on
the number of vehicle which can start from the same satellite. The objective is to
serve customers by minimizing the total transportation cost, satisfying the capacity
constraints of the vehicles. There is a single depot and a fixed number of capac-
itated satellites. All the customer demands are fixed, known in advance, and must
be compulsorily satisfied. Moreover, no time window is defined for the deliveries
and the satellite operations. For the 2nd stage, the demand of each customer is
smaller than each vehicles capacity and cannot be split in multiple routes of the
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