Environmental Engineering Reference
In-Depth Information
Fig. 3 Timeline showing the start and end of the time horizon, and the start and end of the time
window access restriction
Fig. 4 Representation of the
times of arrival and departure
at customer i in a vehicle's
route
t i ¼ Arrival time to customer i for the vehicle visiting that customer.
t i ¼ Departure time from customer i towards customer i þ 1, with t i ¼ t i þ h.
Going back to the timeline in Fig. 4 , we have represented these two times, with
Pi representing customer or stop i in the route of a vehicle.
2.2 General Case Analysis of the VRPATW
After defining the problem, the time window, the restricted zone and the related
terminology, we now proceed to analyze the different cases that may arise when
calculating vehicle routes. Starting with the general scenario of a vehicle moving
from one customer to the next one until the end of its route, we will describe those
cases, their interaction with the time window and the restricted zone, and what
should be the reaction of the algorithm in each one of them.
2.2.1 Case Description
If a vehicle has to visit a determined sequence of customers, the default situation
establishes that it starts its route at the depot at the starting time of the day t o . Then,
at every customer that is visited, we calculate the corresponding arrival and
departure time, but we also need to take into account whether the customer in
inside the restricted zone and, if so, whether the time window is open or closed. If
no restrictions affect the displacement, the process continues with the following
customer in the sequence, until all the customers have been visited and the end of
the day is reached for the vehicle. The process is the same for all the different
vehicles introduced in the routing planning.
However, if any restriction related to the time window could affect the visit to a
given customer in the route, additional considerations must be introduced. These
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