Time Constraints: The Cost of Sustainability - Sustainable Urban Logistics: Concepts, Methods and Information Systems - page 168

We also define a set T of time costs associated to the different links in the graph.
These costs depend only on the transit of vehicles through links, and not on the
amount of freight carried by those vehicles. In general, we will incur in cost t ij
when travelling from node i to node j. We will also compute the unloading time at
each customer as a time cost h, incurred every time a vehicle visits one of the
customer nodes contained in C.
Within the set of nodes N, we also consider a subset RZ of nodes that
correspond to the restricted zone, and which cannot be crossed or visited during a
pre-specified closed time window period (CWT), which period will obviously be
smaller than the overall time horizon. We asume that C \ RZ 6¼; and that
C \ RZ 6¼; .
A schematic description of the problem is shown in Fig. 2 .
Before describing the different situations that have to be considered in the
routing process, we define here the concepts and terminology involved. For
example, with respect to the time window:
t VC ¼ Window

closing time, that is, the instant when the time window

restriction starts operating.
t VA ¼ Window opening time, that is, the instant when the time window
restriction ends.
With respect to the time horizon, linked to a full day or rather the business
hours of a given day, we define:
t o ¼ Starting time for the day.
t f ¼ End-of-day time, when the business hours end.
All these instants are represented in the timeline shown in Fig. 3 .
The cost h models the fact that the vehicle, when visiting a customer, needs to
spend a given amount of time unloading the goods and making the final delivery.
This is why we distinguish a time of arrival and a time of departure for all the
nodes in subset C for the analysis and interpretation of the problem. The termi-
nology used is as follows:

Fig. 2 Schematic
representation of a city where
a VRPATW applies