The contributions of this paper are as follows.
(i) Taking account of the random and time-varying
characters of traffic conditions, a robust optimization
based method is applied in the proposed model,
which is able to compute the stochastic timedependent
optimal paths (STDOP) connecting any
pair of customer nodes efficiently. Being different
from many existing approaches, the robust approach
does not require the probability distributions of link
travel times and only takes the range of uncertainty
which can be derived from historical data and experience
of the decision-makers.
(ii) The STDVRP model we proposed here can be converted
into a time-dependent VRP (TDVRP). The
simplified problem will not lead to an increase in
the computing time and can be solved efficiently
by conventional algorithms. The proposed model
is capable of addressing STDVRPTW of practical
sizes on a real-world urban network, demonstrated
here on the road network of Shenzhen, China, with
computational instances of up to 150 customers.
(iii) The model we proposed can improve the level of
customer service by guaranteeing the time-window
constraint satisfied without leading to cost increase
or environmental impacts. The improvement can be
significant especially for large-scale network delivery
tasks.