  We study the vehicle routing problem with time windows (VRPTW) and stochastic
travel times, in which the decision-maker observes related contextual
information, represented as feature variables, before making routing decisions.
Despite the extensive literature on stochastic VRPs, the integration of feature
variables has received limited attention in this context. We introduce the
contextual stochastic VRPTW, which minimizes the total transportation cost and
expected late arrival penalties conditioned on the observed features. Since the
joint distribution of travel times and features is unknown, we present novel
data-driven prescriptive models that use historical data to provide an
approximate solution to the problem. We distinguish the prescriptive models
between point-based approximation, sample average approximation, and
penalty-based approximation, each taking a different perspective on dealing
with stochastic travel times and features. We develop specialized
branch-price-and-cut algorithms to solve these data-driven prescriptive models.
In our computational experiments, we compare the out-of-sample cost performance
of different methods on instances with up to one hundred customers. Our results
show that, surprisingly, a feature-dependent sample average approximation
outperforms existing and novel methods in most settings.
