  We study a routing and appointment scheduling problem with uncertain service
and travel times arising from home service practice. Specifically, given a set
of customers within a service region that an operator needs to serve, we seek
to find the operator's route and time schedule. The quality of routing and
scheduling decisions is a function of the total operational cost, consisting of
customers' waiting time, and the operator's travel time, idle time, and
overtime. We propose and rigorously analyze a stochastic programming model and
two distributionally robust optimization (DRO) models to solve the problem,
assuming a known and unknown service and travel time distribution,
respectively. We consider two popular types of ambiguity sets for the DRO
models, namely, the mean-support and 1-Wasserstein ambiguity set. We derive
equivalent mixed-integer linear programming (MILP) reformulations of both DRO
models that can be implemented and efficiently solved using off-the-shelf
optimization software, thereby enabling practitioners to use these models. In
an extensive numerical experiment, we investigate the proposed models
computational and operational performance, demonstrating where significant
performance improvements can be gained with each proposed model and derive
insights into the problem.
