Stochastic Optimization Models for a Home Service Routing and Appointment Scheduling Problem with Random Travel and Service Times

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.