Distributionally robust appointment scheduling with moment-based ambiguity set

We study appointment scheduling under random service duration with unknown distributions. Given a sequence of appointments arriving at a single server, we assign their planned arrival time to minimize the expected total waiting time, while using a chance constraint to restrict the probability of server overtime. We consider a distributionally robust formulation based on an ambiguity set that uses the first two moments, and derive an approximate semidefinite programming model. We conduct computational studies by testing outpatient treatment scheduling instances.