Minimizing the expected waiting time of emergency jobs

We consider a scheduling problem where a set of known jobs needs to be assigned to a set of given parallel resources such that the expected waiting time for a set of uncertain emergency jobs is kept as small as possible. On the basis of structural insights from queuing theory, we develop deterministic scheduling policies that reserve resource capacity in order to increase the likelihood of resource availability whenever an emergency job arrives. Applications of this particular scheduling problem are, for instance, found in the field of surgical operations scheduling in hospitals, where high-priority but uncertain emergencies compete for scarce operating room capacity with elective surgeries of lower priority. We compare our approaches with other policies from the literature in a comprehensive simulation study of a surgical operations unit.