Appointment Scheduling with Discrete Random Durations∗

We consider the problem of determining optimal appoint-ment schedule for a given sequence of jobs (e.g., medical procedures) on a single processor (e.g., operating room, ex-amination facility), to minimize the expected total underage and overage costs when each job has a random processing duration given by a joint discrete probability distribution. Simple conditions on the cost rates imply that the objective function is submodular and L-convex. Then there exists an optimal appointment schedule which is integer and can be found in polynomial time. Our model can handle a given due date for the total processing (e.g., end of day for an oper-ating room) after which overtime is incurred and, no-shows and emergencies. 1 Introduction and Motivation