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appointment scheduling with discrete random durations

 

We consider the problem of determining optimal appointment schedule for a given sequence of jobs (e.g., medical procedures) on a single processor (e.g., operating room, examination 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 functionis 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 operating room) after which overtime is incurred, as well as no-shows and emergencies.
 
This is joint work with Mehmet Begen (Sauder School of Business,University of British Columbia).