Appointment Scheduling with Discrete Random Durations

Authors:
Mehmet A. Begen;Maurice Queyranne
Affiliations:
Ivey School of Business, University of Western Ontario, London, Ontario N6A 3K7, Canada;Sauder School of Business, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
Venue:
Mathematics of Operations Research
Year:
2011

Citing 11
Cited 1

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Abstract

We consider the problem of determining an optimal appointment schedule for a given sequence of jobs (e.g., medical procedures) on a single processor (e.g., operating room, examination facility, physician), 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 that 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 some emergencies.