Key result
An optimal appointment schedule for jobs with discrete random durations can be found in polynomial time to minimize expected total underage and overage costs.
The study provides a polynomial-time solution for optimal appointment scheduling with discrete random durations, applicable to medical procedures and operating rooms.
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May enable efficient optimal scheduling for cardiology procedures; extends theory to discrete durations but leaves clinical impact open.
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 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 operating room) after which overtime is incurred and, no-shows and emergencies.
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Begen et al. (2009) studied this question. Optimal appointment scheduling model was evaluated on Expected total underage and overage costs. An optimal appointment schedule for jobs with discrete random durations can be found in polynomial time to minimize expected total underage and overage costs.
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