Optimal appointment scheduling with no-shows and exponential service time considering overtime work

Appointment systems are used by health clinics to manage access to service providers. In such systems, a specified number of patients are scheduled in advance, but certain patients may not arrive or ‘show up’ to their appointments. The existence of no-show behaviour influences both the operational cost of the clinics and the waiting time of the patients. In this paper, we determine an optimal schedule that takes no-show behaviour into account to determine the time intervals between patients under the framework of the individual-block/variable-interval rule for minimising the overall cost of the patient waiting time, the practitioner idle time and overtime. Under the condition that the service time of each patient is exponentially distributed, we compare the results with a schedule designed for the same expected number of patients in the absence of no-shows and analyse the effect on the system performance from the perspectives of day-length, expected workload, no-show probability, ratio of overtime costs a...

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