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/variableinterval 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 and no-golf policy.We extend our results to an equally-spaced appointment system,which is commonly used in practice.Our results show that not only do no-shows greatly affect the system performance compared with an appointment system with the same expected workload without no-shows,but they also affect the optimal scheduling behaviours in the dome-shaped distribution.In addition,overtime cannot be eliminated completely even if the day length is adequate for all patients because of the stochastic characteristic of service time.
