Abstract: Given an appointment system with fixed length of appointment time interval,an optimal sequential scheduling scheme has been designed to realize online scheduling of heterogeneous patients with different service durations and no-show behaviors. This paper deploys the approach to incorporate an overbooking strategy to address and remediate patient no-shows. The sequencing problem of patients can be modeled by mixed integer programming with the objective to minimize the waiting time cost of patients,idle time and overtime cost of physician. Based on the service sequence rule,a heuristic sequential scheduling policy is proposed to determine the service time of each patient as soon as they request for an appointment. Furthermore,a block-scheduling scheme has been introduced to deal with the issue that service time of different patients may vary from each other. Numerical results illustrate that block scheduling can reduce idle time and overtime of physician. Furthermore,when different types of patients vary considerably in service time,patients' heterogeneity have a significant impact on the optimal schedule,and under this condition,block scheduling can greatly improve system efficiency.