Sequential Appointment Scheduling Considering Walk-In Patients

This paper develops a sequential appointment algorithm considering walk-in patients. In practice, the scheduler assigns an appointment time for each call-in patient before the call ends, and the appointment time cannot be changed once it is set. Each patient has a certain probability of being a no-show patient on the day of appointment. The objective is to determine the optimal booking number of patients and the optimal scheduling time for each patient to maximize the revenue of all the arriving patients minus the expenses of waiting time and overtime. Based on the assumption that the service time is exponentially distributed, this paper proves that the objective function is convex. A sufficient condition under which the profit function is unimodal is provided. The numerical results indicate that the proposed algorithm outperforms all the commonly used heuristics, lowering the instances of no-shows, and walk-in patients can improve the service efficiency and bring more profits to the clinic. It is also noted that the potential appointment is an effective alternative to mitigate no-show phenomenon.