Multiserver Time Window Allowance Appointment Scheduling Problem for Coordinating Online and Offline Patients

Internet healthcare is becoming increasingly popular, which allows doctor–patient communication through messages, phone calls, or videos. Considering stochastic heterogeneous behaviors of patients and physicians (e.g. time-dependent no-shows, service times), it is critical to determine the optimal appointment schedule to maximize the online and offline integrated system’s operational efficiency. In this paper, through adding time window constraints in the model, we investigate a multiserver time window allowance appointment scheduling problem that restricts only certain types of patients to be served during the particular period. Optimal scheduling decisions include physician allocation and appointment arrival time arrangement for different types of patients. We formulate the problem as a stochastic mixed-integer program and develop a stabilized Benders decomposition algorithm to effectively solve the model. Numerical results indicate that nearly in all cases of integrated online and offline patients’ scheduling, the proposed multiserver time window allowance schedules obtained perform better than previous solutions. Compared with the separated single-server model, scheduling multiple servers jointly can be beneficial when there is significant heterogeneity between physicians for treating online and offline patients. In addition, adopting appropriate time window allowance schedule for online patients will significantly affect system performance under different time-dependent no-show patterns of online and offline patients.