Multi-server Sequential Appointment Scheduling With General Service Time Distributions

As the economy is growing steadily and the aging population is accelerating,the demand for a effective and efficient medical care system is becoming more and more urgent.Although large hospitals have introduced various appointment methods such as online appointments,how to allocate scarce resources reasonably to centralized demands is still a problem.Patients’ waiting time usually includes registration and queueing for diagnosis.If the waiting time is too long,patients’ satisfaction declines significantly.A well-designed outpatient appointment system can improve the utilization rate of medical resources,alleviate aimless visits of patients and the congestion in the waiting area and achieve the purposes of improving the experience of patients and increasing the utility of diagnosis.This paper investigates the multi-server sequential appointments scheduling problem with the general distribution of patients service time and incorporates the patients’ preference for doctors and slots in the formulation.The appointment scheduling model is established by considering various performance measures.The waiting time and overtime costs are calculated according to patient types and their preferences.When a preferred doctor is assigned,the hospital gains a higher revenue.If the patient is not provided with a preferred slot,he or she has a probability to reject the arrangement or accepts this inconvenient assignment with a greater no-show rate.The objective of multi-server sequential appointment scheduling is searching for an optimal decision maximizing the system profit.This paper also investigates the impacts of patients’ revisits on the basis of original model,where both outpatient and inspection departments are simulated in that scenario.After initial diagnosis in the outpatient department,each patient knows whether further inspection is necessary.Moreover,patients maybe returns to the physician or leave directly after getting the results of inspecting.It is assumed that revisit patients always join the queue in the next slot of the physician if they decide to return.The revisiting model determines the myopic schedule with maximum profit by considering two departments simultaneously.After analyzing impacts of the patient preference,no-show probabilities and the cost coefficients,this paper concludes that when patient preference is incorporated,the system’s profit increases significantly as well as the physician utilization.Meanwhile,the number of patients who refuse scheduling declines.For the sequential appointment scheduling model with patients revisits,this paper proposes a variety of approximate models to save running time.The numerical experiments demonstrate high-quality solutions and fast running time for the approach with approximate number of revisits and service time.