Performance evaluation of candidate appointment schedules using clearing functions

This study is concerned with the problem of reducing the waiting times of outpatients. Both scheduled patients and walk-ins are included among the outpatients to reflect the typical medical environment in Japan. The consultation time of a hospital is divided into several blocks, and each scheduled patient is given the start time of a block as his or her scheduled time of the consultation as an appointment. It is assumed that all scheduled patients arrive at the hospital at their scheduled times, while walk-ins arrive randomly. A set of candidate appointment schedules is given, and the process of selecting promising schedules in terms of average waiting times is the focus of the work. To support the selection process without conducting a conventional simulation, the notion of a clearing function is adopted to evaluate each candidate schedule. The clearing function of a system gives the expected output or throughput of the system under varying levels of workload of the system. Although it is necessary to conduct exploratory experiments in advance to obtain the clearing function, the expected waiting time can be estimated by simple calculations with the aid of the clearing function. The average waiting times of four schedules in two scenarios are calculated and compared with those obtained from conventional simulations. It is revealed that the proposed procedure based on the clearing function gives acceptable estimated average values.