Design appointment in outpatient department with bulk service

Appointment system of outpatients is used by clinics to manage patients' access at the system inter-day planning stage. Appointment rules, which include the booking window length, the block capacity and the block service time, lie at the intersection of efficiency and timely access to healthcare delivery. With the additional impact of patient cancellation, the system performance will become even more difficult to measure. In this paper, we are interested in how the design of appointment rules will affect a provider's operational efficiency. A stochastic model is developed to describe the inter-day appointment planning which is a novel extend of bulk server queue. Based on the steady-state system distribution, we build 4 measures to evaluate the efficiency, and further use them to obtain the optimal appointment rule that will not only help to improve the timely access, but also lead to the system's multi-objective optimization. The numerical experiment qualitatively shows that extending booking window is insignificant to reduce the system congestion, while a narrowed appointment block is a better design for highly demand physicians. Finally, the case study provides an optimal appointment rule design based on a programming model, where the quantitatively solution is consistent with the insights derived from numerical analysis. The improved appointment rule design is practical and useful for hospital managers in decision making.