Appointment scheduling with multiple providers and stochastic service times

In many appointment scheduling systems with multiple providers, customers are assigned appointment times but they are not assigned a specific provider in advance – that is, customers can be seen by any available provider. This type of system is common in a variety of service sectors, such as healthcare, banking, and legal counseling. The majority of the existing literature assumes constant service times or does not consider customer no-shows, which are unrealistic assumptions in many situations. In this paper, we overcome this shortcoming by developing an appointment scheduling model that considers stochastic service times along with customer no-shows for multiple-provider systems with identical providers. The objective is to minimize the weighted sum of customers’ waiting time, and providers’ idle time and overtime. We model this problem as a time-inhomogeneous Discrete-Time Markov Chain process. We use analytical results to reduce the space of optimal schedule candidates, and we employ machine learning techniques to detect patterns among optimal or near-optimal schedules. We then develop an effective heuristic method which provides schedules that perform better than the ones generated by existing models. We test our heuristic both on simulated data and a real-world application. As the real-world application, we collaborate with a local counseling center to implement the schedules suggested by our method. Results from this field experiment reveal an average schedule cost reduction of 16% per day, with a maximum reduction of 40% per day.