The Effect of Flexible Service Rates in Appointment Scheduling Systems
32 Pages Posted: 24 Jun 2020
Date Written: June 1, 2020
Recent research offers overwhelming evidence that service workers, including healthcare providers in ambulatory care settings, exercise flexible service rates. While theoretical models of service rate control in steady-state queues explain service rate changes in response to queue length, there are no comparable models explaining the drivers of optimal service rate in appointment systems. In this paper, we analyze service rate control when the provider is responsible for serving a finite number of patients who arrive by prior appointments in a session of finite duration. Under general assumptions on random service times, we show that a provider should optimally increase the service rate in response to the queue length and the delay in starting a patient's service. In addition to the novel analytical finding on delay-driven speed-up behavior, we show that both congestion-driven and delay-driven speed-up behaviors persist even when the patient wait is costless. We also show that the provider may speed-up or slow-down while serving sequential arrivals in the appointment schedule, depending on the relative magnitudes of the cost of patient waiting and the cost of the provider's time. Finally, we explore implications of flexible service rates on the operational performance of appointment systems, and find that flexible service rates result in shorter, fairer, and less uncertain waiting times for patients in most situations.
Keywords: Appointment systems, Flexible service rates, Service rate control
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