Appointment Scheduling for Multiple Servers

Appointment schedules, in essence, balance supply and demand and are often employed in settings where resources are scarce and thus a high utilization is realized (e.g., healthcare). Whereas most of the existing literature focuses on the single-server case, a framework is developed to study appointment scheduling in multiserver settings. Relying on phase-type approximations, general service-time distributions are modeled, which are fed into a recursive approach allowing evaluation and optimization of an objective function that balances expected waiting times and idle times. Studying optimized schedules for multiple servers reveals that the start and end of a session can deviate greatly from the dome-shaped pattern as established for the single-server case. Furthermore, a comparison of various multiserver setups shows that significant performance gains can be achieved when servers are pooled. This allows an explicit quantification of the cost of continuity of care. In addition, session overtime as well as early finish of servers can be incorporated in the approach; the benefits of the additional flexibility that a multiserver setting provides are summarized. For the stationary plateau of the dome, to which the optimal interarrival times converge, steady-state appointment schedules are obtained by exploiting the embedded Markov chain; these schedules are shown and argued to converge quickly to optimal solutions obtained in a heavy-traffic regime. In this regime, algebraic solutions are derived, which provide interesting managerial guidelines when the pooling of servers is considered in appointment scheduling.