Optimal appointment scheduling in continuous time: The lag order approximation method

摘要

The service provider is able to schedule arriving clients with the help of an appointment schedule so that the client can arrive for receiving the service at the scheduled time. This can be considered as a two stage problem. In the first stage, the provider schedules the appointments and in the second stage, the server executes the service. The clients present themselves in the random order and request for including them in the schedule. This article discusses the scheduling problem of the service provider in the first stage. A new approximation method of clients service-time distribution is developed that provides a good approximation. In this case a finite number of clients are scheduled before the starting of the service. The service time distribution, and clients loss function due to waiting time, as well as the servers lateness (overtime) are supposed to be known then the objective is to minimize the sum of service idle time, and lateness, and the clients waiting time. Since the exact solution to the problem is computationally difficult, the lag order approximation (the number of predecessors taken in to account) method is proposed that provides reasonably good solutions to the problem. (25 refs.)