Appointment scheduling with non-punctual arrivals

In this paper, we consider the scheduling of appointments at a service facility, such as a health clinic. There are M customers requesting service with service times being independent and identically distributed random variables. Customers are served one at a time in the order of their arrivals. The arrivals of customers to the service facility are driven by their appointment times. However, customers are non-puctual and may show up earlier or later than their appointment times. Customers may also not show up altogether. The lateness of customers is assumed to follows a general distribution with finite support. For a given vector of appointment times, we develop a methodology for evaluating various performance measures. We also describe procedures for optimizing the scheduling of appointments.