Utility‐Based Appointment Scheduling in Continuous Time: The Lag Order Approximation Method

Abstract

An appointment schedule aims to achieve a proper balance between different interests: the waiting time for the customers and the waiting time for the service providers, the so called idle time. These interests are truly conflicting; focusing on small idle time results in large waiting times for the customer and vice versa. This thesis considers the area of appointment scheduling for a single server in continuous time with punctual customers. There is a vast amount of literature addressing this topic, however, there is not a generic approach to generate large schedules analytically with general service time distributions. First, we study the characteristics of this problem with exponential service times. Next, we propose an approximation method that enables us to design appointment schedules with general service time distributions. This method is the lag order approximation method, which is the main result of this thesis. Another method is proposed to overcome the dimensionality problem, when designing appointment schedules for a large number of customers. We will present both methods, and investigate their performance and applicability.