Appointment scheduling using optimisation via simulation

In this study we consider the optimal scheduling of a certain number of appointments in a given number of time slots. Given a set of appointment slots, we assume that customers can arrive early or late according to a known distribution around the scheduled arrival time. Analytical methods exist for this problem when all customers are assumed to be punctual, but evaluating methods when this assumption is relieved do not yet exist. The reason why this is difficult, is that the order of service is no longer fixed when possible arrival times of two consecutive customers overlap. Therefore we use simulation to evaluate schedules, and optimisation via simulation techniques to optimize schedules. We develop and compare several strategies, among which random local search and nested partitions. Numerical experiments show that significant improvements can be achieved compared to standard scheduling practice.