On-line Appointment Sequencing and Scheduling

We formulate and solve a new stochastic integer programming model for dynamic sequencing and scheduling of appointments to a single stochastic server. We assume that service durations and the number of customers to be served on a particular day are uncertain. Customers are sequenced and scheduled dynamically (on-line) one at a time as they request appointments. We present a two-stage stochastic mixed integer program which uses a novel set of non-anticipativity constraints to capture the dynamic multistage nature of appointment requests as well as the sequencing of customers. We describe several ways to improve computational efficiency of decomposition methods to solve our model. We also present some theoretical findings based on small problems to help motivate decision rules for larger problems. Our numerical experiments provide insights into optimal sequencing and scheduling decisions and the performance of the solution methods we propose.