Optimal Dynamic Appointment Scheduling of Base and Surge Capacity

We study dynamic stochastic appointment scheduling when delaying appointments increases the risk of incurring costly failures, such as readmissions in health care or engine failures in preventative maintenance. When near-term base appointment capacity is full, the scheduler faces a trade-off between delaying an appointment at the risk of costly failures versus the additional cost of scheduling the appointment sooner using surge capacity. Most appointment scheduling literature in operations focuses on the trade-off between waiting times versus utilization. In contrast, we analyze preventative appointment scheduling and its impact on the broader service supply network when the firm is responsible for service and failure costs. We adopt a stochastic dynamic programming (DP) formulation to characterize the optimal scheduling policy and evaluate heuristics. We present sufficient conditions for the optimality of simple policies. When analytical solutions are intractable, we solve the DP numerically and present optimality gaps for several practical policies in a health care setting. Intuitive appointment policies used in practice are robust under moderate capacity utilization, but their optimality gap can quadruple under high load.