MRI appointment scheduling with uncertain examination time

This paper addresses the appointment scheduling problem for a single diagnostic facility—the magnetic resonance imaging equipment, which provides several services to the appointed patients. The examinations have random service durations given by a joint discrete probability distribution. We consider two performance criteria: (1) the expected cost incurred from the equipment idle time and the examination overtime representing the operating costs of the hospital; and (2) the expected cost incurred from the patient waiting time reflecting the customer satisfaction. The overall goal is to identify the examination sequence and the scheduled start times for the appointed patients so as to minimize simultaneously the aforementioned criteria by determining all the Pareto-optimal schedules. The problem is first formulated as a two-stage stochastic integer programming model and it is shown to be NP-hard in the strong sense even for the case with only two scenarios. An improved multi-objective evolutionary algorithm is then proposed in the MOEA/D framework, where the uncertainty is simulated by constructing a number of different scenarios. To replace the time-consuming simulations during the process of evaluating the rescheduling cost, we integrate the algorithm with a support vector regression surrogate model which efficiently improves the robustness of the baseline schedule and the quality of the solution. Finally, using the real medical data, we assess the feasibility and effectiveness of the proposed model by comparing with the classical NSGA-II and the MOEA/D algorithm, and extract some appropriate management inspirations to medical staffs for decision-making references.