A nested Benders decomposition-based algorithm to solve the three-stage stochastic optimisation problem modeling population-based breast cancer screening

Population-based cancer screening programmes invite high-risk population groups to screenings in order to increase the probability of an early diagnosis. In this paper, we study the organisation of preventive breast cancer screening, accounting for both scheduling of patients and planning of resources. Mammography screening comprises a two-stage healthcare process, encompassing a patient scan in a mammography unit and a scan examination by a central coordination center. Objectives are to minimise patient flow times and maximise resource efficiency and number of patients treated. Performance of population-based screening programmes is hampered due to large rates of patient no-shows, which is partially remedied by giving patients the option to cancel or reschedule their appointment. We model the scheduling problem as a three-stage stochastic optimisation problem and propose a diving heuristic relying on Sample Average Approximation and nested Benders decomposition to find high-quality integer solutions. Computational experimentation is performed on real-life instances to benchmark the proposed method to alternative methodologies. Results demonstrate that the proposed heuristic yields a stable performance for instances of different sizes. However, integrating the three decision stages increases significantly the complexity, such that larger-sized instances are preferably solved via two separate solution stages to improve resource efficiency. In addition, insights are provided in the value of stochastic optimisation and strategies to cancel or reschedule appointments mitigating the impact of no-show uncertainty.