Optimizing physician schedules with resilient break assignments

This article presents a novel model for building biweekly rosters for physicians according to the regulations of a German teaching hospital, while also ensuring the viability of breaks. Currently, rosters are manually prepared by experienced physicians with basic spreadsheet knowledge, leading to significant costs and time consumption because of the complexity of the problem and the individual working conditions of the physicians. Unfortunately, manually generated rosters frequently prove to be non-compliant with labor regulations and ergonomic agreements, resulting in potential overtime hours and employee dissatisfaction. A particular concern is the inability of physicians to take mandatory breaks, which negatively affects both employee motivation and the hospital service level. To address these challenges, we propose a data-driven formulation of an operational physician scheduling problem, considering overstaffing and overtime hours as primary cost drivers and integrating shift preferences and break viability as ergonomic objectives. We develop and train a survival regression model to predict the viability of breaks, allowing practitioners to define break-time windows appropriately. Given the limitations of standard solvers in producing high-quality solutions within a reasonable timeframe, we adopt a Dantzig-Wolfe decomposition to reformulate the proposed model. Furthermore, we develop a branch-and-price algorithm to achieve optimal solutions and introduce a problem-specific variable selection strategy for efficient branching. To assess the algorithm's effectiveness and examine the impact of the new break assignment constraint, we conducted a comprehensive computational study using real-world data from a German training hospital. Using our approach, healthcare institutions can streamline the rostering process, minimize the costs associated with overstaffing and overtime hours, and improve employee satisfaction by ensuring that physicians can take their legally mandated breaks. Ultimately, this contributes to better employee motivation and improves the overall level of hospital service.