Open Access

The healthcare sector, and hospitals in particular, are confronted with an increasing challenge of staff shortages. To effectively address this issue, hospitals must enhance their workforce planning and scheduling processes in a manner that ensures fairness for employees. The application of operations research/management science methods offers significant promise for the integration of fairness into these processes. To assist researchers and practitioners in capitalizing on this potential, we present a comprehensive review of the extant literature. This review examines the current trends in the integration of fairness into workforce planning and scheduling in hospitals. It analyses 97 papers, providing insightful metadata and categorising the literature based on three key questions: what constitutes fairness, what metrics are crucial for assessing fairness, and how fairness can be quantitatively measured. By structuring our review around these questions, we identify gaps in existing research and suggest potential avenues for future research.

In recent years, the importance of achieving staffing flexibility to balance supply and demand in unpredictable environments, such as hospitals, has grown. This study focuses on shift design with task rotations for a multi-skilled workforce, specifically in service contexts characterized by pronounced demand variability. We introduce a mathematical programming model designed to identify optimal shift start times with task assignments for both full-time and part-time employees, where workers can rotate between multiple tasks during their shifts. We develop a column generation approach that allows us to solve realistically-sized problem instances. Our analysis, derived from staffing data of a university hospital’s radiation oncology department, reveals the model's robust applicability across varying demand landscapes. We demonstrate that incorporating task rotations in the shift design can improve workload balancing when task demands fluctuate considerably. Remarkably, our column generation technique produces optimal integer solutions for realistic problem instances, outperforming the compact mixed-integer formulation which struggles to achieve feasible results. We find that the success of embedding task rotations in shift design decisions is directly influenced by the demand profile, which in turn affects the necessary qualification mix of the workforce.

Hospitals are facing organizational and financial challenges in planning and scheduling. This dissertation presents three contributions which evaluate the surplus of considering flexibility in the resource planning processes. The research evaluates and discusses flexible room-changing opportunities in operating room scheduling, flexible shift types in staffing decisions, and flexible performance metrics in predicting patient diseases.

Many hospitals in Germany are facing escalating economic pressures. After several years of stagnation, the number of inpatient hospital treatments dropped by in 2020 compared to the previous year. This negative tendency can also be seen in operating theaters (OTs). Strategic management of the case mix in hospital OTs now necessitates a solid data foundation. The case mix and the case mix index have become central economic indicators in contemporary hospital operations. In this work, we develop a mathematical model for case mix optimization at Augsburg University Hospital in Germany, which is based on an extensive data analysis with descriptive methods. The optimization model is subject to rigorous testing and evaluation through an extensive series of scenario analyses. The primary objective is to calculate a revenue-maximizing patient mix while respecting the available scarce personnel resources in the OT and intensive care unit. This research marks a pioneering effort in delineating the practical integration of case mix planning into a hospital’s routine operations using mathematical optimization. The analyses reveal a strong correlation between an upsurge in revenue and an increased number of cases. Furthermore, the results demonstrate that strategic planning of the patient mix has the potential to enhance revenue with existing resources. Even though the optimal patient mix may not be directly implementable in practice, the findings yield valuable insights for managerial decision-making. A critical examination of these results also fosters a nuanced discourse on the utilization of optimization models as decision support tools within hospital management.

Objective The explicit prohibition of discontinuing intensive care unit (ICU) treatment that has already begun by the newly established German Triage Act in favor of new patients with better prognoses (tertiary triage) under crisis conditions may prevent saving as many patients as possible and therefore may violate the international well-accepted premise of undertaking the “best for the most” patients. During the COVID-19 pandemic, authorities set up lockdown measures and infection-prevention strategies to avoid an overburdened health-care system. In cases of situational overload of ICU resources, when transporting options are exhausted, the question of a tertiary triage of patients arises. Methods We provide data-driven analyses of score- and non-score-based tertiary triage policies using simulation and real-world electronic health record data in a COVID-19 setting. Ten different triage policies, for example, based on the Simplified Acute Physiology Score (SAPS II), are compared based on the resulting mortality in the ICU and inferential statistics. Results Our study shows that score-based tertiary triage policies outperform non-score-based tertiary triage policies including compliance with the German Triage Act. Based on our simulation model, a SAPS II score-based tertiary triage policy reduces mortality in the ICU by up to 18 percentage points. The longer the queue of critical care patients waiting for ICU treatment and the larger the maximum number of patients subject to tertiary triage, the greater the effect on the reduction of mortality in the ICU. Conclusion A SAPS II score-based tertiary triage policy was superior in our simulation model. Random allocation or “first come, first served” policies yield the lowest survival rates, as will adherence to the new German Triage Act. An interdisciplinary discussion including an ethical and legal perspective is important for the social interpretation of our data-driven results.

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.

The COVID-19 pandemic has given rise to a broad range of research from fields alongside and beyond the core concerns of infectiology, epidemiology, and immunology. One significant subset of this work centers on machine learning-based approaches to supporting medical decision-making around COVID-19 diagnosis. To date, various challenges, including IT issues, have meant that, notwithstanding this strand of research on digital diagnosis of COVID-19, the actual use of these methods in medical facilities remains incipient at best, despite their potential to relieve pressure on scarce medical resources, prevent instances of infection, and help manage the difficulties and unpredictabilities surrounding the emergence of new mutations. The reasons behind this research-application gap are manifold and may imply an interdisciplinary dimension. We argue that the discipline of AI ethics can provide a framework for interdisciplinary discussion and create a roadmap for the application of digital COVID-19 diagnosis, taking into account all disciplinary stakeholders involved. This article proposes such an ethical framework for the practical use of digital COVID-19 diagnosis, considering legal, medical, operational managerial, and technological aspects of the issue in accordance with our diverse research backgrounds and noting the potential of the approach we set out here to guide future research.

Physical therapy in acute care hospitals plays an important role in the rehabilitation of patients. Nevertheless, the profession must deal with staff shortages caused by a lack of potential employees and absenteeism which are results of high physical and mental workloads. The therapist shortage negatively affects the total number of daily appointments the department can fulfill. For appointments that can be successfully scheduled, continuity of care with the same therapist cannot be guaranteed for individual patients. Lack of continuity of care negatively influences the therapist's satisfaction. Therapist preferences for individual appointments in general cannot always be guaranteed when designing schedules, which also hurts satisfaction. This paper develops a multi-criteria model for the daily therapy appointment-scheduling problem. The primary objective is to minimize the total sum of priority violations for unscheduled appointments. To improve therapist satisfaction, we consider therapist preferences including continuity of care as a secondary objective. Here, our integer programming formulation aims to minimize the total sum of preference violations for scheduled appointments. We are dealing with an operational planning problem with a daily planning horizon. The operational objective is to achieve therapist schedules in at most two hours. The therapists’ schedules together need to include several hundred appointments for a planning day. Due to intractability, the developed integer program cannot provide schedules for such problem sizes. Therefore, we develop a customized Greedy Randomized Adaptive Search Procedure (GRASP) with six innovative local search operations to improve an initially constructed solution. We test the heuristic algorithm on realistic data instances. The metaheuristic provides high-quality schedules for various problem sizes in short runtimes, i.e., within minutes. Comparisons with the optimal solutions for small problem instances show very good results of the GRASP with a similar number of scheduled appointments and good adherence to continuity of care and therapist preference requirements.