Reexamining the Nurse Scheduling Problem: Staffing Ratios and Nursing Shortages*

Patient-to-nurse ratios: Balancing quality, nurse turnover, and cost

We consider the problem of setting appropriate patient-to-nurse ratios in a hospital, an issue that is both complex and widely debated. There has been only limited effort to take advantage of the extensive empirical results from the medical literature to help construct analytical decision models for developing upper limits on patient-to-nurse ratios that are more patient- and nurse-oriented. For example, empirical studies have shown that each additional patient assigned per nurse in a hospital is associated with increases in mortality rates, length-of-stay, and nurse burnout. Failure to consider these effects leads to disregarded potential cost savings resulting from providing higher quality of care and fewer nurse turnovers. Thus, we present a nurse staffing model that incorporates patient length-of-stay, nurse turnover, and costs related to patient-to-nurse ratios. We present results based on data collected from three participating hospitals, the American Hospital Association (AHA), and the California Office of Statewide Health Planning and Development (OSHPD). By incorporating patient and nurse outcomes, we show that lower patient-to-nurse ratios can potentially provide hospitals with financial benefits in addition to improving the quality of care. Furthermore, our results show that higher policy patient-to-nurse ratio upper limits may not be as harmful in smaller hospitals, but lower policy patient-to-nurse ratios may be necessary for larger hospitals. These results suggest that a "one ratio fits all" patient-to-nurse ratio is not optimal. A preferable policy would be to allow the ratio to be hospital-dependent.

Optimization models for patient and technician scheduling in hemodialysis centers

Patient and technician scheduling problem in hemodialysis centers presents a unique setting in healthcare operations as (1) unlike other healthcare problems, dialysis appointments have a steady state and the treatment times are determined in advance of the appointments, and (2) once the appointments are set, technicians will have to be assigned to two types of jobs per appointment: putting on and taking off patients (connecting to and disconnecting from dialysis machines). In this study, we design a mixed-integer programming model to minimize technicians' operating costs (regular and overtime costs) at large-scale hemodialysis centers. As this formulation proves to be computationally challenging to solve, we propose a novel reformulation of the problem as a discrete-time assignment model and prove that the two formulations are equivalent under a specific condition. We then simulate instances based on the data from our collaborating hemodialysis center to evaluate the performance of our proposed formulations. We compare our results to the current scheduling policy at the center. In our numerical analysis, we reduced the technician operating costs by 17% on average (up to 49%) compared to the current practice. We further conduct a post-optimality analysis and develop a predictive model that can estimate the number of required technicians based on the center's attributes and patients' input variables. Our predictive model reveals that the optimal number of technicians is strongly related to the time flexibility of patients and their dialysis times. Our findings can help clinic managers at hemodialysis centers to accurately estimate the technician requirements.

Probabilistic forecasting of hourly emergency department arrivals

An accurate forecast of Emergency Department (ED) arrivals by an hour of the day is critical to meet patients' demand. It enables planners to match ED staff to the number of arrivals, redeploy staff, and reconfigure units. In this study, we develop a model based on Generalised Additive Models and an advanced dynamic model based on exponential smoothing to generate an hourly probabilistic forecast of ED arrivals for a prediction window of 48 hours. We compare the forecast accuracy of these models against appropriate benchmarks, including TBATS, Poisson Regression, Prophet, and simple empirical distribution. We use Root Mean Squared Error to examine the point forecast accuracy and assess the forecast distribution accuracy using Quantile Bias, PinBall Score and Pinball Skill Score. Our results indicate that the proposed models outperform their benchmarks. Our developed models can also be generalised to other services, such as hospitals, ambulances or clinical desk services.

A Hybrid Personnel Scheduling Model for Staff Rostering Problems

The problem of staff scheduling in the airline industry is extensively investigated in operational research studies because efficient staff employment can drastically reduce the operational costs of airline companies. Considering the flight schedule of an airline company, staff scheduling is the process of assigning all necessary staff members in such a way that the airline can operate all its flights and construct a roster line for each employee while minimizing the corresponding overall costs for the personnel. This research uses a rostering case study of the ground staff in the aviation industry as an example to illustrate the application of integrating monthly and daily schedules. The ground staff in the aviation industry case is a rostering problem that includes three different types of personnel scheduling results: fluctuation-centered, mobility-centered, and project-centered planning. This paper presents an integrated mixed integer programming (MIP) model for determining the manpower requirements and related personnel shift designs for the ground staff at the airline to minimize manpower costs. The aim of this study is to complete the planning of the monthly and daily schedules simultaneously. A case study based on real-life data shows that this model is useful for the manpower planning of ground services at the airline and that the integrated approach is superior to the traditional two-stage approach.

Interpretation of Hospital Nurse Fatigue Using Latent Profile Analysis

There has been a lack of consensus in the literature related to the conceptualization, definition, and measurement of hospital nurse fatigue. Using latent profile analysis, the Hospital Nurse Force Theory provided a conceptual format to identify 3 profiles of nurse fatigue from subjective reports of hospital patient care nurses in a survey cohort. All fatigue and adaptation variables demonstrated significant inverse relationships. Describing nurse fatigue in profiles that include measures of acute, chronic, physical, and mental fatigue dimensions provided a new and expanded view of nurse fatigue to monitor trends comprehensively and evaluate fatigue risk management strategies.

Analyzing the nursing organizational structure and process from a scheduling perspective

The efficient and effective management of nursing personnel is of critical importance in a hospital's environment comprising approximately 25 % of the hospital's operational costs. The nurse organizational structure and the organizational processes highly affect the nurses' working conditions and the provided quality of care. In this paper, we investigate the impact of different nurse organization structures and different organizational processes for a real-life situation in a Belgian university hospital. In order to make accurate nurse staffing decisions, the employed solution methodology incorporates shift scheduling characteristics in order to overcome the deficiencies of the many phase-specific methodologies that are proposed in the academic literature.

Hospital nurse force theory: a perspective of nurse fatigue and patient harm

This article is focused on the primary finding of the 2010 Institute of Medicine report asserting that nurses practice to the full extent of their education and training. An evolving theoretical perspective for hospital nursing practice is proposed as a basis for reaching this goal. This article describes the background and current factors influencing professional hospital nursing practice, presents a theoretical model for future research designed to optimize the power of hospital nursing practice, using a newly evolved concept of "nurse force," and discusses the implications of nurse force theory on perspectives of hospital nurse fatigue and patient harm.

Role stress amongst nurses at the workplace: concept analysis

AIM

The present study explicates the concept of role stress amongst nurses through an analysis adopted from Walker and Avant; Strategies for Theory Construction in Nursing, 4th edn, Prentice Hall, New Jersey, NY.

BACKGROUND

Role stress has become a significant problem amongst nurses and has created much distress leading to burnout among many in the nursing profession. It is significant to analyse the concept of role stress and its relative attributes and consequences, in order to recognize the necessary antecedents needed to create better conditions for nurses at the workplace.

EVALUATION

A modified method developed by Walker and Avant was used for this concept analysis.

KEY ISSUES

A model representing the concept of role stress was developed through careful consideration of the attributes, consequences, antecedents and empirical referents of role stress.

CONCLUSION

The concept analysis of role stress among nurses at the workplace recognized the vulnerability of the nursing discipline towards burnout and distress in general.

IMPLICATIONS FOR NURSING MANAGEMENT

It is critical to be aware of the current state of health care and note the increased workload created for nurses. Nurses are at a greater vulnerability for role stress, making it imperative for health care organizations to critically evaluate and establish preventative measures for the concept of role stress.

The production economics of nursing: A discussion paper

Nursing is numerically the largest health profession providing direct care, and this, plus the imperative for effective cost control, makes their costs and impact a legitimate study focus and policy target. Production theory techniques can help nurse executives maximize outcome and minimize costs, yet little of such evidence currently exists in mainstream nursing workforce research. The balance of available evidence supports an inverse association between nurse staffing levels and adverse outcomes. However, 'adequate' staffing levels may be perceived as expensive and some providers may try to reduce them. The response, in some US and Australian states, is legislation to force hospitals to implement mandatory minimum patient-to-nurse (P/N) ratios. In this paper, existing data from Aiken et al. [2003. Education levels of hospital nurses and patient mortality. Journal of the American Medical Association 290, 1617-1623] is re-interpreted using production theory, to illustrate the possible relationship between two key workforce variables "Staff Level" and "Staff Mix", and clinical outcome, and show how this informs decision making. Consistent with other studies, this suggests that diminishing returns to each variable exist. This preliminary analysis suggests that increasing the number of graduate RNs in the workforce might be the most cost-effective way to expand the nursing workforce. However, more detailed and rigorous research is needed to estimate speciality specific cost and production functions and compute the optimal solution. This can predict the most cost-effective staff combination for a set outcome, or the set of inputs yielding best outcome for a given budget. With this, nurse executives can systematically maintain service quality or safety in the most economical way.

Capacity management of nursing staff as a vehicle for organizational improvement

Background

Capacity management systems create insight into required resources like staff and equipment. For inpatient hospital care, capacity management requires information on beds and nursing staff capacity, on a daily as well as annual basis. This paper presents a comprehensive capacity model that gives insight into required nursing staff capacity and opportunities to improve capacity utilization on a ward level.

Methods

A capacity model was developed to calculate required nursing staff capacity. The model used historical bed utilization, nurse-patient ratios, and parameters concerning contract hours to calculate beds and nursing staff needed per shift and the number of nurses needed on an annual basis in a ward. The model was applied to three different capacity management problems on three separate groups of hospital wards. The problems entailed operational, tactical, and strategic management issues: optimizing working processes on pediatric wards, predicting the consequences of reducing length of stay on nursing staff required on a cardiology ward, and calculating the nursing staff consequences of merging two internal medicine wards.

Results

It was possible to build a model based on easily available data that calculate the nursing staff capacity needed daily and annually and that accommodate organizational improvements. Organizational improvement processes were initiated in three different groups of wards. For two pediatric wards, the most important improvements were found to be improving working processes so that the agreed nurse-patient ratios could be attained. In the second case, for a cardiology ward, what-if analyses with the model showed that workload could be substantially lowered by reducing length of stay. The third case demonstrated the possible savings in capacity that could be achieved by merging two small internal medicine wards.

Conclusion

A comprehensive capacity model was developed and successfully applied to support capacity decisions on operational, tactical, and strategic levels. It appeared to be a useful tool for supporting discussions between wards and hospital management by giving objective and quantitative insight into staff and bed requirements. Moreover, the model was applied to initiate organizational improvements, which resulted in more efficient capacity utilization.