A network model for nursing staff scheduling

The staffing of hospital nurses has become critical in recent years. As a means of containing skyrocketing costs, many hospitals are reducing nursing staff to a bare minimum. At the same time, the hospitals must maintain some minimal staffing level as insufficient staff could lead to a life threatening situation possibly with detrimental social, economic, and legal consequences. This article will present a model which can be used to determine the optimal scheduling of nursing staff under varying conditions. A typical problem will illustrate its use.     

Literature review on multi-appointment scheduling problems in hospitals

This paper presents a review of the literature on multi-appointment scheduling problems in hospitals. In these problems, patients need to sequentially visit multiple resource types in a hospital setting so they can receive treatment or be diagnosed. Therefore, each patient is assigned a specific path over a subset of the considered resources and each step needs to be scheduled. The main aim of these problems is to let each patient visit the resources in his or her subset within the allotted time to receive timely care. This is important because a delayed diagnosis or treatment may result in adverse health effects. Additionally, with multi-appointment scheduling, hospitals have the opportunity to augment patient satisfaction, allowing the patient to visit the hospital less frequently. To structure the growing body of literature in this field and aid researchers in the field, a classification scheme is proposed and used to classify the scientific work on multi-appointment scheduling in hospitals published before the end of 2017. The results show that multi-appointment scheduling problems are becoming increasingly popular. In fact, multi-appointment scheduling problems in hospitals are currently gaining progressively more momentum in the academic literature.     

The impact of incorporating nurse-specific characteristics in a cyclical scheduling approach

Nursing staff in various hospitals in Belgium are principally cyclically scheduled. The employed cyclic schedules embody, however, only a weak reflection of the ultimate nurse rosters constructed for a specific month. In this paper, we investigate the benefits of integrating nurse-specific characteristics in the cyclic scheduling approach. Moreover, we analyse to what extent these characteristics should be incorporated and compare this approach with a general and more robust cyclical scheduling approach and the flexible acyclical rostering of nursing personnel.     

Impact of productivity on cross-training configurations and optimal staffing decisions in hospitals

Cross-training of nursing staff has been used in hospitals to reduce labor cost, provide scheduling flexibility, and meet patient demand effectively. However, cross-trained nurses may not be as productive as regular nurses in carrying out their tasks because of a new work environment and unfamiliar protocols in the new unit. This leads to the research question: What is the impact of productivity on optimal staffing decisions (both regular and cross-trained) in a two-unit and multi-unit system. We investigate the effect of mean demand, cross-training cost, contract nurse cost, and productivity, on a two-unit, full-flexibility configuration and a three-unit, partial flexibility and chaining (minimal complete chain) configurations under centralized and decentralized decision making. Under centralized decision making, the optimal staffing and cross-training levels are determined simultaneously, while under decentralized decision making, the optimal staffing levels are determined without any knowledge of future cross-training programs. We use two-stage stochastic programming to derive closed form equations and determine the optimal number of cross-trained nurses for two units facing stochastic demand following general, continuous distributions. We find that there exists a productivity level (threshold) beyond which the optimal number of cross-trained nurses declines, as fewer cross-trained nurses are sufficient to obtain the benefit of staffing flexibility. When we account for productivity variations, chaining configuration provides on average 1.20% cost savings over partial flexibility configuration, while centralized decision making averages 1.13% cost savings over decentralized decision making.     

The Impact of Teaching on Hospital Costs: A Budgetary Approach to Non-market Institutions

NHS hospitals contribute to medical education, training nurses and research, as well as to the care of patients. In the past they have been funded largely on the basis of resources employed, with additional funding for medical education and training nurses. The intellectual basis for the funding of medical education is a single econometric study of English hospitals in the financial year 1969-70. The methodology used has since been criticized, and it has been suggested that actual expenditure has been very much less than that earmarked by the health departments. New estimates are obtained using Scottish data for the financial year 1985-86. The method used is to proceed in a two-stage fashion, identifying via regression techniques variables measuring hospital activity and resources which contribute significantly to hospital costs. We then assess the significance of medical education, nurse training and hospitals' teaching status against this background. Our conclusions include: (1) actual expenditure on medical education was probably less than the funding formula allowed, but the error of margin is too large to suggest overfunding; (2) training nurses incurs significant financial costs, even after the explicit allowances made; and (3), major teaching hospitals tended to cost more, but not significantly more than their non-teaching counterparts. These financial implications for NHS hospitals should be borne in mind given the current NHS review.     

Dimensioning hospital wards using the Erlang loss model

How many beds must be allocated to a specific clinical ward to meet production targets? When budgets get tight, what are the effects of downsizing a nursing unit? These questions are often discussed by medical professionals, hospital consultants, and managers. In these discussions the occupancy rate is of great importance and often used as an input parameter. Most hospitals use the same target occupancy rate for all wards, often 85%. Sometimes an exception is made for critical care and intensive care units. In this paper we demonstrate that this equity assumption is unrealistic and that it might result in an excessive number of refused admissions, particularly for smaller units. Queuing theory is used to quantify this impact. We developed a decision support system, based on the Erlang loss model, which can be used to evaluate the current size of nursing units. We validated this model with hospital data over the years 2004–2006. Finally, we demonstrate the efficiency of merging departments.     

Suitability and managerial implications of a Master Surgical Scheduling approach

Operating room (OR) planning and scheduling is a popular and challenging subject within the operational research applied to health services research (ORAHS). However, the impact in practice is very limited. The organization and culture of a hospital and the inherent characteristics of its processes impose specific implementation issues that affect the success of planning approaches. Current tactical OR planning approaches often fail to account for these issues. Master surgical scheduling (MSS) is a promising approach for hospitals to optimize resource utilization and patient flows. We discuss the pros and cons of MSS and compare MSS with centralized and decentralized planning approaches. Finally, we address various implementation issues of MSS and discuss its suitability for hospitals with different organizational foci and culture.     

An Implicit Tour Scheduling Model with Applications in Healthcare

Motivated by difficult staff scheduling problems arising in healthcare institutions, we have developed an implicit tour scheduling model which includes full and part-time tour types as well as intra-tour start time flexibility. Potential benefits of intra-tour start time flexibility are demonstrated through a computational experiment. The model has been embedded in a decision support system at a large tertiary care hospital and has been used in numerous studies to help estimate staffing needs and to analyze the impact of scheduling policies and practices.     

Nursing workload measurement as management information

Goal of the study presented in this paper was to balance the supply and demand of nursing care at nursing units within general hospitals. A ‘management control framework’ is developed, containing the relevant decision levels, the goal variable and the information needed to control the balance between supply and demand. A nursing workload measurement instrument is introduced, and an experiment is set up to test the performance of the framework and the measurement system in the daily practice of eight nursing units in two hospitals, during 20 consecutive weeks. Intervention has taken place in both the staffing and patient planning processes. The effects upon the goal variable has been measured. The variation coefficient of the work pressure is used as an indicator for the stability of the balance. The results of the experiment are presented.     

The federal nursing minimum basic data set and hospital management in Belgium: A case study of a nursing department

Since the introduction of the Nursing Minimum Data Set on a nationwide basis in 1988, this nursing care information system has been used by the government, in defining hospitals budgets, as well as by individual hospitals, in their nursing management. The article is focusing on the information and communication tools the NMDS inherates. The case study illustrates the typical approach of the NMDS for the management of personal resources in hospitals.     

System dynamics applications to European health care issues

Taking a European perspective, a review is made of some system dynamics models which address health care issues. Suggestions are made for the types of role which these models should take, bearing in mind the strategic orientation of system dynamics modelling. Examples are described of qualitative models where influence diagrams are the main analytical tool. Quantitative system dynamics models have a contribution to make in epidemiological studies and have been used to analyse the AIDS epidemic. A detailed example of one aspect of model formulation is given. This concerns the AIDS incubation time distribution and shows how real-world complications arising from virological staging and treatment effects are handled in a model of AIDS spread.     

A branch-and-price approach for integrating nurse and surgery scheduling

A common problem at hospitals is the extreme variation in daily (even hourly) workload pressure for nurses. The operating room is considered to be the main engine and hence the main generator of variance in the hospital. The purpose of this paper is threefold. First of all, we present a concrete model that integrates both the nurse and the operating room scheduling process. Second, we show how the column generation technique approach, one of the most employed exact methods for solving nurse scheduling problems, can easily cope with this model extension. Third, by means of a large number of computational experiments we provide an idea of the cost saving opportunities and required solution times.     

Assigning patients to nurses in neonatal intensive care

An intensive care nursery provides health care for critically ill newborn infants. During a typical shift, infants range from those needing only occasional care to those requiring constant attention. At the beginning of each shift, the head nurse groups the patients for assignment to staff nurses. Typically each nurse cares for one group of infants throughout the shift. The large variation in infant conditions along with several complicating side constraints makes it difficult to develop balanced nurse work loads. We develop a mathematical programming approach for achieving better workload balance. We first develop a detailed neonatal acuity system that quantifies the nursing workload of each patient. We then develop an integer linear program that assigns patients to nurses while balancing nurse workloads. Because this model is computationally intractable, we develop a heuristic that exploits the fact that most nurseries are divided into a number of physical zones. We use ten case studies taken from a major university hospital to benchmark the performance of this heuristic. We also perform a designed experiment using randomly generated problems that examines the effect of nursery parameters on heuristic performance.     

A subproblem-centric model and approach to the nurse scheduling problem

The number of hospitals in Japan exceeds 10,000, and every month nurses are scheduled to shifts in about 30,000 units in total. There is serious demand for automating this scheduling task. In this paper, we introduce a mathematical programming formulation of the nurse scheduling problem in Japan, and develop a meta-heuristic approach to solve the problem. This scheduling problem is a hard combinatorial problem due to tight constraints involving such factors as the skill level of a team, the need to balance workload among nurses, and the consideration of nurses' preferences, even though the number of the nurses to be scheduled is not large, at between 20 and 40. The performance of our approach is demonstrated by the successful solution of data taken from actual scheduling problems. The proposed model and approach can be adapted for the majority of hospitals in Japan, as well as for some hospitals in other countries, and is likely applicable to many other scheduling problems in the fields of business and logistics. Key words.nurse scheduling – block-angular problem – subproblem – integer programming – relaxation – tabu search – branch-and-boundMathematics Subject Classification (1991):20E28, 20G40, 20C20     

Incorporating health outcomes in Pennsylvania hospital efficiency: an additive super-efficiency DEA approach

The health care sector is one of the fastest growing sectors in the United States. Researchers are interested in conducting studies in the area of health economics in order to propose solutions to curb the rapid increase in health care spending and to improve the efficiency of the health care system in the United States. Specifically, hospital efficiency is one important research area in health economics. In this paper, data envelopment analysis (DEA) is used to assess hospital efficiency. An additive super-efficiency model is presented and applied to a sample of general acute care hospitals in Pennsylvania. In addition to the conventional choice of input and output variables, we include the survival rate as a quality measure of health outcome in the set of output variables. Thus our model takes both the quantity and the quality of the output into account. With the results obtained from our proposed DEA model, inefficiencies can be identified for hospitals to address without sacrificing the quality of care.     

The utility of returns to scale in DEA programming: An analysis of Michigan rural hospitals

In 1984, Banker, Charnes, and Cooper introduced the capability of using data envelopment analysis to assess increasing, decreasing, or constant returns to scale. This analysis would appear to make an important contribution to the health care field because of the regulatory environment within which the industry exists and the competition among hospitals for additional services and capacity. In many states, hospitals must submit a “certificate of need” to prove eligibility to add capacity or services. Agency administrators at the state level should analyze each hospital's production performance to determine the effectiveness of resource utilization. Residents of a state where hospitals are regulated need to know the effectiveness of agencies in allowing resources to be properly allocated to hospitals. Returns to scale analysis can help provide answers to these concerns. We examine Michigan rural hospitals and propose a simple, yet logical procedure for evaluating returns to scale for technically inefficient hospitals.     

Administrative days in acute care facilities: a queueing-analytic approach.

After acute care services are no longer required, a patient in an acute care hospital often must remain there while he or she awaits the provision of extended care services by a nursing home, through social support services, or by a home health care service. This waiting period is often referred to as "administrative days" because the time is spent in the acute facility not for medical reasons, but rather for administrative reasons. In this paper we use a queueing-analytic approach to describe the process by which patients await placement. We model the situation using a state-dependent placement rate for patients backed up in the acute care facility. We compare our model results with data collected from a convenience sample of 7 hospitals in New York State. We conclude with a discussion of the policy implications of our models.     

Using system dynamics principles for conceptual modelling of publicly funded hospitals

This paper examines the long-standing operational issue of patients boarding in the emergency department (ED), who have been admitted to hospital (inpatient ‘boarders’). From this analysis we design a conceptual model that provides a roadmap to create sustainable improvements in ED waiting times. The conceptual model is built using system dynamics methodology, and illustrates the use of system archetypes, a set of common causal feedback loops that illustrate how well-intended decisions have unintentional side effects. This paper outlines the journey taken by one large academic health centre to address these issues, and highlights the larger implications and recommendations that are applicable to other publicly funded hospitals.