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

Legislators at the state and national levels are addressing renewed concerns over the adequacy of hospital nurse staffing to provide quality care and ensure patient safety. At the same time, the well‐known nursing shortage remains an ongoing problem. To address these issues, we reexamine the nurse scheduling problem and consider how recent health care legislation impacts nursing workforce management decisions. Specifically, we develop a scheduling model and perform computational experiments to evaluate how mandatory nurse‐to‐patient ratios and other policies impact schedule cost and schedule desirability (from the nurses' perspective). Our primary findings include the following: (i) nurse wage costs can be highly nonlinear with respect to changes in mandatory nurse‐to‐patient ratios of the type being considered by legislators; (ii) the number of undesirable shifts can be substantially reduced without incurring additional wage cost; (iii) more desirable scheduling policies, such as assigning fewer weekends to each nurse, have only a small impact on wage cost; and (iv) complex policy statements involving both single‐period and multiperiod service levels can sometimes be relaxed while still obtaining good schedules that satisfy the nurse‐to‐patient ratio requirements. The findings in this article suggest that new directions for future nurse scheduling models, as it is likely that nurse‐to‐patient ratios and nursing shortages will remain a challenge for health care organizations for some time.     

An integrated nurse staffing and scheduling analysis for longer-term nursing staff allocation problems

The efficient and effective management of nursing personnel is of critical importance in a hospital's environment comprising a vast share of the operational costs. The adopted nurse workforce practices and policies highly affect the nurses' working conditions and the provided quality of care. Policy decisions on the staffing level have an impact on the outcome of the scheduling level and vice versa. Isolated reasoning typically leads to suboptimal decisions often resulting in ineffective outcomes of care. In order to overcome these inefficiencies, we propose in this paper a new integrative nurse staffing and shift scheduling approach. We test and assess the benefits of our approach in a reallife environment. Moreover, we examine the impact of several personnel policies on the staffing decision.     

Strategies for Addressing the Nursing Shortage: Coordinated Decision Making and Workforce Flexibility

In this article, we present strategies to help combat the U.S. nursing shortage. Key considerations include providing an attractive work schedule and work environment—critical issues for retaining existing nurses and attracting new nurses to the profession—while at the same time using the set of available nurses as effectively as possible. Based on these ideas, we develop a model that takes advantage of coordinated decision making when managing a flexible workforce. The model coordinates scheduling, schedule adjustment, and agency nurse decisions across various nurse labor pools, each of differing flexibility levels, capabilities, and costs, allowing a much more desirable schedule to be constructed. Our primary findings regarding coordinated decision making and how it can be used to help address the nursing shortage include (i) labor costs can be reduced substantially because, without coordination, labor costs on average are 16.3% higher based on an actual hospital setting, leading to the availability of additional funds for retaining and attracting nurses, (ii) simultaneous to this reduction in costs, more attractive schedules can be provided to the nurses in terms of less overtime and fewer undesirable shifts, and (iii) the use of agency nurses can help avoid overtime for permanent staff with only a 0.7% increase in staffing costs. In addition, we estimate the cost of the shortage for a typical U.S. hospital from a labor cost perspective and show how that cost can be reduced when managers coordinate.     

Centralized nurse scheduling to simultaneously improve schedule cost and nurse satisfaction

Nursing managers are faced with rising turnover and shortages of qualified nursing staff. At the same time they are under increased pressure to simultaneously increase patient care and satisfaction while reducing costs. In this study, we examine the impact of centralizing scheduling decisions across departments in a hospital. By pooling nurses from multiple units and scheduling them in one model, improved costs and reduced overtime result. Reduced overtime improves schedules for nurses. Improved satisfaction levels can positively impact turnover rates among nurses. Our results show that by using a centralized model, nursing managers in hospitals can improve the desirability of nurse schedules by approximately 34% and reduce overtime by approximately 80% while simultaneously reducing costs by just under 11%.     

Centralized nurse scheduling to simultaneously improve schedule cost and nurse satisfaction

Nursing managers are faced with rising turnover and shortages of qualified nursing staff. At the same time they are under increased pressure to simultaneously increase patient care and satisfaction while reducing costs. In this study, we examine the impact of centralizing scheduling decisions across departments in a hospital. By pooling nurses from multiple units and scheduling them in one model, improved costs and reduced overtime result. Reduced overtime improves schedules for nurses. Improved satisfaction levels can positively impact turnover rates among nurses. Our results show that by using a centralized model, nursing managers in hospitals can improve the desirability of nurse schedules by approximately 34% and reduce overtime by approximately 80% while simultaneously reducing costs by just under 11%.     

A Stochastic Goal Program for Employee Scheduling*

Deterministic goal programs for employee scheduling decisions attempt to minimize expected operating costs by assigning the ideal number of employees to each feasible schedule. For each period in the planning horizon, managers must first determine the amount of labor that should be scheduled for duty. These requirements are often established with marginal analysis techniques, which use estimates for incremental labor costs and shortage expenses. Typically, each period in the planning horizon is evaluated as an independent epoch. An implicit assumption is that individual employees can be assigned to schedules with as little as a single period of work. If this assumption violates local work rules, the labor requirements parameters for the deterministic goal program may be suboptimal. As we show in this research, this well-known limitation can lead to costly staffing and scheduling errors. We propose an employee scheduling model that overcomes this limitation by integrating the labor requirements and scheduling decisions. Instead of a single, externally determined staffing goal for each period, the model uses a probability distribution for the quantity of labor required. The model is free to choose an appropriate staffing level for each period, eliminating the need for a separate goal-setting procedure. In most cases this results in better, less costly decisions. In addition, the proposed model easily accommodates both linear and nonlinear under- and overstaffing penalties. We use simple examples to demonstrate many of these advantages and to illustrate the key techniques necessary to implement our model. We also assess its performance in a study of more than 1,700 simulated stochastic employee scheduling problems.     

Reconstructing nurse schedules: Computational insights in the problem size parameters

Managing nursing personnel properly is of critical importance as these resources comprise a vast share of the hospital's operational costs. The organisational support and the managerial policy decisions on the scheduling level are important determinants for the nurses' working conditions and the related quality of care. In this paper, we gain insights and understanding in the consequences and outcomes of various personnel re-rostering characteristics and strategies. We explore the boundaries of the time horizon and the nurse staffing size to consider for the nurse re-rostering problem based on computational experiments in a real-life problem environment.     

Staffing a Multiskilled Workforce with Varying Levels of Productivity: An Analysis of Cross-training Policies*

Service operations that utilize cross-trained employees face complex workforce staffing decisions that have important implications for both cost and productivity. These decisions are further complicated when cross-trained employees have different productivity levels in multiple work activity categories. A method for policy analysis in such environments can be beneficial in determining low-cost staffing plans with appropriate cross-training configurations. In this paper, we present an integer linear programming model for evaluating cross-training configurations at the policy level. The objective of the model is to minimize workforce staffing costs subject to the satisfaction of minimum labor requirements across a planning horizon of a single work shift. The model was used to evaluate eight cross-training structures (consisting of 36 unique cross-training configurations) across 512 labor requirement patterns. These structures, as well as the labor requirement patterns, were established based on data collected from maintenance operations at a large paper mill in the United States. The results indicate that asymmetric cross-training structures that permit chaining of employee skill classes across work activity categories are particularly useful.     

COMPARISON OF NURSE ALLOCATION POLICIES-A MONTE CARLO MODEL*

Many hospitals have historically used a fixed staffing policy for allocating nursing personnel, in which the daily demand in each ward is met by nurses who are permanently assigned to the specific wards. In recent years, the concept of variable staffing has been proposed as a means of increasing manpower efficiency. A variable staffing policy is one which provides for staffing adjustments to meet work load through the use of a common pool of cross-trained nurses. In this paper, a model is formulated to evaluate the relative benefits of variable and fixed staffing policies. Results from a Monte Carlo evaluation of the model demonstrate how the hospital administrator can assess the sensitivity of savings to changes in policy and operating parameters. Several criteria which an administrator might adopt for equating levels of patient care under alternative staffing schemes are suggested and studied. The proposed method of analyzing benefits of alternative allocation procedures shows promise for evaluating policy choices in hospitals, as well as other service organizations with similar characteristics.     

Home healthcare integrated staffing and scheduling

Workforce planning for home healthcare represents an important and challenging task involving complex factors associated with labor regulations, caregivers’ preferences, and demand uncertainties. This task is done manually by most home care agencies, resulting in long planning times and suboptimal decisions that usually fail to meet the health needs of the population, to minimize operating costs, and to retain current caregivers. Motivated by these challenges, we present a two-stage stochastic programming model for employee staffing and scheduling in home healthcare. In this model, first-stage decisions correspond to the staffing and scheduling of caregivers in geographic districts. Second-stage decisions are related to the temporary reallocation of caregivers to neighboring districts, to contact caregivers to work on a day-off, and to allow under- and over-covering of demand. The proposed model is tested on real-world instances, where we evaluate the impact on costs, caregiver utilization, and service level by using different recourse actions. Results show that when compared with a deterministic model, the two-stage stochastic model leads to significant cost savings as staff dimensioning and scheduling decisions are more robust to accommodate changes in demand. Moreover, these results suggest that flexibility in terms of use of recourse actions is highly valuable as it helps to further improve costs, service level, and caregiver utilization.     

Service Completion Estimates for Cross‐trained Workforce Schedules under Uncertain Attendance and Demand

Although cross‐trained workers offer numerous operational advantages for extended‐hour service businesses, they must first be scheduled for duty. The outcome from those decisions, usually made a week or more in advance, varies with realized service demand, worker attendance, and the way available cross‐trained workers are deployed once the demands for service are known. By ignoring the joint variability of attendance and demand, we show that existing workforce scheduling models tend to overstate expected schedule performance and systematically undervalue the benefits of cross‐training. We propose a two‐stage stochastic program for profit‐oriented cross‐trained workforce scheduling and allocation decisions that is driven by service completion estimates obtained from the convolution of the employee attendance and service demand distributions. Those estimates, reflecting optimal worker allocation decisions over all plausible realizations of attendance and demand, provide the gradient information used to guide workforce scheduling decisions. Comparing the performance of workforce scheduling decisions for hundreds of different hypothetical service environments, we find that solutions based on convolution estimates are more profitable, favor proportionately more cross‐trained workers and fewer specialists, and tend to recommend significantly larger (smaller) staffing levels for services under high (low) contribution margins than workforce schedules developed with independent expectations of attendance and demand.     

Time‐Staged Overtime Staffing for Services with Updated Forecasts and Availabilities

This article develops a framework for staffing in a service environment when multiple opportunities exist for prescheduling overtime prior to the start of a shift. Demand forecasts improve as the shift approaches, while the availability of workers to be scheduled for overtime decreases. First, a single‐shift model is developed and used in computational studies to evaluate the benefits of time‐staged overtime staffing, which include slightly lower costs and significant reductions in unscheduled overtime and outside agents. A multishift model is then developed to consider constraints on consecutive hours worked and minimum rest intervals between shifts. A multishift computational study shows how the benefits of time‐staged overtime staffing depend on problem characteristics when interactions between shifts are considered. The article discusses how single‐shift and multishift models relate to each other and alternative ways the models may be used in practice, including decentralized open shift management and centralized overtime scheduling.     

Emergency Department Staff Planning to Improve Patient Care and Reduce Costs

In the face of high staffing costs, uncertain patient arrivals, and patients unsatisfied with long wait times, staffing of medical emergency departments (EDs) is a vexing problem. Using empirical data collected from three active EDs, we develop an analytic model to provide an effective staffing plan for EDs. Patient demand is aggregated into discrete time buckets and used to model the stochastic distribution of patient demand within these buckets, which considerably improves model tractability. This model is capable of scheduling providers with different skill profiles who work either individually or in teams, and with patients of varying acuity levels. We show how our model helps to balance staffing costs and patient service levels, and how it facilitates examination of important ED staffing policies.     

Schedule Recovery: Unplanned Absences in Service Operations*

The U.S. service sector loses 2.3% of all scheduled labor hours to unplanned absences, but in some industries, the total cost of unplanned absences approaches 20% of payroll expense. The principal reasons for unscheduled absences (personal illness and family issues) are unlikely to abate anytime soon. Despite this, most labor scheduling systems continue to assume perfect attendance. This oversight masks an important but rarely addressed issue in services management: how to recover from short‐notice, short‐term reductions in planned capacity. In this article, we model optimal responses to unplanned employee absences in multi‐server queueing systems that provide discrete, pay‐per‐use services for impatient customers. Our goal is to assess the performance of alternate absence recovery strategies under various staffing and scheduling regimes. We accomplish this by first developing optimal labor schedules for hypothetical service environments with unreliable workers. We then simulate unplanned employee absences, apply an absence recovery model, and compute system profits. Our absence recovery model utilizes recovery strategies such as holdover overtime, call‐ins, and temporary workers. We find that holdover overtime is an effective absence recovery strategy provided sufficient reserve capacity (maximum allowable work hours minus scheduled hours) exists. Otherwise, less precise and more costly absence recovery methods such as call‐ins and temporary help service workers may be needed. We also find that choices for initial staffing and scheduling policies, such as planned overtime and absence anticipation, significantly influence the likelihood of successful absence recovery. To predict the effectiveness of absence recovery policies under alternate staffing/scheduling strategies and operating environments, we propose an index based on initial capacity reserves.     

On‐Call Overtime for Service Workforce Scheduling when Demand Is Uncertain

This article builds on prior research to develop shift scheduling models that include on‐call overtime for service environments where demand is uncertain. The research is motivated by recent developments in nurse scheduling, such as laws prohibiting mandatory overtime and the popularity of self‐scheduling systems. For single‐period scenarios, models are developed, solution methods are described, and results are explored for a variety of environments. Results show that the use of on‐call overtime can reduce costs slightly, with the amount of savings dependent on characteristics of the scheduling environment. The factor that most significantly affects cost savings is the cost of outside agency workers relative to overtime workers. In addition to lowering costs, on‐call overtime greatly reduces reliance on outside agency workers, which can have important practical implications in terms of quality of service and workforce morale. Results based on single‐period models motivate multiperiod formulations for single‐ and multidepartment scenarios, and solution methods are outlined for those cases. The possibility of using multiperiod models within a rolling horizon framework with forecast updating is discussed. This goes along with an extension of the traditional workforce management hierarchy that separates overtime and regular‐time scheduling, as seen in practice with self‐scheduling and shift‐bidding systems.     

Sequential and Simultaneous Decision Making for Optimizing Health Care Resource Flexibilities

Health care administrators commonly employ two types of resource flexibilities (demand upgrades and staffing flexibility) to efficiently coordinate two critical internal resources, nursing staff and beds, and an external resource (contract nurses) to satisfy stochastic patient demand. Under demand upgrades, when beds are unavailable for patients in a less acute unit, patients are upgraded to a more acute unit if space is available in that unit. Under staffing flexibility, nurses cross‐trained to work in more than one unit are used in addition to dedicated and contract nurses. Resource decisions (beds and staffing) can be made at a single point in time (simultaneous decision making) or at different points in time (sequential decision making). In this article, we address the following questions: for each flexibility configuration, under sequential and simultaneous decision making, what is the optimal resource level required to meet stochastic demand at minimum cost? Is one type of flexibility (e.g., demand upgrades) better than the other type of flexibility (e.g., staffing flexibility)? We use two‐stage stochastic programming to find optimal resource levels for two nonhomogeneous hospital units that face stochastic demand following a continuous, general distribution. We conduct a full‐factorial numerical experiment and find that the benefit of using staffing flexibility on average is greater than the benefit of using demand upgrades. However, the two types of flexibilities have a positive interaction effect and they complement each other. The type of flexibility and decision timing has an independent effect on system performance (capacity and staffing costs). The benefits of cross‐training can be largely realized even if beds and staffing levels have been determined prior to the establishment of a cross‐training initiative.     

Optimal and dysfunctional turnover: toward an organizational level model

Dysfunctional turnover is defined here as the level that produces a divergence between the organization's optimal balance of costs associated with turnover and the costs associated with retaining employees. Under this approach, the optimal level of aggregate turnover for most organizations will be (1) greater than zero and (2) variable across organizations, contingent on particular factors influencing retention costs and quit propensities. The model presented posits that individual, organizational, and environmental attributes influence individual quit propensities of employees and, hence, expected turnover rates for the organization.     

Representing employee requirements in labour tour scheduling

In this paper, we use the methodology of simulation to evaluate six approaches for handling employee requirements in an LP-based labour tour scheduling heuristic. We model employee requirements both as minimum acceptable staffing levels—where understaffing is unacceptable—and as target staffing levels—where both under- and overstaffing are acceptable. For each representation of employee requirements, we evaluate forms of the heuristic that use problem-specific and problem-independent information on the costs of employee surpluses and, if appropriate, employee shortages. Over an extensive test data set, the target-staffing approach using problem-specific cost information outperformed all other procedures. Specifically, it generated schedules costing less than 87% of those developed using the approach most commonly found in the literature. Its schedules were also almost 5% cheaper than those of its closest competitor. We discuss the managerial and research implications of the findings and provide suggestions for future research.     

International Migration Dynamics: The Role of Experience and Social Networks

This paper tests the dynamic implications of cumulative causation and network theory on the self‐sustaining nature of the migration process. A sequential migration model is derived and estimated with a panel of Mexican household heads for the years 1980–89. Consistently with cumulative causation and network theory, the empirical results show that, after controlling for unobserved heterogeneity, previous migration experience and migration‐related variables are the strongest predictors of current migration decisions. This persistence in migration patterns implies that immigration policies inducing small changes in expected costs and benefits of US work fail to prevent entry into, or encourage exit from, the US labor market by experienced migrants. However, large temporary disruptions such as the 1994 Mexican peso devaluation may permanently increase migratory flows by inducing new migrants to enter the US labor market.     

A SYSTEMS PERSPECTIVE ON MATERIAL REQUIREMENTS PLANNING*

For many companies, the implementation of material requirements planning systems has failed to produce the expected improvements in manufacturing efficiency. This paper shows that MRP failure can occur in the common situation in which MRP is installed in a manufacturing environment that has evolved around manual methods of material control. A system dynamics simulation model is used to interrelate decision functions (policies) of a manufacturing firm. Simulation runs of the model operating with manual methods of material control show six- to seven-year fluctuations in production, ordering, and labor. A modified version of the model, changed only by the introduction of a requirements explosion to represent MRP, shows that MRP can actually cause more severe production fluctuations, resulting in lower average labor productivity and higher manufacturing costs. The major practical implication of the analysis is that the organizational environment that suits MRP (and utilizes its inherent strengths) is different from the environment that is likely to prevail at the time of implementation.