Team Size and Composition in Home Healthcare: Quantitative Insights and Six Model-Based Principles.

The aim of this constructive study was to develop model-based principles to provide guidance to managers and policy makers when making decisions about team size and composition in the context of home healthcare. Six model-based principles were developed based on extensive data analysis and in close interaction with practice. In particular, the principles involve insights in capacity planning, travel time, available effective capacity, contract types, and team manageability. The principles are formalized in terms of elementary mathematical models that capture the essence of decision-making. Numerical results based on real-life scenarios reveal that efficiency improves with team size, albeit more prominently for smaller teams due to diminishing returns. Moreover, it is demonstrated that the complexity of managing and coordinating a team becomes increasingly more difficult as team size grows. An estimate for travel time is provided given the size and territory of a team, as well as an upper bound for the fraction of full-time contracts, if split shifts are to be avoided. Overall, it can be concluded that an ideally sized team should serve (at least) around a few hundreds care hours per week.

A three-step framework for capacity planning in a nursing home context.

This paper presents a three-step conceptual framework that can be used to structure the care-related capacity planning process in a nursing home context. The proposed framework provides a sound practical vehicle to organise client-centred care without overstretching available capacity. Within this framework, an MILP for shift scheduling and a Genetic Algorithm (GA) for task-scheduling are proposed. To investigate the performance of the proposed framework, it is benchmarked against the current situation. The results show that considerable improvements can be achieved in terms of efficiency and waiting time. More specifically, it is shown that very modest waiting times can be achieved without exceeding available capacity, despite the fluctuations in care demand across the day.

Avoiding Hospital Admissions and Delayed Transfers of Care by Improved Access to Intermediate Care: A Simulation Study.

OBJECTIVE: The current waiting times for intermediate care in the Netherlands prohibit timely access, leading to unwanted and costly hospital admissions. We propose alternative policies for improvement of intermediate care and estimate the effects on the waiting times, hospitalization, and the number of patient replacements. DESIGN: Simulation study. SETTING AND PARTICIPANTS: For our case study, data were used of older adults who received intermediate care in Amsterdam, the Netherlands, in 2019. For this target group, in- and outflows and patient characteristics were identified. METHODS: A process map of the main pathways into and out of the intermediate care was obtained and a discrete event simulation (DES) was built. We demonstrate the use of our DES for intermediate care by evaluating possible policy changes for a real-life case study in Amsterdam. RESULTS: By means of a sensitivity analysis with the DES, we show that in Amsterdam the waiting times are not a result of a lack in bed capacity but are due to an inefficient triage and application process. Older adults have to wait a median of 1.8 days for admission, leading to hospitalization. If the application process becomes more efficient and evening and weekend admissions are allowed, we find that unwanted hospitalization can be decreased substantially. CONCLUSION AND IMPLICATIONS: In this study, a simulation model is developed for intermediate care that can serve as a basis for policy decisions. Our case study shows that the waiting times for health care facilities are not always solved by increasing bed capacity. This underlines the necessity for a data-driven approach to identify logistic bottlenecks and find the best ways to solve them.

Modeling COVID-19 hospital admissions and occupancy in the Netherlands.

We describe the models we built for predicting hospital admissions and bed occupancy of COVID-19 patients in the Netherlands. These models were used to make short-term decisions about transfers of patients between regions and for long-term policy making. For forecasting admissions we developed a new technique using linear programming. To predict occupancy we fitted residual lengths of stay and used results from queueing theory. Our models increased the accuracy of and trust in the predictions and helped manage the pandemic, minimizing the impact in terms of beds and maximizing remaining capacity for other types of care.

Reduced Waiting Times by Preference-Based Allocation of Patients to Nursing Homes.

OBJECTIVES: The long waiting times for nursing homes can be reduced by applying advanced waiting-line management. In this article, we implement a preference-based allocation model for older adults to nursing homes, evaluate the performance in a simulation setting for 2 case studies, and discuss the implementation in practice. DESIGN: Simulation study. SETTING AND PARTICIPANTS: Older adults requiring somatic nursing home care, from an urban region (Rotterdam) and a rural region (Twente) in the Netherlands. METHODS: Data about nursing homes and capacities for the 2 case studies were identified. A set of preference profiles was defined with aims regarding waiting time preferences and flexibility. Guidelines for implementation of the model in practice were obtained by addressing the tasks of all stakeholders. Thereafter, the simulation was run to compare the current practice with the allocation model based on specified outcome measures about waiting times and preferences. RESULTS: We found that the allocation model decreased the waiting times in both case studies. Compared with the current practice policy, the allocation model reduced the waiting times until placement by at least a factor of 2 (from 166 to 80 days in Rotterdam and 178 to 82 days in Twente). Moreover, more of the older adults ended up in their preferred nursing home and the aims of the distinct preference profiles were satisfied. CONCLUSIONS AND IMPLICATIONS: The results show that the allocation model outperforms commonly used waiting-line policies for nursing homes, while meeting individual preferences to a larger extent. Moreover, the model is easy to implement and of a generic nature and can, therefore, be extended to other settings as well (eg, to allocate older adults to home care or daycare). Finally, this research shows the potential of mathematical models in the care domain for older adults to face the increasing need for cost-effective solutions.

Keeping pace with the ebbs and flows in daily nursing home operations.

Nursing homes are challenged to develop staffing strategies that enable them to efficiently meet the healthcare demand of their residents. In this study, we investigate how demand for care and support fluctuates over time and during the course of a day, using demand data from three independent nursing home departments of a single Dutch nursing home. This demand data is used as input for an optimization model that provides optimal staffing patterns across the day. For the optimization we use a Lindley-type equation and techniques from stochastic optimization to formulate a Mixed-Integer Linear Programming (MILP) model. The impact of both the current and proposed staffing patterns, in terms of waiting time and service level, are investigated. The results show substantial improvements for all three departments both in terms of average waiting time as well as in 15 minutes service level. Especially waiting during rush hours is significantly reduced, whereas there is only a slight increase in waiting time during non-rush hours.

Queues on a Dynamically Evolving Graph.

This paper considers a population process on a dynamically evolving graph, which can be alternatively interpreted as a queueing network. The queues are of infinite-server type, entailing that at each node all customers present are served in parallel. The links that connect the queues have the special feature that they are unreliable, in the sense that their status alternates between 'up' and 'down'. If a link between two nodes is down, with a fixed probability each of the clients attempting to use that link is lost; otherwise the client remains at the origin node and reattempts using the link (and jumps to the destination node when it finds the link restored). For these networks we present the following results: (a) a system of coupled partial differential equations that describes the joint probability generating function corresponding to the queues' time-dependent behavior (and a system of ordinary differential equations for its stationary counterpart), (b) an algorithm to evaluate the (time-dependent and stationary) moments, and procedures to compute user-perceived performance measures which facilitate the quantification of the impact of the links' outages, (c) a diffusion limit for the joint queue length process. We include explicit results for a series relevant special cases, such as tandem networks and symmetric fully connected networks.

Flexible bed allocations for hospital wards.

Flexibility in the usage of clinical beds is considered to be a key element to efficiently organize critical capacity. However, full flexibility can have some major drawbacks as large systems are more difficult to manage, lack effective care delivery due to absence of focus and require multi-skilled medical teams. In this paper, we identify practical guidelines on how beds should be allocated to provide both flexibility and utilize specialization. Specifically, small scale systems can often benefit from full flexibility. Threshold type of control is then effective to prioritize patient types and to cope with patients having diverse lengths of stay. For large scale systems, we assert that a little flexibility is generally sufficient to take advantage of most of the economies of scale. Bed reservation (earmarking) or, equivalently, organizing a shared ward of overflow, then performs well. The theoretical models and guidelines are illustrated with numerical examples. Moreover, we address a key question stemming from practice: how to distribute a fixed number of hospital beds over the different units?

Care on demand in nursing homes: a queueing theoretic approach.

Nursing homes face ever-tightening healthcare budgets and are searching for ways to increase the efficiency of their healthcare processes without losing sight of the needs of their residents. Optimizing the allocation of care workers plays a key role in this search as care workers are responsible for the daily care of the residents and account for a significant proportion of the total labor expenses. In practice, the lack of reliable data makes it difficult for nursing home managers to make informed staffing decisions. The focus of this study lies on the 'care on demand' process in a Belgian nursing home. Based on the analysis of real-life 'call button' data, a queueing model is presented which can be used by nursing home managers to determine the number of care workers required to meet a specific service level. Based on numerical experiments an 80/10 service level is proposed for this nursing home, meaning that at least 80 percent of the clients should receive care within 10 minutes after a call button request. To the best of our knowledge, this is the first attempt to develop a quantitative model for the 'care on demand' process in a nursing home.

Scheduling admissions and reducing variability in bed demand.

Variability in admissions and lengths of stay inherently leads to variability in bed occupancy. The aim of this paper is to analyse the impact of these sources of variability on the required amount of capacity and to determine admission quota for scheduled admissions to regulate the occupancy pattern. For the impact of variability on the required number of beds, we use a heavy-traffic limit theorem for the G/G/∞ queue yielding an intuitively appealing approximation in case the arrival process is not Poisson. Also, given a structural weekly admission pattern, we apply a time-dependent analysis to determine the mean offered load per day. This time-dependent analysis is combined with a Quadratic Programming model to determine the optimal number of elective admissions per day, such that an average desired daily occupancy is achieved. From the mathematical results, practical scenarios and guidelines are derived that can be used by hospital managers and support the method of quota scheduling. In practice, the results can be implemented by providing admission quota prescribing the target number of admissions for each patient group.