Practical experience with bed occupancy management and planning systems: an Australian view

Queueing Problems in Emergency Departments: A Review of Practical Approaches and Research Methodologies

Problems related to patient scheduling and queueing in emergency departments are gaining increasing attention in theory, in the fields of operations research and emergency and healthcare services, and in practice. This paper aims to provide an extensive review of studies addressing queueing-related problems explicitly related to emergency departments. We have reviewed 229 articles and books spanning seven decades and have sought to organize the information they contain in a manner that is accessible and useful to researchers seeking to gain knowledge on specific aspects of such problems. We begin by presenting a historical overview of applications of queueing theory to healthcare-related problems. We subsequently elaborate on managerial approaches used to enhance efficiency in emergency departments. These approaches include bed management, fast-track, dynamic resource allocation, grouping/prioritization of patients, and triage approaches. Finally, we discuss scientific methodologies used to analyze and optimize these approaches: algorithms, priority models, queueing models, simulation, and statistical approaches.

Evaluating medical capacity for hospitalization and intensive care unit of COVID-19: A queue model approach

BACKGROUND

The surge of COVID-19 pandemic has caused severe respiratory conditions and a large number of deaths due to the shortage of intensive care unit (ICU) in many countries.

METHODS

We developed a compartment queue model to describe the process from case confirmation, home-based isolation, hospitalization, ICU, recovery, and death. By using public assessed data in Lombardy, Italy, we estimated two congestion indices for isolation wards and ICU. The excess ICU needs were estimated in Lombardy, Italy, and other countries when data were available, including France, Spain, Belgium, New York State in the USA, South Korea, and Japan.

RESULTS

In Lombardy, Italy, the congestion of isolation beds had increased from 2.2 to the peak of 6.0 in March and started to decline to 3.9 as of 9^th May, whereas the demand for ICU during the same period has not decreased yet with an increasing trend from 2.9 to 8.0. The results showed the unmet ICU need from the second week in March as of 9^th May. The same situation was shown in France, Spain, Belgium, and New York State, USA but not for South Korea and Japan. The results with data until December 2020 for Lombardy, Italy were also estimated to reflect the demand for hospitalization and ICU after the occurrence of viral variants.

CONCLUSION

Two congestion indices for isolation wards and ICU beds using open assessed tabulated data with a compartment queue model underpinning were developed to monitor the clinical capacity in hospitals in response to the COVID-19 pandemic.

The 85% bed occupancy fallacy: The use, misuse and insights of queuing theory

Queuing theory can and has been used to inform bed pool capacity decision making, though rarely by managers themselves. The insights it brings are also not widely and properly understood by healthcare managers. These two shortcomings lead to the persistent fallacy of there being a globally applicable optimum average occupancy target, for example 85%, which can in turn lead to over- or under-provision of resources. Through this paper, we aim both to make queuing models more accessible and to provide visual demonstrations of the general insights managers should absorb from queuing theory. Occupancy is a consequence of the patient arrival rate and 'treatment' rate (the number of beds and length of stay). There is a trade-off between the average occupancy and access to beds (measured by, for example, the risk of access block due to all beds being full or the average waiting time for a bed). Managerially, the decision-making input should be the level of access to beds required, and so bed occupancy should be an output. Queuing models are useful to quickly draw the shape of these access-occupancy trade-off curves. Moreover, they can explicitly show the effect that variation (lack of regularity) in the times between arrivals and in the lengths of stay of individual patients has on the shape of the trade-off curves. In particular, with the same level of access, bed pools subject to lower variation can operate at higher average occupancy. Further, to improve access to a bed pool, reducing variation should be considered.

Forecasting Daily Patient Outflow From a Ward Having No Real-Time Clinical Data

Background: Modeling patient flow is crucial in understanding resource demand and prioritization. We study patient outflow from an open ward in an Australian hospital, where currently bed allocation is carried out by a manager relying on past experiences and looking at demand. Automatic methods that provide a reasonable estimate of total next-day discharges can aid in efficient bed management. The challenges in building such methods lie in dealing with large amounts of discharge noise introduced by the nonlinear nature of hospital procedures, and the nonavailability of real-time clinical information in wards.

Time-Series Approaches for Forecasting the Number of Hospital Daily Discharged Inpatients

For hospitals where decisions regarding acceptable rates of elective admissions are made in advance based on expected available bed capacity and emergency requests, accurate predictions of inpatient bed capacity are especially useful for capacity reservation purposes. As given, the remaining unoccupied beds at the end of each day, bed capacity of the next day can be obtained by examining the forecasts of the number of discharged patients during the next day. The features of fluctuations in daily discharges like trend, seasonal cycles, special-day effects, and autocorrelation complicate decision optimizing, while time-series models can capture these features well. This research compares three models: a model combining seasonal regression and ARIMA, a multiplicative seasonal ARIMA (MSARIMA) model, and a combinatorial model based on MSARIMA and weighted Markov Chain models in generating forecasts of daily discharges. The models are applied to three years of discharge data of an entire hospital. Several performance measures like the direction of the symmetry value, normalized mean squared error, and mean absolute percentage error are utilized to capture the under- and overprediction in model selection. The findings indicate that daily discharges can be forecast by using the proposed models. A number of important practical implications are discussed, such as the use of accurate forecasts in discharge planning, admission scheduling, and capacity reservation.

Autologous stem cell transplant in 716 patients with multiple myeloma: low treatment-related mortality, feasibility of outpatient transplant, and effect of a multidisciplinary quality initiative

We report on the feasibility of outpatient transplant in 716 patients undergoing autologous stem cell transplant for multiple myeloma at Mayo Clinic's site in Rochester, MN, from January 1, 2000, through October 31, 2007. We also report on the development and effect of a multidisciplinary quality initiative implemented by the Mayo Clinic Blood and Marrow Transplant Program involving physicians, nurses, pharmacists, dietitians, and financial specialists for outpatient management of patients undergoing stem cell transplant. This approach uses an electronic ordering system for diagnostic tests and chemotherapy to minimize medical errors. Analysis of hospitalization trends since inception of the program showed that 278 (39%) of the 716 patients treated completed the transplant procedure as outpatients. The median duration of hospitalization for all patients was 4 days; age and serum creatinine levels were predictive of the need for and duration of hospitalization. We also assessed recent treatment-related mortality rates during a 33-month period after implementation of the program (between January 1, 2005, and October 1, 2007). The 100-day survival rate was 99.5% for patients with low-risk myeloma (transplant during first plateau; n=201) and 97.2% for patients with high-risk myeloma (refractory, relapsing or second or greater plateau; n=71). The overall 100-day survival rate was 98.9%. Our experience shows that outpatient transplant is feasible for all patients with multiple myeloma and results in shorter hospital stays and low treatment-related mortality rates.

Short term hospital occupancy prediction

Inpatient census, or occupancy, is a primary driver of resource use in hospitals. Fluctuations in occupancy complicate decisions related to staffing, bed management, ambulance diversions, and may ultimately impact both quality of patient care and nursing job satisfaction. We describe our approach in building a computerized model to provide short-term occupancy predictions for an entire hospital by nursing unit and shift. Our model is a comprehensive system built using real hospital data and utilizes statistical predictions at the individual patient level. We discuss the results of piloting an early version of the model at a mid-size community hospital. The primary focus of the paper is on the development and methodology of a second generation of the predictive occupancy model. The results and accuracy of this new model is compared to a variety of other predictive methods based on tests using 2 years of actual hospital data.

Length of stay-based patient flow models: recent developments and future directions

Modelling patient flow in health care systems is vital in understanding the system activity and may therefore prove to be useful in improving their functionality. An extensively used measure is the average length of stay which, although easy to calculate and quantify, is not considered appropriate when the distribution is very long-tailed. In fact, simple deterministic models are generally considered inadequate because of the necessity for models to reflect the complex, variable, dynamic and multidimensional nature of the systems. This paper focuses on modelling length of stay and flow of patients. An overview of such modelling techniques is provided, with particular attention to their impact and suitability in managing a hospital service.

Choice of Models for the Analysis and Forecasting of Hospital Beds

There is growing concern that current health care services are not sustainable. The compartmental flow model provides the opportunity for improved decision-making about bed occupancy decisions, particularly those of a strategic nature. This modelling can be applied to complement infrastructure and workforce-planning methods. Discussion about appropriateness of the level of model complexity, the degree of fit and the ability to use compartmental flow models for generalization and forecasting has been lacking. The authors investigated model selection and assessment in relation to hospital bed compartment flow models. A compartment model for a range of scenarios was created. The training and test data related to the 1998 and 1999 calendar years, respectively. The majority of scenarios tested were based upon commonly used periods that describe periods of time. The goodness-of-fit achieved by optimisation was measured against the training and test data. Model fit improved with increasing complexity as expected. The analysis of model fit against the test data showed that increasing model complexity did result in over-fitting, and better prediction was achieved with a relatively simple model. In terms of generalisation, the seasonal models performed best. Single day census type models, which have been used by Millard and his colleagues, were also generated. The performance of these models was similar, but inferior to that of the models generated from a full year of training data. The additional data make the models better able to capture the variation across the year in activity.

A simple method to optimize hospital beds capacity

OBJECTIVE

The number of acute hospital beds is determined by health authorities using methods based on ratios and/or target bed occupancy rates. These methods fail to consider the variability in hospitalization demands over time. On the other hand, the implementation of sophisticated models requires the decision concerning the number of beds to be made by an expert. Our aim is to develop a new method that is as simple to use as the ratio method while minimizing the roundabout approaches of these methods.

METHOD

A score was constructed with three parameters: number of transfers due to lack of space, number of days with no possibility for S unscheduled admissions and number of days with at least a threshold of U unoccupied beds. The optimal number of beds is the number for which both the mean and the standard deviation of the score reach their minimum. We applied this method to two internal medicine departments and one urological surgery department and we compared the solutions proposed by this method with those put forward by the ratio method.

RESULTS

The solutions proposed by this method were intermediate to those calculated by the local and national length of Stays ratio methods. Simulating an unusual increase in admission requests had no consequence on the bed number selected, indicating that the method was robust.

CONCLUSION

Our tool represents a real alternative to the ratio methods. A software has been developed and is now available for use.

Can the impact of bed closure in intensive care units be reliably monitored?

OBJECTIVE

To assess the properties of various indicators aimed at monitoring the impact on the activity and patient outcome of a bed closure in a surgical intensive care unit (ICU).

DESIGN

Comparison before and after the intervention.

SETTING

A surgical ICU at a university hospital.

PATIENTS

All patients admitted to the unit over two periods of 10 months.

INTERVENTION

Closure of one bed out of 17.

MEASUREMENTS AND RESULTS

Activity and outcome indicators in the ICU and the structures upstream from it (emergency department, operative theater, recovery room) and downstream from it (intermediate care units). After the bed closure, the monthly medians of admitted patients and ICU hospital days increased from 107 (interquartile range 94-112) to 113 (106-121, P=0.07) and from 360 (325-443) to 395 (345-436, P=0.48), respectively, along with the linear trend observed in our institution. All indicators of workload, patient severity, and outcome remained stable except for SAPS II score, emergency admissions, and ICU readmissions, which increased not only transiently but also on a mid-term basis (10 months), indicating that the process of patient care delivery was no longer predictable.

CONCLUSIONS

Health care systems, including ICUs, are extraordinary flexible, and can adapt to multiple external constraints without altering commonly used activity and outcome indicators. It is therefore necessary to set up multiple indicators to be able to reliably monitor the impact of external interventions and intervene rapidly when the system is no longer under control.