A simulation modelling approach to evaluating length of stay, occupancy, emptiness and bed blocking in a hospital geriatric department

Improving service efficiency and throughput of cardiac surgery patients using Monte Carlo simulation: a queueing setting

Bed occupancy rate (BOR) is important for healthcare policymakers. Studies showed the necessity of using simulation approach when encountering complex real-world problems to plan the optimal use of resources and improve the quality of services. So, the aim of the present study is to estimate average length of stay (LOS), BOR, bed blocking probability (BBP), and throughput of patients in a cardiac surgery department (CSD) using simulation models. We studied the behavior of a CSD as a complex queueing system at the Farshchian Hospital. In the queueing model, customers were patients and servers were beds in intensive care unit (ICU) and post-operative ward (POW). A computer program based on the Monte Carlo simulation, using Python software, was developed to evaluate the behavior of the system under different number of beds in ICU and POW. The queueing simulation study showed that, for a fixed number of beds in ICU, BOR in POW decreases as the number of beds in POW increases and LOS in ICU increases as the number of beds in POW decreases. Also, based on the available data, the throughput of patients in the CSD during 800 days was 1999 patients. Whereas, the simulation results showed that, 2839 patients can be operated in the same period. The results of the simulation study clearly demonstrated the behavior of the CSD; so, it must be mentioned, hospital administrators should design an efficient plan to increase BOR and throughput of patients in the future.

Do subsidized nursing homes and home care teams reduce hospital bed-blocking? Evidence from Portugal

Excessive length of hospital stay is among the leading sources of inefficiency in healthcare. When a patient is clinically fit to be discharged but requires support outside the hospital, which is not readily available, they remain hospitalized until a safe discharge is possible -a phenomenon called bed-blocking. I study whether the availability of subsidized nursing homes and home care teams reduces hospital bed-blocking. Using individual data on the universe of inpatient admissions at Portuguese hospitals during 2000-2015, I find that the entry of home care teams in a region reduces bed-blocking by 4 days per episode, on average. Nursing home entry only reduces bed-blocking among patients with high care needs or when the intensity of entry is high. Reductions in bed-blocking do not harm patients' health. The beds freed up by reducing bed-blocking are used to admit additional elective patients.

A systematic review of the prediction of hospital length of stay: Towards a unified framework

Hospital length of stay of patients is a crucial factor for the effective planning and management of hospital resources. There is considerable interest in predicting the LoS of patients in order to improve patient care, control hospital costs and increase service efficiency. This paper presents an extensive review of the literature, examining the approaches employed for the prediction of LoS in terms of their merits and shortcomings. In order to address some of these problems, a unified framework is proposed to better generalise the approaches that are being used to predict length of stay. This includes the investigation of the types of routinely collected data used in the problem as well as recommendations to ensure robust and meaningful knowledge modelling. This unified common framework enables the direct comparison of results between length of stay prediction approaches and will ensure that such approaches can be used across several hospital environments. A literature search was conducted in PubMed, Google Scholar and Web of Science from 1970 until 2019 to identify LoS surveys which review the literature. 32 Surveys were identified, from these 32 surveys, 220 papers were manually identified to be relevant to LoS prediction. After removing duplicates, and exploring the reference list of studies included for review, 93 studies remained. Despite the continuing efforts to predict and reduce the LoS of patients, current research in this domain remains ad-hoc; as such, the model tuning and data preprocessing steps are too specific and result in a large proportion of the current prediction mechanisms being restricted to the hospital that they were employed in. Adopting a unified framework for the prediction of LoS could yield a more reliable estimate of the LoS as a unified framework enables the direct comparison of length of stay methods. Additional research is also required to explore novel methods such as fuzzy systems which could build upon the success of current models as well as further exploration of black-box approaches and model interpretability.

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.

A simulation-based approach for improving the clinical blood sample supply chain

We consider a three-echelon blood sample supply chain comprising the following elements: (i) clinics, where blood samples are taken from patients, (ii) centrifugation centers, where collected blood samples are separated into their different components, and (iii) a centralized testing laboratory, where the samples are analyzed. We focus on the scheduling of vehicles that transport blood samples from clinics to centrifugation centers-a special case of the vehicle routing problem (VRP). Our study presents a novel simulation-based approach to the VRP, designed and implemented in MATLAB, and tailored to the unique constraints of the three-echelon blood sample collection chain. We apply this approach to data from a large Health Maintenance Organization to determine the optimal vehicle fleet size for blood sample transport, while ensuring that the quality of the healthcare service is not compromised. Results suggest that our simulation model can be generalized to serve as a useful and straightforward decision support tool for optimizing resource utilization and service quality in healthcare systems.

A decision support simulation model for bed management in healthcare

PURPOSE

In order to provide access to care in a timely manner, it is necessary to effectively manage the allocation of limited resources. such as beds. Bed management is a key to the effective delivery of high quality and low-cost healthcare. The purpose of this paper is to develop a discrete event simulation to assist in planning and staff scheduling decisions.

DESIGN/METHODOLOGY/APPROACH

A discrete event simulation model was developed for a hospital system to analyze admissions, patient transfer, length of stay (LOS), waiting time and queue time. The hospital system contained 50 beds and four departments. The data used to construct the model were from five years of patient records and contained information on 23,019 patients. Each department's performance measures were taken into consideration separately to understand and quantify the behavior of departments individually, and the hospital system as a whole. Several scenarios were analyzed to determine the impact on reducing the number of patients waiting in queue, waiting time and LOS of patients.

FINDINGS

Using the simulation model, it was determined that reducing the bed turnover time by 1 h resulted in a statistically significant reduction in patient wait time in queue. Further, reducing the average LOS by 10 h results in statistically significant reductions in the average patient wait time and average patient queue. A comparative analysis of department also showed considerable improvements in average wait time, average number of patients in queue and average LOS with the addition of two beds.

ORIGINALITY/VALUE

This research highlights the applicability of simulation in healthcare. Through data that are often readily available in bed management tracking systems, the operational behavior of a hospital can be modeled, which enables hospital management to test the impact of changes without cost and risk.

An approach by human and material resources combination to reduce hospitals crowding

Purpose

This paper aims to propose an approach by human and material resources combination to reduce hospitals crowding. Hospitals crowding is becoming a serious problem. Many research works present several methods and approaches to deal with this problem. However, to the best of the authors’ knowledge – after a deep reading of literature – in all the proposed approaches, human and material resources are studied separately while they must be combined (to a given number of material resources an optimal number of human resources must be assigned and vice versa) to reflect reality and provide better results.

Design/methodology/approach

Hospital inpatient unit is chosen as framework. This unit crowding reduction is carried out by its capacity increasing. Indeed, inpatient unit modeling is performed to find the adequate combinations of human and material resources numbers insuring this unit stability and providing optimal service rates. At first, inpatient unit is modeled using queuing networks and considering only two resources (beds and nurses). Then, the obtained service rate formula is improved by including other resources and parameters using Baskett, Chandy, Muntz and Palecios (BCMP) queuing networks. This work is applied to “Princess Lalla Meryem” hospital inpatient unit.

Findings

Results are patients’ average number reduction by an average (in each block) of three patients, patients’ average waiting time reduction by an average of 9.98 h and non-admitted patients (to inpatient wards) access percentage of 39.26 per cent on average.

Originality/value

Previous works focus their studies on either human resources or material resources. Only a few works study both resources types, but separately. The context of those studies does not meet the real hospital context (where human resources are combined with material resources). Therefore, the provided results are not very reliable. In this paper, an approach by human and material resources combination is proposed to increase inpatient unit care capacity. Indeed, this approach consists of developing inpatient unit service rate formula in terms of human and material resources numbers.

Predictive Modeling for Geriatric Hip Fracture Patients: Early Surgery and Delirium Have the Largest Influence on Length of Stay

BACKGROUND

Averaging length of stay (LOS) ignores patient complexity and is a poor metric for quality control in geriatric hip fracture programs. We developed a predictive model of LOS that compares patient complexity to the logistic effects of our institution's hip fracture care pathway.

METHODS

A retrospective analysis was performed on patients enrolled into a hip fracture co-management pathway at an academic level I trauma center from 2014 to 2015. Patient complexity was approximated using the Charlson Comorbidity Index and ASA score. A predictive model of LOS was developed from patient-specific and system-specific variables using a multivariate linear regression analysis; it was tested against a sample of patients from 2016.

RESULTS

LOS averaged 5.95 days. Avoidance of delirium and reduced time to surgery were found to be notable predictors of reduced LOS. The Charlson Comorbidity Index was not a strong predictor of LOS, but the ASA score was. Our predictive LOS model worked well for 63% of patients from the 2016 group; for those it did not work well for, 80% had postoperative complications.

DISCUSSION

Predictive LOS modeling accounting for patient complexity was effective for identifying (1) reasons for outliers to the expected LOS and (2) effective measures to target for improving our hip fracture program.

LEVEL OF EVIDENCE

III.

The impact of specialization of hospitals on patient access to care; a queuing analysis with an application to a neurological hospital

We study the impact of specialization on the operational efficiency of a multi-hospital system. The mixed outcomes of recently increasing hospital mergers and system re-configuration initiatives have raised the importance of studying such organizational changes from all the relevant perspectives. We consider two configuration scenarios for a multi-hospital system. The first scenario assumes that all the hospitals in the system are general, which implies they can provide care to all types of patients. In the alternative configuration, we specialize each hospital in certain level of care, which means they serve only specific types of patients. By considering an extensive number of possible settings for a multi-hospital system, we characterize the situations in which one scenario outperforms the other in terms of extending access of patients to care. Our results show that whenever the percent of patients with shorter length of stay in the system increases, specialization of healthcare services can maximize the accessibility of care. Also, if the patient load is balanced between all hospitals in the system, it seems more likely that all hospitals benefit from specialization. We conclude that the strategic decision of designing a multi-hospital system requires careful consideration of patient mix among arrivals, relative length of stay of patients, and distribution of patient load between hospitals.

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.

Senior Managed Care System for Hip Fracture in the United States

Background

It is debatable whether a managed care model would affect the quality of care and length of hospital stay in the treatment of hip fractures in elderly patients.

Methods

This prospective study was undertaken to determine whether or not a managed care critical pathway tool shortened hospital stay in a group of 102 senior patients with fractures of the hip during follow-up. We compared our study findings with two equivalent populations of senior hip fracture patients not treated using a critical care pathway concerning specific markers of quality.

Results

The managed care group had a 9% mortality rate, 95% return to prefracture living and 63% return to ambulatory status. The rates compared favorably with previous studies. The quality of care provided before and after the critical pathway was equivalent, while the post-pathway length of stay dropped 30%.

Conclusions

The proposed care protocol is recommended to shorten hospital stay in elderly patients with hip fractures.

Factors affecting delay to surgery and length of stay for patients with hip fracture

PURPOSE

The purpose of this study was to determine factors, including day of week of hospital admission, associated with delay to surgery (DTS) and increased length of stay (LOS) in patients with hip fractures.

DESIGN

Retrospective.

SETTING

Level I Trauma Center.

PATIENTS AND METHODS

Six hundred thirty-five consecutive patients admitted to a single hospital between January 1999 and July 2006 aged 65 years or older with a hip fracture (OTA 31) were identified retrospectively from an orthopaedic database. Demographic data, American Society of Anesthesiologists (ASA) score, hospital admission and discharge dates, the date of surgery, and details of any preoperative cardiac testing were extracted from the hospital record. These data were used to identify the day of week for hospital admission and to calculate days for DTS and hospital LOS. Linear regression was used to identify independent variables associated with DTS and increased LOS.

INTERVENTION

All patients underwent surgical treatment of a hip fracture (OTA 31).

MAIN OUTCOME MEASURES

Factors affecting DTS and LOS.

RESULTS

Independent factors associated with DTS included the day of week for hospital admission, ASA score, and the need for preoperative cardiac testing. Patients admitted Thursday through Saturday had longer DTS (mean, 2.2-2.7 days) than did patients admitted other days (mean, 1.7-1.8). DTS increased for increasing ASA: 1.4 days for ASA 2, 2.0 days for ASA 3, and 3.0 days for ASA 4. Those requiring preoperative cardiac testing had an increased number of days to surgery (mean, 3.2 days) than those without (mean, 1.7 days). Independent factors associated with increasing hospital LOS included ASA, the need for preoperative cardiac testing, male gender, and day of admission. LOS increased for increasing ASA: 6.3 days for ASA 2, 8.1 days for ASA 3, and 10.1 days for ASA 4. Those requiring preoperative cardiac testing had an increased LOS (mean, 9.4 days) than those without (mean, 7.3 days). Male patients had a longer LOS (mean, 9.8 days) than did females (mean, 7.3 days). Patients admitted on Thursday or Friday (mean, 8.5-9.1 days) had longer LOS than those admitted on other days (mean, 7.3-7.9 days).

CONCLUSIONS

This is the first study to consider and identify the day of admission and need for preoperative cardiac tests as determinants of DTS and LOS for geriatric patients with hip fracture. Relative scarcity of weekend hospital resources, when present, may be responsible for these delays. This study also confirms that patient medical condition as measured by ASA affects both DTS and LOS.

LEVEL OF EVIDENCE

Prognostic level II. See Instructions for Authors for a complete description of levels of evidence.

Does process flow make a difference to mortality and cost? An observational study

PURPOSE

The purpose of the paper is to investigate the potential relationships between emergency-care flow, patient mortality and healthcare costs using a patient-flow model.

DESIGN/METHODOLOGY/APPROACH

The researchers used performance data from one UK NHS trust collected over three years to identify periods where patient flow was compromised. The delays' root causes in the entire emergency care system were investigated. Event time-lines that disrupted patient flow and patient mortality statistics were compared.

FINDINGS

Data showed that patient mortality increases at times when accident and emergency (A&E) department staff were struggling to admit patients. Four delays influenced mortality: first, volume increase and mixed admissions; second, process delays; third, unplanned hospital capacity adjustments and finally, long-term capacity restructuring downstream.

RESEARCH LIMITATIONS/IMPLICATIONS

This is an observational study that uses process control data to find times when mortality increases coincide with other events. It captures contextual background to whole system issues that affect patient mortality.

PRACTICAL IMPLICATIONS

Managers must consider cost-decisions and flow in the whole system. Localised, cost-focused decisions can have a detrimental effect on patient care. Attention must also be paid to mortality reports as existing data-presentation methods do not allow correlation analysis.

ORIGINALITY/VALUE

Previous studies correlate A&E overcrowding and mortality. This method allows the whole system to be studied and increased mortality root causes to be understood.

The effects of American Society of Anesthesiologists physical status on length of stay and inpatient cost in the surgical treatment of isolated orthopaedic fractures

OBJECTIVES

To identify the impact of the American Society of Anesthesiologists (ASA) physical status on postoperative length of stay (LOS) and to document the cost due to LOS after surgical management of the 8 most common lower extremity and 2 most common upper extremity isolated orthopaedic fractures.

DESIGN

Retrospective chart review.

SETTING

All patients who presented and underwent one of the 10 selected isolated orthopaedic surgical procedures at a large tertiary care center between January 1, 2000, and December 31, 2010.

PATIENTS/PARTICIPANTS

Charts for patients undergoing the 10 selected isolated orthopaedic surgical fracture procedures more than 10 years were reviewed. Thirteen thousand seven hundred seventy-six distinct operations were identified. One thousand three hundred ninety-eight distinct operations were included in analysis after selection.

INTERVENTION

This was an observational study. Patients who received operative management for isolated orthopaedic fractures were identified utilizing a CPT code search for analysis in a retrospective chart review.

MAIN OUTCOME MEASUREMENTS

LOS and cost secondary to LOS.

RESULTS

ASA physical status proved the strongest predictor of postoperative LOS for the 8 most common lower extremity and 2 most common upper extremity isolated orthopaedic procedures. ASA was also a significant predictor of inpatient cost for all isolated orthopaedic procedures included in the study with the exception of CPT code 27536.

CONCLUSIONS

ASA classification is an indicator for variance in LOS and total inpatient cost for hospitalized patients. Given that ASA classification is a universally collected data point, this method can be used in almost any hospital system and for any operative service. In addition, this study provides a foundation for many other studies to be conducted which will include multiple institutions and fracture types, such that ASA can be used as a more generalizable predictor of LOS and inpatient cost in orthopaedic trauma patients. This model may be used to accurately predict a patient's postoperative course and the expected cost to the health care system of a given procedure.

LEVEL OF EVIDENCE

Prognostic Level IV. See Instructions for Authors for a complete description of levels of evidence.

Formal-Transfer In and Out of Stroke Care Units

The positive impact of stroke care units (SCUs) on patient outcome has been previously reported. In this study, long-term stroke patients that are formally admitted to teaching-hospitals are compared with and without SCUs. The authors focus on the patients’ experience with ongoing care or formal transfers following current care as this cohort is often high users of the system with associated high costs. Bayesian Networks were employed to analyze routinely collected public-hospital administrative data. The results illustrate that the teaching-hospitals with SCUs, while achieving shorter length of stay, in fact deal with younger patients with lower overall patient complexity than non-SCU teaching-hospitals. Other differences include SCUs predominantly treating subarachnoid hemorrhages whereas the non-SCUs treat more cerebral infarctions. This study illustrates the power of Bayesian Networks to expose the nature of caseload and outcomes recorded in hospital-administrative data as a means to gain insight on current practice and create opportunities for benchmarking and improving care.

Analysing management policies for operating room planning using simulation

In this paper we analyse the operating room planning at a department of orthopaedic surgery in Sweden. We focus on the problem of meeting the uncertainty in demand of patient arrival and surgery duration and at the same time maximizing the utilization of operating room (OR) time. With a discrete-event model we simulate how different management polices affect different performance metrics such as patient waiting time, cancellations and the utilization of OR time. The experiments show that the performance of the operating room department can be improved significantly by applying a different policy in reserving OR-capacity for emergency cases together with a policy to increase staff in stand-by. Moreover, the developed simulation model provides estimates for a what-if situation related to the prognosis of an increasing number of hip-joint replacements.

Statistical analysis of patients' characteristics in neonatal intensive care units

The staff in the neonatal intensive care units is required to have highly specialized training and the using equipment in this unit is so expensive. The random number of arrivals, the rejections or transfers due to lack of capacity and the random length of stays, make the advance knowledge of the optimal staff; equipment and materials requirement for levels of the unit behaves as a stochastic process. In this paper, the number of arrivals, the rejections or transfers due to lack of capacity and the random length of stays in a neonatal intensive care unit of a university hospital has been statistically analyzed. The arrival patients are classified according to the levels based on the required nurse: patient ratio and gestation age. Important knowledge such as arrivals, transfers, gender and length of stays are analyzed. Finally, distribution functions for patients' arrivals, rejections and length of stays are obtained for each level in the unit.

A combination of deterministic and stochastic approaches to optimize bed capacity in a hospital unit

Random number of arrivals and random length of stays make the number of patients in a hospital unit behave as a stochastic process. This makes the determination of the optimum size of the bed capacity more difficult. The number of admissions per day, service level and occupancy level are key control parameters that affect the optimum size of the required bed capacity. In this study a new stochastic approximation is developed and applied to a unit of a teaching hospital. Data between 2000 and 2004 was used to obtain the necessary probability distribution functions. Mathematical relationships between the control parameters and size of the bed capacity are obtained using generated data from a constructed simulation model. Nonlinear mathematical models are then used to determine the optimum size of the required bed capacity based on target levels of the control parameters, and a profit and loss analysis is performed.

A three-phase approach for operating theatre schedules

In this paper we develop a three-phase, hierarchical approach for the weekly scheduling of operating rooms. This approach has been implemented in one of the surgical departments of a public hospital located in Genova (Genoa), Italy. Our aim is to suggest an integrated way of facing surgical activity planning in order to improve overall operating theatre efficiency in terms of overtime and throughput as well as waiting list reduction, while improving department organization. In the first phase we solve a bin packing-like problem in order to select the number of sessions to be weekly scheduled for each ward; the proposed and original selection criterion is based upon an updated priority score taking into proper account both the waiting list of each ward and the reduction of residual ward demand. Then we use a blocked booking method for determining optimal time tables, denoted Master Surgical Schedule (MSS), by defining the assignment between wards and surgery rooms. Lastly, once the MSS has been determined we use the simulation software environment Witness 2004 in order to analyze different sequencings of surgical activities that arise when priority is given on the basis of a) the longest waiting time (LWT), b) the longest processing time (LPT) and c) the shortest processing time (SPT). The resulting simulation models also allow us to outline possible organizational improvements in surgical activity. The results of an extensive computational experimentation pertaining to the studied surgical department are here given and analyzed.

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.

Stochastic bed balancing of an obstetrics hospital

Health care is one of the largest industries in the developed world and the top domestic industry in the United States (US). Over the past thirty years there has been a dramatic increase in healthcare costs in the US, of which about one-third can be attributed to hospital spending. One of the key factors in hospital cost containment and revenue enhancement is effective and efficient bed planning and capacity analysis. This study aims to balance bed unit utilizations across an obstetrics hospital and minimize the blocking of beds from upstream units within given constraints on bed reallocation. The methodology includes the assessment and effect of time-dependent patterns of monthly, daily, and hourly demand. Queuing networks are first used to assess the flows between units, establish target utilizations of bed units, and involve stakeholders in a flow characterization that they understand. Discrete-event simulation is then used to maximize the flow through the balanced system including non-homogeneous effects, non-exponential lengths of stay, and blocking behavior. Results of the models are validated against actual data collected from the hospital. Several 'what if' scenarios are studied showing that 38% more patient flow can be achieved with only 15% more patient beds. The results of the study have been implemented.

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.

Modelling Variability in Hospital Bed Occupancy

A stochastic version of the Harrison-Millard multistage model of the flow of patients through a hospital division is developed in order to model correctly not only the average but also the variability in occupancy levels, since it is the variability that makes planning difficult and high percent occupancy levels increase the risk of frequent overflows. The model is fit to one year of data from the medical division of an acute care hospital in Adelaide, Australia. Admissions can be modeled as a Poisson process with rates varying by day of the week and by season. Methods are developed to use the entire annual occupancy profile to estimate transition rate parameters when admission rates are not constant and to estimate rate parameters that vary by day of the week and by season, which are necessary for the model variability to be as large as in the data. The final model matches well the mean, standard deviation and autocorrelation function of the occupancy data and also six months of data not used to estimate the parameters. Repeated simulations are used to construct percentiles of the daily occupancy distributions and thus identify ranges of normal fluctuations and those that are substantive deviations from the past, and also to investigate the trade-offs between frequency of overflows and the percent occupancy for both fixed and flexible bed allocations. Larger divisions can achieve more efficient occupancy levels than smaller ones with the same frequency of overflows. Seasonal variations are more significant than day-of-the-week variations and variable discharge rates are more significant than variable admission rates in contributing to overflows.

Model simulation of the patient flow through a screening centre for diabetic retinopathy

PURPOSE

To construct a quantitative, flexible and simplified mathematical model of the patient flow through the Eye Clinic at the Steno Diabetes Centre (SDC) in order to enable rational dimensioning and assess the effects of modifications.

METHODS

Patient data were drawn from the Eye Care database at the SDC. A simple patient flow model was constructed, allowing simultaneous adjustments of all variables, and the model was tested. Two scenarios were simulated: (1) adjusting the algorithm that assigns the follow-up intervals, and (2) increasing the population size to include all patients with diabetes in Copenhagen County.

RESULTS

The model can describe the patient flow under steady state conditions, but is less precise in predicting transient changes with the present set-up. Accordingly all simulations were run for a substantial number of iterations. The two scenarios illustrate the usefulness of the model by calculating the required photographic examination capacity for the specific population, thereby allowing better estimations of future dimensioning of the organization.

CONCLUSION

The study presents a patient flow model that can be used to illustrate the effects of proposed changes prior to their implementation, specifically with respect to the capacity of the system.

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.

Modeling patient flows using a queuing network with blocking

The downsizing and closing of state mental health institutions in Philadelphia in the 1990's led to the development of a continuum care network of residential-based services. Although the diversity of care settings increased, congestion in facilities caused many patients to unnecessarily spend extra days in intensive facilities. This study applies a queuing network system with blocking to analyze such congestion processes. "Blocking" denotes situations where patients are turned away from accommodations to which they are referred, and are thus forced to remain in their present facilities until space becomes available. Both mathematical and simulation results are presented and compared. Although queuing models have been used in numerous healthcare studies, the inclusion of blocking is still rare. We found that, in Philadelphia, the shortage of a particular type of facilities may have created "upstream blocking". Thus removal of such facility-specific bottlenecks may be the most efficient way to reduce congestion in the system as a whole.

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.