A simulation modelling approach to evaluating length of stay ...

Health Care Management Science 1 (1998) 143–149

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A simulation modelling approach to evaluating length of stay, occupancy, emptiness and bed blocking in a hospital geriatric department E. El-Darzi a , C. Vasilakis b , T. Chaussalet a and P.H. Millard b a University

of Westminster, London, UK E-mail: [email protected] b St. George’s Hospital Medical School, London, UK

The flow of patients through geriatric hospitals has been previously described in terms of acute (short-stay), rehabilitation (mediumstay), and long-stay states where the bed occupancy at a census point is modelled by a mixed exponential model using BOMPS (Bed Occupancy Modelling and Planning System). In this a patient is initially admitted to acute care. The majority of the patients are discharged within a few days into their own homes or through death. The rest are converted into medium-stay patients where they could stay for a few months and thereafter either leave the system or move on to a long-stay compartment where they could stay until they die. The model forecasts the average length of stay as well as the average number of patients in each state. The average length of stay in the acute compartment is artificially high if some would-be long-term patients are kept waiting in the short-stay compartment until beds become available in long-stay (residential and nursing homes). In this paper we consider the problem as a queueing system to assess the effect of blockage on the flow of patients in geriatric departments. What-if analysis is used to allow a greater understanding of bed requirements and effective utilisation of resources. Keywords: simulation, geriatric medicine, queueing systems, bed occupancy

1. Introduction The constant increase in the aged population increases the demand for better planning, usage and management of health services for the elderly. Conventional methods (such as waiting lists and length of stay averages) used in order to quantify the process of care and measure the quality of services in geriatric departments fail to represent fully the interaction between acute, rehabilitative, and long-stay care [21]. The aim of this paper is to assess the benefits of a model that examines the impact of bed blockage, occupancy and emptiness on patient flow in a geriatric inpatient unit. Departments of geriatric medicine provide an acute, rehabilitative and long-stay service for older people with complex medical and social needs. The specialty developed after hospital consultants were given responsibility for the chronic sick in long-stay care [8]. Now, fifty years later, beds allocated to consultants in geriatric medicine are still classified as long-stay, despite the fact that the majority of the work being done is acute. When NHS planning was based on normative provision, the lack of differentiation between acute, rehabilitative and long-stay care was of little significance. Health care planning is failing because decision makers ignore what is happening in the occupied beds [26]. Typical measurements of bed usage are waiting lists, number of admissions and discharges, the average length of stay, bed occupancy and emptiness, and the turnover interval. Millard [22] has shown that these methods of data analysis are  Baltzer Science Publishers BV

flawed; therefore mistakes in planning are made. The current national crisis in acute care provision and the need to rebuild rehabilitative services [9] increase the importance of introducing new methods to measure the process of care. How much emptiness does an acute hospital need? Hospital bed occupancy and emptiness is normally counted at midnight. Although planned admissions usually arrive during normal working hours, emergency admissions can arrive at any time during the day or night. In inefficiently organised hospitals, or hospitals with too few beds, all too often planned admissions patients arrive to find that emergency patients are occupying their beds. When sufficient numbers of beds are unavailable, patients tend to wait for beds on trolleys in the Accident and Emergency Department. Consequently planned admissions are turned away, and bed blockages occur. Clinically, bed blocking occurs when patients are kept waiting in one ward or hospital until free beds are available in a more suitable ward or hospital. For instance, rehabilitation or long-stay patients can be kept waiting in the acute wards until beds become available elsewhere, effectively blocking the availability of the beds for other patients. In this paper we first discuss the benefits and limitations of flow modelling. Then we report the development of a simulation model of a queueing system which gives valuable insight into the interaction between emptiness in long-stay care and acute care. Finally, we consider further possibilities for research in this field of endeavour.

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2. Background to the methods 2.1. Flow modelling Flow modelling is based on a behavioural theory of flow [10], the concept being that staff interact with patients and resources to establish specialty specific, locally determined streams of flow [24]. Words used to describe the necessary facilities for the medical care of older people such as intensive, acute, rehabilitation, continuing care and long-stay contain dimensions of time as well as dimensions of staffing and resources. Confirmation of an observation that curves generated by mixed exponential equations fit bed census data led first to a mathematical solution to a two compartment model of flow [12], then to a three compartment model of flow [11]. Task specific software (BOMPS) generates performance statistics based upon the fit between a mixed exponential curve and bed census data [19,27]. Dependent on whether the best-fit mixed exponential equation has one, two or three components, one, two or three compartment statistics are generated. When three compartments are identified the method gives insight into the interactions between acute, rehabilitative and long-stay care. Statistics generated from data collected by a one day census concern the overall bed allocation and expected stay, the estimated daily admissions, the number of beds in each compartment, the average length of stay of short, medium and long-stay patients, the likelihood that a patient will be discharged from each compartment, and the conversion rates between the short-stay and medium-stay and medium-stay and longstay. Furthermore, because the model is based on a dynamic theory of flow the outcome of different decisions can be pre-tested. This flow model is extensively used in St. George’s Hospital (and other hospitals in UK) to assist in the planning and the decision making process of geriatric departments. Although the model gives important insights into the process of care there are limitations to its usefulness as a decision making tool. A major limitation is that the model produces single numbers for the observed variables rather than ranges and it is deterministic in nature. Furthermore, questions concerning bed allocation, occupancy and emptiness and bed blocking cannot be answered using this tool. Seeking to overcome this deficit we propose an alternative model based on simulation. 3. The simulation model Discrete event simulation is used to model the flow of patients through the system. Discrete event simulation concerns the modelling of a system as it evolves over time by a representation in which the state variables change instantaneously at separate points in time [16]. These points in time are the ones at which an event occurs, where an event is defined as an instantaneous occurrence that may change the state of the system. Clinical examples of this

would represent patient events such as joining the waiting list, admission, successful treatment and discharge, referral for rehabilitation and eventual discharge or transfer to long-stay. Basic components of the system are: (a) Entities: these are the elements of the system which are being simulated and can be individually identified and processed. In this model the entities are the patients. (b) Activities: these are the operations and procedures which are initiated at each event and which transform the state of the entities. In this model the activities are the three compartments and the queues. (c) System state: this is the collection of state variables necessary to describe the system at a certain point in time, for example, the number of available beds, the waiting time in a queue, etc. Discrete event simulation models have been applied extensively for planning and managing health care departments [1–6,14]. It is believed that the reason behind this phenomenon is that this technique permits simulated patients to have attributes which influence their progress through the system [7]. Other possible reasons are the availability of survival distributions and the introduction of constraints. The last two capabilities are essential for a successful model in the area of health care services. In particular, the use of constraints is a very important feature as it allows us to explore situations where the resources are not assumed to be infinite. Discrete event simulations provide, in general, flexibility, robustness and accuracy. They can as easily deal with problems at a national level as with the problems and constraints of a single hospital unit. 3.1. Queueing A queueing system consists of one or more servers that provide service of some kind to arriving customers [16]. In our model, beds are the server units and patients are the customers. If a customer arrives and finds all servers busy, generally, he or she would join one or more queues. Similarly, patients waiting in queues within the health care system create bed blockage. In the behavioural theory of flow the beds occupied by patients in the different streams of acute, rehabilitative and long-stay care are separated by decision making thresholds [20]. For instance, the decision that a rehabilitative patient cannot be discharged represents a decision that this patient must wait in the rehabilitative stream until a long-stay bed is available. So this forms an internal queue. If a patient arrives for admission and no acute beds are available then an external queue (the waiting list) is created. By considering the problem as a queueing system it is possible to assess the effect of changes in referral rates, length of stay, occupancy and emptiness and bed blockage on the flow of patients through the system under study.

E. El-Darzi et al. / Simulating the flow of patients in a geriatric department

A queueing system is characterised by three components: arrival process, service mechanism, and queue discipline. As geriatric patients are referred to departments of geriatric medicine by their general practitioner randomly and independently of each other, their interarrival times can be considered to be independent, identically distributed variables (IID). Hence they can be described by an exponential distribution [15]. Thus, the number of patients arriving in the hospital follows a Poisson distribution. Although admission to a department of geriatric medicine is nearly always preceded by a stage of review, at this stage of model building the admission rate is considered to be the same as the arrival rate. The service mechanism is described by the number of servers, the number of queues, and the probability distribution of customer service times. Although the numerical distribution of departure times in geriatric medicine is represented by a log-normal and exponential function [18], the mathematical solution to the behavioural theory of flow [12] gives an exponential survival time in each compartment. So the service times in each compartment for each patient are IID random variables that can be described by an exponential distribution. The chosen queue discipline is the First In First Out (FIFO). Clinically, this is not always the case as many factors influence the decision that a patient will leave the waiting list and be admitted to hospital, such as the patient’s general medical condition, the severity of the case and the location of the available bed. Nevertheless, the FIFO assumption simplifies the modelling process and is adequate for the purposes of this model.

4. The geriatric department studied Mitchell et al. [23] reported the benefits that they obtained by introducing an age-related (75 and over) admission policy into a department of geriatric medicine in a North London Health District. The changes involved the closure of peripheral hospital beds and the allocation of some general medical beds in the district general hospital as geriatric beds. In reporting cost efficiency savings the authors commented on increased annual admissions, increased turnover per bed, decreased medical emptiness and shortened length of stay. Unfortunately, these measures gave no indication of the role that rehabilitation played in improving performance. Because Mitchell et al. [23] had arranged for an annual bed census to be taken on the 1st of January each year, Parry [24] was able to use the bed census flow rate methodology (BOMPS software package) to evaluate the outcome of introducing a new style of in-patient management into the district general hospital. The analysis indicated that a major factor in the improvement of acute admissions was linked to the improvement of the off-site rehabilitation unit. In the next section we will use simulation to evaluate bed occupancy by using this data.

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Figure 1. The unconstrained model.

5. The simulation models 5.1. The unconstrained model The unconstrained three compartment model contains no queues or bed constraints (see figure 1). Starting parameters were set as in Parry [24]. Those parameters are: • admission rate: 19 patients per day, • average length of stay in the acute, rehabilitation and long-stay: 9, 67 and 863 days, respectively, • conversion rate from acute to rehabilitation: 7%, • conversion rate from rehabilitation to long-stay: 17%. The patients enter the system through the acute compartment where they stay an exponential average of 9 days and then either exit the system at 93% or are converted into rehabilitation patients at a rate of 7%. These remaining patients will stay an additional 67 days on exponential average in the rehabilitation compartment and after that they leave the system at a rate of 83%. However, the remaining 17% will become long-stay patients where, on average, they stay an additional 863 days. All long-stay patients leave the system, usually by death. The simulation model was executed 10 times using different random seeds. In this model we have taken one day to be the time division. Data were collected after the model had reached steady state. Figure 2 shows that it takes 5.5 years (2000 days) for the system with its current long-stay configuration to reach steady state. This is because patients in the long-stay compartment accumulate gradually due to the high exponential average length of stay in long-term care (863 days). Table 1 demonstrates the results from the simulation model, the 95% confidence limits (using the Student t distribution) and the estimates from the flow model. It can be seen that the expected bed occupancies obtained from the flow model (BOMPS) and the unconstrained simulation model are very close, despite the fact that the flow model results are outside the 95% confidence intervals of the simulation model.

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Figure 2. The steady-state of the system. Table 1 Simulation results from the initial model (from 10 separate runs).

Acute Mean Standard deviation Min Max 95% CL− 95% CL+ Flow model estimates

Mean number of occupied beds Rehab Long-stay

170.7 0.95 124 226 170.1 171.4 175

89.3 2.12 52 126 87.7 90.8 94

188.6 8.11 139 229 182.9 194.4 204

The figures reported in Parry [24] were rounded up and as we will see in the next sections, the simulation model is very sensitive to even minor changes in the conversion rate values. This could provide a plausible explanation as to why these results are slightly different. 5.2. The basic model In this model the concept of queues is introduced. The queues are used to measure bed blockage between the acute and rehabilitation, and the rehabilitation and long-stay compartments (see figure 3). As in the previous model the patients enter the system through the acute compartment if beds are available. Otherwise, they will be rejected from the system (in reality those rejected patients are treated by other specialties). Patients who are due to be converted from acute stay to rehabilitation will join Queue 1 if there is no bed available in the rehabilitation compartment. Until they exit from the queue those patients occupy beds in the acute compartment. Similarly, Queue 2 represents bed blockage between rehabilitation and long-stay compartments. The number of beds of each compartment was determined from the simulation results. The mean number of

Figure 3. The basic model.

occupied beds was used and an assumption was made that the hospital operates under different levels of emptiness in each compartment. These levels were chosen as follows: 20% for the acute, 5% for the rehabilitation, and 1% for the long-stay compartment, and the number of beds were set at 214, 94, and 191, respectively. For example, the number of beds in the acute compartment was calculated as follows: 171 ÷ 0.8 ≈ 214 beds. These levels of emptiness were based on clinical judgement. In addition, the conversion rates were set as follows: 6.5% from acute to rehabilitation and 16.5% from rehabilitation to long-stay. 5.3. The basic model executed with the replication/deletion method The simulation model starts from emptiness and the output data is collected after it reaches steady state. It was executed 20 times using the replication/deletion method. The warm-up period, calculated from the previous model, remains unchanged as the parameters have not been altered.

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Table 2 Results from model with the replication/deletion method (20 runs). Acute % of patients Avg. % of refused admission emptiness Mean SD 95% CL− 95% CL+

0.2% 0.3% 0.0% 0.3%

Rehab Avg. time spent in the queue

Max queue length

Avg. % of emptiness

2.4 3.1 1.0 3.8

2.0 2.5 0.8 3.1

30.3 16.3 22.6 37.9

11.4% 2.0% 10.5% 12.4%

19.1% 1.3% 18.5% 19.7%

Avg. # of patients in the queue Mean SD 95% CL− 95% CL+

Avg. # of patients in the queue

Long-stay Avg. time spent in the queue

0.8 1.4 0.1 1.5

3.9 7.0 0.6 7.1

Max queue length

Avg. % of emptiness

7.4 8.5 3.4 11.3

9.8% 3.4% 8.2% 11.4%

Table 3 Results from model with the batch means approach (20 batches). Acute % of patients Avg. % of refused admission emptiness Mean SD 95% CL− 95% CL+

0.3% 0.5% 0.0% 0.5%

Rehab Avg. time spent in the queue

Max queue length

Avg. % of emptiness

2.9 3.0 1.5 4.3

2.4 2.4 1.2 3.5

37.8 16.7 30.0 45.6

10.5% 1.8% 9.7% 11.4%

19% 1.1% 18.4% 19.5%

Avg. # of patients in the queue Mean SD 95% CL− 95% CL+

Avg. # of patients in the queue

Long-stay Avg. time spent in the queue

1.2 1.3 0.6 1.8

Thus, roughly 5.5 years (2000 days; warm-up period) are needed for the system to warm up, then it runs for another 11 years (4000 days; steady-state period). Data is collected during the steady state period of the system. Table 2 shows the results. The first column shows the percentage of patients rejected from the system over the total number of patients admitted. The average percentage of emptiness shows the proportion of free beds during the execution of the system. The third column shows the average number of patients waiting in each queue, and the fourth column shows the average time spent in the queue by all the patients who passed through the compartment and not only by those who actually queued. The maximum queue length is the average figure obtained from the maximum number of patients waiting in the queue at a certain instant. It can be seen that the number of patients refused entrance into the system was small, only 0.2% on average or roughly 14 patients per year. The average percentage of emptiness in the acute compartment remained very close to the level it was set, around 19%. The average number of patients who waited in the rehabilitation queue was

5.8 6.4 2.8 8.8

Max queue length

Avg. % of emptiness

15.1 8.3 11.1 19.0

7.9% 2.3% 6.8% 9.0%

2.4 and the average time spent in the queue by all the patients who passed through the rehabilitation compartment was 2 days. The average maximum number of patients in the queue at any one time was 30. The emptiness in this compartment was 11%, which is greater than the 5% we originally stated. Although the average number of patients who waited in the long-stay queue was less (0.8 patients) than the number in rehabilitation (2.4 patients), they waited for almost twice the time (3.9 days). This can be attributed to the considerably longer length of stay at this compartment. The maximum queue length was also considerably shorter: 7.4 patients. However, the average emptiness in the long-stay compartment (9.8%), as in rehabilitation, was higher than the figure initially stated. 5.4. The basic model executed with the batch means method The system was also run using the batch means method. This method is based on a single long run which was divided into 20 batches. Each batch represents 6000 days of steady state and the initial warming up period was 5000 days. See table 3 for the results obtained from this method.

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The results obtained from this method are almost the same as for the previous method. A small increase can be observed in the queueing variables and consequently, a small decrease in the emptiness of the compartments. However, this method gave us a slightly steadier system as the standard deviation is smaller in every variable measured. The percentage of the rejected patients is 0.3% and the average emptiness in the acute compartment is 19%. The figures for the queue between the acute and the rehabilitation compartments are: 2.9 patients waiting, 2.4 days blockage for all the patients and the maximum queue length of 37.8 patients. The average emptiness in this compartment is 10.5%. The figures for the queue between the rehabilitation and the long-stay compartments are: 1.2 patients waiting, 5.8 days blockage for all the patients, maximum queue length of 15.1 patients, and average emptiness in this compartment of 7.9%. 5.5. Technical details The models were built using the MicroSaint simulation package. MicroSaint is an icon-based, network simulation software package that lets the user build models to simulate real-life processes. The computer used was an IBM PC compatible with a 166 MHz Pentium processor and 32 MB of RAM. The operating system was the Windows NT 3.5.1 version. The average running time was 20–25 minutes for one separate run in the replication method and about 6 hours for the single long run in the batch means method.

6. Discussion and conclusions In this paper we used a simulation and flow model to evaluate the flow of patients within a geriatric department. Our results show that the flow model and the unconstrained simulation are equally viable tools to measure bed occupancy in a geriatric department. Different constrained simulation configurations were used to model the internal process and measure its effectiveness. Statistics such as emptiness, waiting time and rejected number of patients can be easily derived from this model. As in other situations where queues form, a key explanation for problems with admission is difficulty in servicing the long-stay patients. In the unconstrained model considerable fluctuations occurred in the levels of occupancy and emptiness in the acute, rehabilitative and long-stay beds, which are relevant from a clinical point of view. Further work is needed to determine the necessary emptiness in the acute beds to prevent admission queues forming, as it is clearly an unrealistic option to minimise admission queues by providing significant emptiness in long-stay. In the constrained model extensive what-if analysis has been carried out to examine the sensitivity to changes in all parameters of the model. The constrained model turned out to be extremely sensitive to even small changes in conversion rates and to a lesser extent to the duration of stay

in long-stay care. The simulation at the original conversion rate values was highly unstable. By changing the original values from 7% and 17% to 6.5% and 16.5%, respectively, we were able to obtain reasonable results. The results could be further improved if conversion rates were reduced again by a small amount. Although most of the patients referred to a department of geriatric medicine are short-stay, the model showed that the outcome of rehabilitative management is also important. This conclusion is in line with the findings of Parry [24]. Given that staff adjust admissions rather than change discharge behaviour [21], small changes in long-stay referral would have a considerable impact on the availability of acute beds. Between 1981 and 1993 open access to private and voluntary nursing homes was promoted by the government. Closure of open access in 1993 by the Community Care Act may therefore be the explanation for current problems in admitting patients. In supermarkets separate server units are set aside for customers with baskets and less than eight items. Also extra server units are opened when queues increase. Similar concepts may need to be introduced into hospitals. Closure of acute hospital beds, coupled with day surgery, may have left insufficient flexibility within the hospital system. A possible way forward would be to estimate the optimal average emptiness that needs to be provided in order to ensure a twenty-four hour a day acute service. Horrocks [13] estimated the necessary emptiness to be 15%. Mitchell et al. [23] reported the average emptiness after change to be 16%. Our simulation results showed the average emptiness to be around 19%. Further work needs to be done on the simulation model to experiment with different arrival and admission methods and/or with data from other hospitals. Also seasonal variations as well as weekends and public holidays may need to be considered as they have been proved to influence referral and admission [17,25]. Finally, we believe these simulation models could be used to assist hospital planners in evaluating the effectiveness of a geriatric department by experimenting with different policy parameters such as level of emptiness, number of beds available for each compartment, conversion rates, length of stay and admissions. They can also be used to demonstrate to hospital planners and clinicians the long term effects of any radical changes in the current system.

References [1] P. Crofts, J. Barlow and R. Edwards, A cliniqueue solution, OR Insight 10 (1997) 22–27. [2] H.O. Davies and R. Davies, Simulating health systems: modelling problems and software solutions, European Journal of Operational Research 87 (1995) 35–44. [3] H.O. Davies and R. Davies, A simulation model for planning services of renal patients in Europe, Journal of Operational Reseach Society 38 (1997) 693–700.

E. El-Darzi et al. / Simulating the flow of patients in a geriatric department [4] R. Davies, An interactive simulation in the Health Service, Journal of Operational Reseach Society 36 (1985) 597–606. [5] R. Davies, An assessment of models of a health system, Journal of Operational Reseach Society 36 (1985) 679–687. [6] R. Davies, Simulation for planning services for patients with coronary artery disease, European Journal of Operational Research 71 (1994) 323–332. [7] R. Davies and T. Davies, Using simulation to plan health service resources: discussion paper, Journal of the Royal Society of Medicine 79 (1986) 154–157. [8] DHSS, Report of a study on the respective roles of the general acute and geriatric sectors in the care of the elderly hospital patient, ISBN 0-902650-34-3, Department of Health, London, 1981. [9] DoH, Circular HSG(95)8, NHS responsibilities for meeting continuing health care needs, London, DoH, 1996. [10] M.S. Feldstein, Operational research and efficiency in the Health Service, Lancet 1 (1963) 491–493. [11] G.W. Harrison, Compartmental models of hospital patient occupancy patterns, in: Modelling Hospital Resource Use: a Different Approach to the Planning and Control of Health Care Systems, eds. P.H. Millard and S.I. McClean (Royal Society of Medicine, London, 1994) pp. 53–61. [12] G.W. Harrison and P.H. Millard, Balancing acute and long term care: the mathematics of throughput in departments of geriatric medicine, Meth. Inform. Med. 30 (1991) 221–228. [13] P. Horrocks, The components of a comprehensive district health service for elderly people – a personal view, Age Ageing 15 (1986) 321–342. [14] P.E. Hudson, V. Peel and A. Rayner, Using computer simulation to plan Accident & Emergency services, British Journal of Health Care Management 3 (1997). [15] V. Irvine and S.I. McClean, Stochastic models for geriatric in-patient behaviour, IMA J. Math. App. Med. Biol. 11 (1994) 207–216. [16] M.A. Law and W.D. Kelton, Simulation Modeling & Analysis, 2nd ed. (McGraw-Hill, 1991).

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[17] C. Lee, C. Vasilakis, D. Kearney, R. Pears and P.H. Millard, An analysis of admission, discharge and bed occupancy of stroke patients aged 65 and over in English hospitals, Health Care Management Science 1 (1998), this issue. [18] S.I. McClean and P.H. Millard, Patterns of length of stay after admission in geriatric medicine: an event history approach, The Statistician 42 (1993) 263–274. [19] S.I. McClean and P.H. Millard, A decision support system for bedoccupancy management and planning hospitals, IMA J. Math. App. Med. Biol. 12 (1995) 225–234. [20] P.H. Millard, Geriatric medicine: a new method of measuring bed usage and a theory for planning, MD thesis, University of London, 1989. [21] P.H. Millard, Throughput in a department of geriatric medicine: a problem of time, space and behaviour, Health Trends 24 (1992) 20– 24. [22] P.H. Millard, Current measures and their defects, in: Modelling Hospital Resource Use: a Different Approach to the Planning and Control of Health Care Systems, eds. P.H. Millard and S.I. McClean (Royal Society of Medicine, London, 1994) pp. 29–37. [23] J. Mitchell, K. Kafetz and B. Rossiter, Benefits of effective hospital services for elderly people, Br. Med. J. 295 (1987) 980–993. [24] A. Parry, An age-related service revisited, in: Go with the Flow: a Systems Approach to Healthcare Planning, eds. P.H. Millard and S.I. McClean (Royal Society of Medicine, London, 1996) pp. 127–130. [25] I.C. Taylor and J.G. McConnell, Patterns of admission and discharge in an acute geriatric medical ward, The Ulster Medical Journal 64 (1995) 58–63. [26] D.W. Vere, Assessing and allocating beds in acute medicine in East London, Br. Med. J. 287 (1983) 849–850. [27] S. Wyatt, The occupancy management and planning system (BOMPS), Lancet 345 (1995) 243–244.