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Eighty-two per cent

Is there is a magic number when it comes to hospital bed occupancy?


I was in London last Thursday, speaking at an NHS England demand and capacity seminar. One of the other speakers showed a slide with a reference to The Hitchhiker's Guide to the Galaxy. Just as it was ridiculous to think that the number 42 could be the answer to the question of life, the universe and everything, so it was equally ridiculous to think that any one number (82%, for example) could be the answer to the question of hospital bed occupancy.

I thought I'd show you three typical hospital wards and let you make up your own minds. For each ward, the chart on the left shows the 365 number-of-beds-occupied-at-midnight jagged line superimposed over the ward's static bed complement. And the histogram on the right shows the same data displayed as a frequency distribution. Number of beds occupied at midnight along the horizontal axis; number of midnights in the year up the vertical axis.

We'll start off with relatively high occupancy. Here's a 30-bed medical ward in calendar year 2012 operating at 95% average bed occupancy:

Next, a 29-bed General Surgery ward operating at 83% average bed occupancy:

And, finally, a 20-bed Paediatrics ward operating at 68% average bed occupancy:

Can we form a judgement from these graphs about the way these three wards are making use of their beds? Can we say that the children's ward can afford to lose beds whereas the medical ward hasn't got enough? Do we need to know more about the mix of elective and non-elective admissions to each ward (or should that not affect our judgement)? Do we need to know more about the day-to-day variability of demand in each of these wards? Do we need to know if variability in discharge is a factor? Do we need to know if the General Surgery ward is Vascular, Colo-rectal, Upper GI or Breast Surgery? Do we need to know if the medical ward is an Assessment Unit or a specialty ward?

Rodney Jones is a man who knows a lot more than most people about hospital beds and he concluded 12 years ago that the magic number of 82% was probably arrived at by the Department of Health as part of the work on the National Beds Inquiry. He also put forward the view that using a one-size-fits-all occupancy figure for hospital beds was a misguided approach. Instead, you have to take account of size and variability. A better measure of how well we match supply to demand is to use his concept of turn-away, a measure of how often a bed is not available when it should be.

Amen to that. Me, I'm growing tired of average percentage bed occupancy as a way of describing how we use hospital beds. I'm growing particularly tired of the idea of some magic number that we should all aspire to. We need visual ways of understanding the relationship between size, variability and length of stay.

Anyway, back to the number 42. Douglas Adams was the author of The Hitchhiker's Guide to the Galaxy and he was once asked how he came up with the number 42 as the answer to question of life, the universe and everything. He replied:

"I sat at my desk, stared into the garden and thought: '42 will do'. I typed it out. End of story."

[16 July 2013]


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Comments on this article

16 July 2013:

Sure, the key thing is variability. If you start with a couple of desirable goals, say "I don't want to turn anyone away" and "I don't want to pay for empty beds" the perfect situation would be 100% predictable: I know precisely how many patients I will have every day, there are no empty beds and no one turned away. Now find the demand variability - in general higher variability means you will have to have more empty beds. But where to make the compromise? Can you assume a cost for the patient turned away, and another for the empty bed? Now the maths is not too hard, at least for the simple one ward situation. But it's complicated...

Harry Longman

Engineer, Patient Access

16 July 2013:

Back in the days of the Cancer Collaborative I used a simple model to demonstrate Erlang’s original observation that, in a telephone exchange in which there is a variation in demand (number of request for a call × length of time of the call), the time waiting to be connected to the call increased dramatically once 82% (or thereabouts) of the switchboard connections were in use. This resonated with the biologists (medics) we were working with because we all know what happens if you try to drive a biological system at 100% capacity. The waiting times and backlog of waste products to be processed goes up dramatically and we get sick.

My hypothesis is that two things happened.

1. A bunch of doctors and managers thought ‘Great! 82% is the answer: we have the Gurus’ words that we need more beds + the scientific evidence (paper for the telephone industry) that this is the case’.

2. As per usual doctors and managers got confused between storage capacity (beds) and processing capacity (man-hours of people). The telephone exchange was measuring processing capacity: a combination of the ability of the switch board staff and the availability of empty plugs to connect calls (processing capacity).

Now the manufacturing engineers woke-up to the significance of Erlang’s work in the 1980s and realised that if you design your processing capacity (hours of manpower available) at anything less than approx. 85% of the peaks of the normal variations in demand (requests × cycle time), you end up with a rapidly rising backlog which then requires hours and hours of wasted man hours to get on top of. What is more, the more the variation in the demand, the more the capacity required to cope. The secret, as Deming said, was management is all about understanding variation. What is the cause of the demand variation? And usually the original customer demand is smooth and/or predictable. The distortion happens upstream within the system itself. Control the variations in the system’s capacity and the variation in downstream demand reduces and therefore the amount of man-hours required to cope is less. (Forrester)

I think we are now getting to the stage that some NHS folks are understanding that the issue is the relationship between the variation demand (patients referred or presenting × processing time) and the variation in man-hours.

Kate Silvester

Managing Director, Kate Silvester Ltd

16 July 2013:

I’m with Rod Jones (and you) about occupancy. If you have been researching Barber-Johnson you will know that occupancy is derived from length of stay and turnover interval (length of bed emptiness). The formula is O = L / (L + T). The shorter the average LOS (as in Paediatrics) and the harder you have to work to achieve high levels of occupancy.

Variation plays an enormous part too.

Mike Davidge

Director, NHS Elect

17 July 2013:

Nice article, Neil, and right on point. No-one I've come across appears to have cottoned on to the fact that a continuous measure of occupancy is critical to making the most of this - even the midnight snapshot gives a badly distorted picture. What should bed occupancy be? 100% at the peak of demand. No more, no less. At other times? Roll on demand predictors, call centre style rota management, a flexible workforce, and good protocols for bed-borrowing.

Matthew Bishop

IM Transformation Consultant & Director, Perspicacity Ltd

17 July 2013:

I think the 82% came from an OR model of daily bed utilization. But it was a bad generalization that tended to encourage people not to think about their actual real problems and possible solutions. And it built in assumptions that arrivals (and probably departures) are random which they are not.

And, worse, it encouraged people to focus on daily (midnight) utilization. A good ward and hospital should know their hourly utilization as this helps decide how to coordinate flows to create free beds at the point in time where they are needed. Since many discharges are done late in the day despite peak emergency arrivals happening in the morning this can be a major problem. Even simple calculations show better coordination of this can generate 15-20% more free beds at the point of need.

If the flows are well coordinated, midnight utilization is meaningless or nearly so.

Steve Black

Consultant, PA Consulting

18 July 2013:

Many years ago I developed a discrete event simulation model (in Witness) that we used with real ITU data to simulate the size of an ITU. The main determinant was to reduce turn-away to zero (this was on the basis that we didn't want to send anyone out of the city). Within the model we had flexibility to hold someone knowing that a bed was about to be free in a few hours. What surprised me (at the time) was that the optimal occupancy was around 63%.

Paul Harriman

Assistant Director - Service Improvement, Sheffield Teaching Hospitals