Home
Patient Flow
FlowModels Percept World Class Commissioning
Breast Screening Simulation Tools
Mental Health
18 Weeks 'Lean Thinking'
Bed Management
Client Comments
More About Us
Contact Us
The Directors of Focused_On Health have significant experience of implementing "Culture Change" in commercial organisations. With the benefit of this experience and their Health Service knowledge they hold some fairly firm views about the most successful way of introducing this sort of change in NHS Trusts. There are specific considerations due to complexity, diversity and multiple management objectives. The views of Focused_On Health can be seen at How can a NHS Hospital become a 'Lean' Hospital (PDF)
It is a mathematical fact that systems and resources that are run far in excess of just 75% for prolonged periods tend to become highly stressed, prone to catastrophic failure, and have very little in-built flexibility.
This is widely understood outside of the NHS but its lack of recognition within the NHS causes some severe problems. For example, it is generally acknowledged that Medical Beds in many Acute and Mental Health Hospitals are often run dangerously close to 100% Occupancy.
The NHS drive for "Efficiency" has often resulted in situations where other resources are also being utilised at levels approaching 100%. The consequences of this will certainly be long Wait Times, long Queues and reduced Staff Efficiency. This doesn't even consider the stress and frustration imposed on Staff who are not able to perform their tasks as they would wish.
These bad consequences of excessively high levels of Utilisation are not NHS specific - they are the highly predictable consequences of the mathematics of Queuing Theory. The basic principles are, therefore, illuminating when we are considering what we should do to organise a Health Care delivery system.
It is essential to the future day-to-day performance of the NHS that NHS executives, management, clinicians, and healthcare professionals accept the rigour of Operational Research (OR) and leverage the benefits of basic Management Science.
Let us focus on just two of the main principles involved:
In any system involving random arrivals, random service times and a number of service channels (such as A&E or a Medical Ward), if u represents overall Utilisation (e.g. 0.75 = 75%), then we can expect:-
Wait time for the system to be proportional to [1/(1-u)]
And,
Number of patients in the queue to be proportional to [u/(1-u)]
If you are mathematically inclined, then an authoritative paper can be found at the homepage of Ivo Adan of the Department of Mathematics and Computer Science, Technical University of Eindhoven ( Chapter 5 M/M/c queue, Equations 5.2 and 5.3 - Note I have used u rather than the Greek rho ).
The time "lost" by Frontline Staff trying to place patients into queues or select patients from queues probably varies (within limits) according to the square of the queue length.
Of course, limits exist in real life because if there are several hundred patients queued, then the staff just have to stop worrying about the queue and get on with their jobs. Some Patients will eventually drop out of the health system one way or another.In the following chart the Red line is the expected Wait Time, the Yellow line is the expected Queue Length and the Green line is an estimate of the Time Wasted on queue administration. These are plotted against varying levels of utilisation.

Every day you might see the bad consequences of the NHS not applying simple OR / Management Science - you just need to look at your Service Levels, Patient satisfaction, Staff Efficiency and Morale.
Your own particular Ward, A&E Unit, or Clinic may have different arrival rates and different service times or numbers of service channels, but the general principle which applies is:
Once we start to exceed 70% utilisation, the waits and queue lengths start to increase. When we get to 80% utilisation, this increase begins to get much quicker.
Utilisations in the range 90-100% cause alarming increases.
This is not complex management science - It is simply the predictable and real-life effect of widely understood mathematics and the exponential shape of the curve: W=1/(1-u) [with u in range (0,1)]
In other words, the NHS must learn how to become more "Efficient" by managing its Resource Utilisation and Bed Occupancy levels down and consistently below 85%
OPTIMISED RESOURCES : GREATER PATIENT CARE