Matching supply and demand with discrete event simulation
The crisis in the NHS has dominated the news agenda. Reports have been consistent across the country of staffing shortages, fewer beds, overcrowded departments, longer wait times and diverted ambulances amidst a backdrop of claims of chronic underfunding undermining care, particularly in emergency settings.
It is becoming more and more apparent that the current NHS crisis is one of a system unable to cope with the demand for healthcare. This imbalance, where demand is higher than available supply, inevitably leads to strain on the system with resulting poor quality and risks in care provision.
A lot of commentary on the topic has centred on the need for more central funding that often results in circling back to conversations around how to find those funds e.g.
- ever more efficiency savings
- higher taxation e.g. a penny on National Insurance Contributions
- private health insurance coverage
- patients paying (or co-paying) at the point of care
However none of these conversations really address why we’ve got to a point where the acute healthcare system in England wasn’t prepared for the demands placed upon it, particularly since previous winters have been difficult and there’s plenty of data available.
In situations such as these it is worth considering just how difficult it can be to match supply and demand in complex systems. It isn’t as simple a matter as hiring a few extra doctors or having a few extra beds and hoping. Forecasting and modeling is required and even then all that is possible is to match supply and demand within a range.
To offer an idea of how complex and multifaceted the situation can be in modeling for an overcrowded hospital here are some questions we may need to answer:
Scenario 1 - What if five extra ‘see and treat’ cubicles were available in an overcrowded A&E department?
Should we repurpose them for triage, resuscitation or even as a designated paediatric area?
What about recovery space for patients who’ve just been treated in an ED theatre (where they still exist)?
What about ending trolley waits or situations where patients receive attention in corridors?
Who would staff the cubicles? For example, how much additional capacity can be generated with an extra Band 5 Nurse in A&E?
Scenario 2 - How many patients can be admitted if we had 13 extra unstaffed inpatient beds available in a specialty ward? Is it as simple as 13 extra admissions? What is the full impact?
- Should we place boarders (patients known to need admission, but who do not have a bed to go to) in wards that aren’t clinically inappropriate for them, interfering with the delivery of safe and effective care? If so, should we only send those who are stable, orientated and not receiving active treatment or requiring intensive monitoring?
- Having more patients in beds than the capacity to treat them all only stretches staff, potentially reducing care quality so do we divert existing staff or do we need more staff resource? If so, what’s the sweet spot?
- Does this mean more ambulances can unload? If so, when? Immediately or in a few hours?
- Do we still have capacity available to isolate patients suspected of infectious intestinal disease (e.g. norovirus)? Should we reduce it to make more space?
- Isn’t it true that more frequent board rounds and early morning discharges need to be planned or discharge capacity will fall leading to a downward spiral?
These are not frivolous questions and are presented to highlight the inherent complexity involved in these situations means that modeling is required. When the questions involve some element of activity over time then discrete event simulation (DES) modeling comes into its own.
DES is based on a chronological sequence of connected but discrete events. The model moves forward in time at discrete intervals (at each event) and the events themselves are discrete (mutually exclusive). The system therefore changes instantaneously in response to certain discrete events. These factors give DES the flexibility and efficiency to be used over a very wide range of problems.
The core concepts of DES are entities, attributes, events, resources, queues, and time. Entities are agents (e.g. patients). Entities have attributes (e.g. hip fractures). Entities experience events (e.g. emergency admissions). Events take up resources (e.g. triage nurses). If resources are occupied when an entity needs it then there’s a queue. A clock runs to show time and the next event begins without any interim calculation.
As DES only calculates at discrete points and does not require any calculations between events it differs from continuous simulation, which calculates at each and every time points (continuously) regardless of events like a flight simulator.
DES generates pseudo-randomised numbers that introduce a stochastic element and means it can model non- linear systems. It is increasingly used in healthcare particularly during the planning phase for major service transformation because it is visual, transparent and logical while also enabling users to collaborate to make changes on the fly.
It is likely that DES models could have supported the planning and forecasting for major hospitals ahead or even during the crisis but this is not to imply or suggest that this kind of modeling would have prevented the crisis. Rising demand is a serious and recognized issue. Furthermore, this is not to suggest in anyway that we treat patients as units in an abstract model. Patients, even with minor complaints, deserve the highest standards of care throughout. Instead it is simply to state that complex systems need modeling in order to find a balance between supply and demand.
Hassan Chaudhury is a founder director at Health iQ and Honorary Research Officer in eHealth at Imperial College London