Perfect World Model of the EU

withAndrew Nelson, Kesh Baboolal, Jeff Griffiths, Cheryl Voake

Problem

whether further investment in the emergency department was indeed warranted;

whether the allocation of resources within the emergency and assessment units could be improved;

whether capacity within the emergency department was being used to compensate for constraints beyond the emergency unit.

Cardiff and Vale Health Board approached the OR Group within Cardiff School of Mathematics to help determine:

EU Department

A&E

MAU

SAU

Resus

Minors Paeds.

Majors

Majors

Resus

Paed. Minors

Paed.Majors

Minors

GP Ref.

Demand patterns

3 Phases of the day: 1000-1800 1800-0200 0200-1000

3 Phases of the week: Monday Tue/Wed/Thu/Fri Sat/Sun

Majors hourly arrival rate

Majors Pathway

EU Department

A&E

MAU

SAU

Resus

Minors Paeds.

Majors

Majors

Resus

Paed. Minors

Paed.Majors

Minors

GP Ref.

GP Referral hourly arrival rate

GP Referral Pathway

EU Department

A&E

MAU

SAU

Resus

Minors Paeds.

Majors

Majors

Resus

Paed. Minors

Paed.Majors

Minors

GP Ref.

Simulation ModelResus HDU

TB

Minor

Paed.

MAU

SAU

Different Staffing Patterns

Registrars, Consultants, Nurse Assessors Clinical Decision Makers:

18 02 10

11 7 14

11 Members of Staff between 1800 and 0200.

7 Members of Staff between 0200 and 1000.

14 Members of Staff between 1000 and 1800.

Different Staffing Patterns

Closer Look at 8.6.11

Reducing the number of TB, MAU and SAU beds:

Conclusions

Not a perfect world:

Service

(To remove “blockage” ward needs to accommodate an arrival every 30 minutes)

Vile J, Gillard J, Harper PR and Knight VA (2012), “Forecasting Welsh Ambulance Demand

Using Singular Spectrum Analysis”. Journal of the Operational Research Society 63: 1556-1565.

Knight VA, Harper PR and Smith L (2012), “Ambulance Allocation for Maximal Survival with

Heterogeneous Outcome Measures”. OMEGA - The International Journal of Management

Science. 40: 918–926

Knight VA and Harper PR (2012), “Modelling Emergency Medical Services with Phase-type

Distributions”. Health Systems 1: 58-68

Baboolal K, Griffiths J, Knight VA, Nelson AV, Voake C and Williams JE. (2012), “How Efficient

can an Emergency Unit be? A Perfect World Model”. Emergency Medicine Journal. 29:972-977

Sahu SK, Baffour B, Harper PR, Minty JH and Sarran C (2013), “A Hierarchical Bayesian Model

for Improving Short-Term Forecasting of Hospital Demand by Including Meteorological

Information”. To appear in the Journal of the Royal Statistical Society, Series A.

www.profpaulharper.com www.vincent-knight.com