Using Singular Spectrum Analysis to obtain staffing level requirements in emergency units

Abstract

Many operational research (OR) techniques use historical data to populate model input parameters. Although the majority of these models take into account stochastic variation of the inputs, they do not necessarily take into account seasonal variations and other stochastic effects that might arise. One of the major applications of OR lies within healthcare, where ever increasing pressure on healthcare systems is having major implications on those who plan the provision of such services. Coping with growing demand for healthcare, as well as the volatile nature of the number of arrivals at a healthcare facility makes modelling healthcare provision one of the most challenging fields of OR. This paper proposes the use of a relatively modern time series technique, Singular Spectrum Analysis (SSA), to improve existing algorithms that give required staffing levels. The methodology is demonstrated using data from a large teaching hospital's emergency unit. Using time dependent queueing theory, as well as SSA, staffing levels are obtained. The performance of our technique is analysed using a weighted mean square error measure, introduced in this paper.

Keywords:

• Singular Spectrum Analysis
• time dependent queueing theory
• staffing
• healthcare

Acknowledgements

The authors thank Professor Paul Harper (Cardiff School of Mathematics) for his constructive advice throughout the preparation and writing of this paper.