Affiliations: [a] School of Mathematics, Cardiff University, Cardiff, UK | [b] Rookwood Hospital, Cardiff, UK
Correspondence:
[*]
Address for correspondence: Jeff Griffiths, School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, UK.
E-mail: griffiths@cardiff.ac.uk
Abstract: Background:To date, little research has been published regarding the effective and efficient management of resources (beds and staff) in neurorehabilitation, despite being an expensive service in limited supply. Objective:To demonstrate how mathematical modelling can be used to optimise service delivery, by way of a case study at a major 21 bed neurorehabilitation unit in the UK. Methods:An automated computer program for assigning weekly treatment sessions is developed. Queue modelling is used to construct a mathematical model of the hospital in terms of referral submissions to a waiting list, admission and treatment, and ultimately discharge. This is used to analyse the impact of hypothetical strategic decisions on a variety of performance measures and costs. The project culminates in a hybridised model of these two approaches, since a relationship is found between the number of therapy hours received each week (scheduling output) and length of stay (queuing model input). Results:The introduction of the treatment scheduling program has substantially improved timetable quality (meaning a better and fairer service to patients) and has reduced employee time expended in its creation by approximately six hours each week (freeing up time for clinical work). The queuing model has been used to assess the effect of potential strategies, such as increasing the number of beds or employing more therapists. Conclusions:The use of mathematical modelling has not only optimised resources in the short term, but has allowed the optimality of longer term strategic decisions to be assessed.
Keywords: Health resources, personnel management, systems theory, operations research, personnel staffing and scheduling, database management systems
