A variable returns to scale data envelopment analysis model for the joint determination of efficiencies with an example of the UK health service

A multi-activity DEA model for the joint determination of efficiencies with variable returns to scale is developed in this paper. The model contains an element of complexity that is not present in the previous DEA models for estimating returns to scale. It is found that apparent overall efficiency may hide scale inefficiency in individual activities. The model is applied to study the performance of individual specialties of National Health Services Trusts in the UK. It is argued that efficiency can be defined from two different perspectives: either as the most efficient internal allocation of resources, or the most efficient overall allocation of resources. This distinction becomes important when looking at the efficiency of parts of inefficient DMUs. The relationship between size and returns to scale is also explored. This method allows the determination of optimal size of an activity.