The joint determination of efficiencies in dea: returns to scale and an application to the UK national health service trusts

Tsai, Pai-fang (1999) The joint determination of efficiencies in dea: returns to scale and an application to the UK national health service trusts. University of Southampton, Doctoral Thesis.

Abstract

Organisations which are involved in several activities simultaneously may have some resources and outputs which are allocated solely to a particular activity, and some resources and outputs which are shared between all activities. This thesis introduces a DEA model for the joint determination of efficiencies to estimate technical efficiency and returns to scale for organisations in this situation. The model developed is based on defining a group of production possibility sets. One for each of the individual activities within the different organisations, and the efficiency is estimated using the Shephard's distance function. The mathematical properties of this model are examined to provide insight into the nature of the optimal solution. It is found that if a solution exists, it will be a global solution. Moreover, the nature of the returns to scale status of every activity in an organisation is estimated using the dual formulation of the model. The analysis, based on the Kuhn-Tucker conditions, indicates that it is possible for a given organisation to operate under constant returns to scale as a whole while its activities operate under increasing or decreasing returns to scale. Furthermore, it is shown that the model can be used to redirect resources internally so as to improve the overall efficiency of inefficient organisations.

The applicability of the model is also demonstrated in this thesis using data from the NHS Trusts in 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 allocations of resources. This distinction becomes important when looking at the efficiency of parts of inefficient DMUs. The estimation of technical efficiency and returns to scale is carried out from both perspectives. The relationship between size and returns to scale is explored. It is found that apparent overall efficiency may hide scale inefficiency in individual activities.

The results of the case study are further examined through the concept of cross-efficiency.

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