A generalized goals-achievement model in data envelopment analysis : an application to efficiency improvement in local government finance in Japan

Data Envelopment Analysis (DEA) has become an established tool in comparative analyses of efficiency strategies in both the public and the private sector. The aim of this paper is to present and apply a newly developed, adjusted DEA model – emerging from a blend of a Distance Friction Minimization (DFM) and a Goals Achievement (GA) approach on the basis of the Charnes-Cooper-Rhodes (CCR) method – in order to generate a more satisfactory efficiency-improving projection model in conventional DEA. Our DFM model is based on a generalized Euclidean distance minimization and serves to assist a Decision Making Unit (DMU) in improving its performance by the most appropriate movement towards the efficiency frontier surface. Standard DEA models use a uniform proportial input reduction or a uniform proportial output increase in the improvement projections, but our DFM approach aims to generate a new contribution to efficiency enhancement strategies by deploying a weighted projection function. In addition, at the same time, it may address both input reduction and output increase as a strategy of a DMU. A suitable form of multidimensional projection functions that serves to improve efficiency is given by a Multiple Objective Quadratic Programming (MOQP) model using a Euclidean distance. Another novelty of our approach is the introduction of prior goals set by a DMU by using a GA approach. The GA model specifies a goal value for efficiency improvement in a DFM model. The GA model can compute the input reduction value or the output increase value in order to achieve a pre-specified goal value for the efficiency improvement in an optimal way. Next, using the integrated DFM- GA model, we are able to develop an operational efficiency-improving projection that provides a clear, quantitative orientation for the actions of a DMU.