A distance friction minimization-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 approach in the analysis of efficiency problems in both public and private sectors. 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 appropriate efficiency-improving projection model in conventional DEA. Our DFM model is based on a generalized distance friction function and serves to assist a Decision Making Unit (DMU) in improving its performance by a proper movement towards the efficiency frontier surface. Standard DEA models use a uniform input reduction or a uniform output augmentation in the improvement projections, but our DFM approach aims to generate a new contribution to efficiency enhancement strategies by deploying a weighted projection function, while it may address both input reduction and output augmentation as a strategy of a DMU. A suitable form of multidimensional projection functions mapping out efficiency improvement is given by a Multiple Objective Quadratic Programming (MOQP) model in conformity with 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 augmentation value in order to achieve in an optimal way a pre-specified goal value for the efficiency improvement. Using next the integrated DFM-GA model, we are able to develop an operational efficiency-improving projection that provides a clear orientation for actions of a DMU. The above-mentioned DFM-GA model will be empirically illustrated by using a data set on cities in Hokkaido prefecture in Japan, where the aim is to increase the efficiency of local government finance mechanisms in these cities, based on various input and output performance characteristics. In summary, this paper presents a practical policy instrument that may have a great added value for decision making and planning of both public and private actors.