A Stepwise Projection Data Envelopment Analysis for Public Transport Operations in Japan

With tightening budgets and increasingly critical reviews of public expenditure, there is a need for a careful analysis of the performance of public bodies in terms of an efficient execution of their tasks. These questions show up everywhere in the public domain, for instance, in the provision of medical facilities, the operation of postal services, or the supply of public transport. A standard tool to judge the efficiency of such agencies is Data Envelopment Analysis (DEA). In the past years, much progress has been made to extend this approach in various directions. Examples are the Distance Friction Minimization (DFM) model and the Context-Dependent (CD) model. The DFM model is based on a generalized distance friction function and serves to improve the performance of a Decision Making Unit (DMU) by identifying the most appropriate movement towards the efficiency frontier surface. Standard DEA models use a uniform proportional input reduction (or a uniform proportional output increase) in the improvement projections, but the DFM approach aims to enhance efficiency strategies by introducing a weighted projection function. This approach may address both input reduction and output increase as a strategy of a DMU. A suitable form of multidimensional projection functions is given by a Multiple Objective Quadratic Programming (MOQP) model using a Euclidean distance. Likewise, the CD model yields efficient frontiers in different levels, while it is based on a level-by-level improvement projection. The present paper will first offer a new integrated DEA tool – emerging from a blend of the DFM and CD model using the Charnes-Cooper-Rhodes (CCR) method - in order to design a stepwise efficiency-improving projection model for a conventional DEA. The above-mentioned stepwise-projection model is illustrated on the basis of an application to the efficiency analysis of public transport operations in Japan.