Input efficiency profiling: An application to airlines

Data envelopment analysis (DEA) can produce results which lack discrimination, one consequence of this is that a large proportion of decision-making units (DMUs) appear to be efficient. In addition, because it is a radial measure of efficiency it assumes that all inputs at a naturally enveloped production unit need to be reduced by the same proportion for efficiency to be achieved. It would seem to be more realistic to expect different inputs to have different efficiencies associated with them. A method is presented which retains the original spirit of DEA in trying to extract as much information as possible from the data without applying value judgments in the form of additional constraints. We propose that inputs which are not substitutes for each other be assessed separately and only with respect to outputs which consume them or to which they are otherwise related. In this way input-specific efficiency ratings are derived giving a profile for each DMU. When applied to a data set of 14 airlines the method uncovers inefficiencies which DEA could not find. Whereas DEA found half of the airlines to be fully efficient in all factors, our profiling approach was more discriminating and showed that none of the airlines were efficient in all three of the inputs considered. This highlights a significant difference with DEA: by investigating the utilisation of individual inputs we are able to identify best-practice in each area. It is quite possible that no unit demonstrates best-practice in every area and so each unit will have targets to work toward this is intuitively appealing as well as providing a link with the philosophy of best practice benchmarking. BIOGRAPHICAL MATERIAL Chris Tofallis is a Senior Lecturer in O.R. at the University of Hertfordshire Business School. He holds a first class degree in physics, a masters degree in operational research and a doctorate in applied mathematics, all from London University. His research interests include the development of methods for (i) model building from data with multiple dependent variables and (ii) efficiency estimation. He also originated the chaotic bank account model as a means of teaching deterministic chaos.