Pergamon Omega, Int. J. Mgmt Sci. Vol. 24, No. 3, pp. 365-366, 1996

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Improving Discernment in DEA Using Profiling: A Comment

Data envelopment analysis (DEA) was orig- inally conceived as a tool for examining the relative efficiency of production units on the basis of ex post data on outputs produced and inputs consumed. Latterly, DEA-inspired ap- proaches have assumed status within the toolkit of investigators concerned with multi-attribute decision making. In its original environment, DEA essentially classifies the production units into two groups: the relatively efficient and the relatively inefficient. However, in the multi- attribute decision making environment it is often desired to rank a set of alternatives or select a shortlist from the set for more detailed scrutiny. With an emphasis on ranking or selection, discrimination in DEA, or its lack, becomes an issue.

As Tofallis notes [2], there are now numerous devices for improving discrimination/discern- ment within DEA. His proposed approach is clearly a legitimate addition to these to the extent that a decision maker finds it useful in adding value to the data under his~her perusal. Obviously, his profiling technique requires an investigator to restructure the totality of input and output factors into sensible clusters and appropriately handle the resulting multiple performance measures.

In arguing toward his approach, Tofallis draws attention to what he calls 'nonsense ratios' arising in conventional DEA, his example being: number of megawatts generated per village evacuated. This requires discussion for several reasons.

Firstly, nobody would argue that there is a direct causal link between evacuating villages and the production of electricity, i.e. villages are not an input in the sense that they are directly consumed in the process of electricity pro- duction. Nevertheless, villages do need to be

evacuated to provide a (safe) site for the power station which actually will produce the elec- tricity. Ali and Seiford [1, p. 121] are instructive here:

" . . . in data envelopment analysis each data component is classified as either an input or an output. DEA can be applicable, however, in scenarios where the data components can- not be strictly interpreted as inputs or outputs and there is no direct functional relationship between the measures. In such situations a general guideline for the classification is that inputs are components for which lower levels are better while outputs are those measures for which higher levels are more des i red . . . "

Secondly, the ratio is actually the weighted number of megawatts generated per weighted villages evacuated. The weights are assumed to be so dimensioned that the numerator and denominator are both dimensionless virtual out- puts and inputs.

Thirdly, Tofallis may be more concerned by the fact that this ratio arises because other factors which should appear in the ratio effec- tively disappear as they are zero-weighted. This very common occurrence in DEA happens be- cause the alternative being evaluated is not properly enveloped by the empirically deter- mined efficient frontier. In a nutshell, this sig- nals that the point on the frontier against which the alternative is being evaluated is not itself efficient as there are slacks in the outputs and inputs corresponding to the zero weights.

This third point concerns us also and is in fact one of the reasons why we have advocated some form of average cross-evaluation as a measure of performance. Evaluating each alternative against a number of sets of weights and averag- ing the resulting evaluations approximates the effect of evaluating each alternative against the same composite set of weights. Further none of

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these composite weights will be zero unless the same weight is zero for each of the alternatives, an extremely unlikely eventuality.

Tofallis is perceptive in pointing to the possi- bility of 'ganging together' in cross-evaluation, although he may be over-anthropomorphising the computational process. In the context of studies of ex post performance, the data are historical facts. If a number of alternatives turn out to be similar in terms of 'voting' for the same facet of the frontier, i.e. essentially the same set of weights, we would regard this as interesting information. In the case of ex ante

data where the alternatives do not necessarily yet exist, indeed the purpose of the analysis is to determine which one should exist, there is possibly a cause for caution in interpretation. This of course depends on how the alternatives get into the field of analysis. If some agency, knowing that cross-evaluation were to be used, flooded the field with similar alternatives to

obtain a desired result by 'ganging together', this would be problematic. However, if the field consisted of alternatives which are in principle different but collectively typical of the range of options available, and placed there by a decision maker interested in investigating his/her prefer- ences, we would regard similarity in voting for frontier facets as informative.

REFERENCES

I. Ali AI and Seiford LM (1993) The mathematical programming approach to et~ciency analysis. In The Measurement of Productive Efficiency (Edited by Fried HO, Knox Lovell CA and Schmidt SS). Oxford University Press, Oxford.

2. Tofallis C (1996) Improving discernment in DEA using profiling. Omega 24, 361-364.

School of Management University of Bath Bath BA2 7A Y UK

Rodney Green John Doyle

(November 1995)