# 8 – Issues in DEA

The concern with the DEA approach is that by a judicious choice of weights a high proportion of units in the set will turn out to be efficient and DEA will thus have little discriminatory power. The first thing to note is that a unit which has the highest ratio of one of the outputs to one of the inputs will be efficient, or have an efficiency very close to one by putting as much weight as possible on that ratio and the minimum weight () on the other inputs and outputs. In a typical analysis each such ratio may be associated with a different unit and the number of such ratios will be the product of the number of inputs and the number of outputs. Hence in an analysis with six inputs and six outputs, there is a clear possibility of 36 efficient units. In general if there are t outputs and m inputs we would expect the order of tm efficient units, suggesting that the number of units in the set should be substantially greater than tm, in, order for there to be suitable discrimination between the units.

This highlights one of the concerns regarding DEA analysis. A unit can appear efficient simply because of its pattern of inputs and outputs and not because of any inherent efficiency. An approach to resolving this issue is to constrain the weights in some way. Determining a minimum weight for any input and output would ensure that each input and output played some part in the determination of the efficiency measure. Similarly, a maximum limit could be placed on weights to avoid any input or output being over-represented. Clearly these limits should not be heavily constraining as this would tend towards each unit being measured using a common set of weights. Hence a compromise is sought between weights flexibility on the one hand and a common set throughout the system on the other.

An arbitrary application of weights restrictions would be difficult to justify, but recognising that the weights imply value or a cost associated with an input or an output then investigation of the particular context may lead to justifiable restrictions on the weights. This issue has been addressed for the case of a single input by Dyson and Thanassoulis(7) in the context of a Local Authority Department. Here there was a single cost input so that the weights on the outputs related to the cost expended supporting a unit of the output. Given this economic interpretation on the weights of the output a range of possible weights can be justified. For example, if one output measures the number of households that rates must be collected from, or the number of individuals liable to a community charge, then the weight represents the cost of collection from one household or individual. Clearly there is some minimum cost associated with such a collection task and this minimum cost could be estimated and become a lower bound on the weight associated with that output. Constraining weights in this way will of course enhance the discriminatory power of DEA.

A key aspect of DEA is incorporating environmental factors into the model as either inputs or outputs. Resources available to units are classed as inputs whilst activity levels or performance measures are represented by outputs. One approach to incorporating environmental factors is to consider whether they are effectively additional resources to the unit in which case they can be incorporated as inputs, or whether they are resource users in which case they may be better included as outputs. For example in comparing efficiency of schools research has indicated that in general parents of higher educational attainment provide greater support to their children and therefore are effectively an additional resource to the schools and should be classed as an input. An appropriate measure might be simply the number of parents in the higher social classes. In a retailing environment, the strength of competition would be an environmental factor, but in this case the greater that strength the more resources a unit will need to compete. Hence competition is a resource user and a measure of competition should be included as an output. Where possible direct measures of environmental factors should be used, but sometimes surrogate measures are required. For example if social deprivation is seen as an environmental factor which is a resource user then this might be represented by, for example, the number of children qualifying for free lunches in the context of schools, or the number of individuals whose first language is not English in the context of say Social Services Departments.

If the set of organisational units is part of the profit-making sector of the economy (e.g. bank branches) it could be argued that profitability is the only performance measure of relevance. The main argument against this is that environmental factors can affect the attainment of profitability. A profitable retail outlet may be being managed efficiently or it may be just enjoying favourable environmental factors, whilst an unprofitable one may be being badly managed or simply experiencing unfavourable pressures from the environment. If poor profitability is not a sufficient measure of performance in the profit-making sector, neither can it be ignored. In making decisions about units, both efficiency and profitability are relevant and one approach would be to use DEA to determine efficiency and to separately determine profitability. Units could then be assessed on an efficiency/profitability matrix which has similarities in structure to the product portfolio matrix. This is displayed in figure 2.

Organisational units whose profitability and efficiency located them in the star quadrant are the flagship units and should provide examples of good operating practice and are probably also in a favourable environment. The sleepers are profitable but this is more to do with favourable environmental conditions than good management They are candidates for an efficiency drive leading to even greater profits. The question marks have potential for a greater efficiency and possibly greater profits. Attempts should be made to increase their efficiency and this may lead to greater profitability. The dogs are efficiently operated units but low on profitability due to an unfavourable environment. In the extreme case it may be sensible to divest of these and relocate the staff to other units. This approach thus sees efficiency and profitability as two key performance measures, each of which can help with the management of the overall system of units.