What is Data Envelopment Analysis?

Data Envelopment Analysis (DEA) is a powerful method widely used in the evaluation of performance of Decision Making Units (DMUs). These can be business units (for example points of sales, bank branches, dealers, franchisees), government agencies, police departments, hospitals, educational institutions, and even people (DEA has been used in the assessment of athletic, sales and student performance).

Although the mathematics of DEA are difficult for the general user, the assumptions and the underlying idea of the algorithm are quite simple.

• All DMUs under comparison are assumed to operate homogeneously: they receive the same inputs and produce the same outputs (in differing quantities, of course) and these inputs and outputs are representative of the whole population. The figure below shows an indicative model for a bank branch.

In this example, one would exclude branches operating in some special way (for example retail only) or branches involved in a special promotion campaign, to ensure the homogeneity condition.

• The efficiency of each DMU is the ratio (sum of weighted outputs)/(sum of weighted inputs), adjusted to be a number between 0 and 1. This is a very common definition of productivity, typically used with empirical weights. The less inputs consumed and the more outputs produced, the more efficient is a DMU.
• Importantly, in DEA the weights are not known in advance, and are not even the same among DMUs. In fact, the weights for each DMU are calculated to be the most favorable for that particular DMU. This is the unique feature of DEA and introduces the required element of objectivity which is missing when applying arbitrary weights. In a way, each DMU attempts to "promote" the inputs and outputs where it is best (and demote the rest). In the majority of cases this does not suffice to achieve an efficiency of 1, simply because the inputs and outputs levels are not good enough.
• Those DMUs which do attain an efficiency of 1 form a mathematical space (the "efficient frontier") which "envelops" all the other DMU points, hence the name Data Envelopment Analysis. Although difficult to visualize, this frontier is very precisely defined and allows the calculation of potential improvements for the inefficient DMUs. The following figure shows a very special case with only one input (employees) and two outputs (customers and sales). Units A,B,C and D define the efficient frontier, while units E,F and G are inefficient. E could become efficient and move to the efficient frontier at point E', by increasing its outputs or decreasing its input. Unit A is the closest "efficient peer" of E, and in fact it is the model unit for the inefficient unit E. This is another distinct characteristic of DEA. Apart from the efficiency scores, it also provides guidelines for improvement and specific targets for the inefficient DMUs.

The use of such frontiers is not new. Similar methods are applied for example in econometrics for many years. But DEA introduces a new mathematical programming approach to the estimation of efficient frontiers.

Therefore, DEA is a multi-criterial approach, capable of handling multiple inputs and outputs which are expressed in different measurement units. This type of analysis cannot be done with classical statistical methods. Furthermore, because DEA is not a statistical method, one is not constrained in the type and the relations of the data used, as in regression techniques. Inputs and outputs can be anything, including qualitative measurements. In the bank branches example, the quality of service output could be such a measurement, based on the results of a customers survey.

It is out of scope here to say more about DEA. Some more points   are also discussed in the description of XLDEA results. There are many good sources of DEA-related information in the Web. One of the best is Ali Emrouznejad's DEA homepage at http://www.deazone.com

XLDEA provides this sophisticated analysis in the most suitable environment, the MS Excel. It produces extensive results for the main DEA models used today, and automatically creates Excel charts. In view of the analyst's need to present his/ her results in a professional way, XLDEA also supports the production and customization of Macromedia Shockwave Flash charts which can be easily transferred to any browser-based environment.