How Data Envelopment Analysis Measures Efficiency Across Organizations

Data Envelopment Analysis

In 1978, renowned operations researchers A. Charnes, W.W. Cooper, and E. Rhodes introduced Data Envelopment Analysis (DEA), a method for evaluating the relative efficiency of similar decision‑making units, often referred to as DEA‑efficient.

Their first model, called the C2R model, studies production units with multiple inputs and outputs that are both scale‑efficient and technically efficient. In 1985, Charnes, Cooper, B. Golany, L. Seiford, and J. Stutz presented the C2GS2 model to examine technical efficiency among production units.

In 1987, Charnes, Cooper, W. Qianling, and H. Zhimin developed the cone‑ratio DEA model—C2WH—which handles cases with many inputs and outputs, allowing decision‑maker preferences to be reflected in the choice of cone. This model can classify or rank DEA‑efficient decision units identified by the C2R model.

DEA opened a new research field in operations research. One early successful application evaluated public school projects for children with intellectual disabilities, using intangible outputs such as self‑esteem and inputs like parental care and education level—variables that lack market prices and clear weighting, highlighting DEA’s advantage.

The method’s benefits have led to widespread adoption in areas such as U.S. military aircraft flight, base maintenance, army recruitment, city planning, banking, and more. DEA can also compare alternative proposals (e.g., investment project evaluation) or predict the relative effect of a decision before implementation (e.g., assessing a new factory’s efficiency relative to existing ones). It evaluates the input scale and technical efficiency of decision units, measuring the economic and social benefits generated from allocated resources.

Evaluating Technical and Scale Efficiency with the C2R Model

Assume there are n homogeneous enterprises (decision units), each with m types of inputs and p types of outputs.

The input‑output relationships of these n units are illustrated below:

Each decision unit’s efficiency index is defined, and the relative efficiency optimization model for unit j₀ is formulated as a fractional programming problem. The known parameters are derived from historical or forecast data, while the weight coefficients are treated as variables. The model seeks to maximize the efficiency index of unit j₀ subject to constraints imposed by the efficiency indices of all units.

Because the model is a fractional program, it must be transformed into a linear programming problem for solution. By introducing appropriate variable substitutions, the original model (1) is converted into a linear form, which can be expressed in vector notation. Its dual problem is also presented in vector form.