2.2 NDEA Model description
Data Envelopment Analysis (DEA) is a non-parametric method for the
relative assessment of a set of homogenous decision-making units. This
method has wide applications in managerial assessment and recognizing
inefficient units. Traditional DEA models cannot provide accurate
information about the inefficiency of various units. This problem has
been solved by network DEA models in real world. In this research, the
internal structure of each lab consists of three stages (pre-test, test,
and post-test).
Assume that there are n DMUs (in this paper the DMUs are labs). Assume
that each\(\mathrm{\text{DMU}}_{\mathrm{j}}\mathrm{(}\mathrm{j}\mathrm{=1,2,}\mathrm{\ldots}\mathrm{,}\mathrm{n}\mathrm{)}\)uses m inputs \(x_{\text{ij}}(i=1,2,\ldots.,m)\) and produces s
outputs\({\ y}_{\text{rj}}(j=1,2,\ldots,s)\). The inputs have unequal
shares in producing the outputs. Technically, their impact coefficients
are not the same. Charnes and Cooper 21 managed to
solve the problem of coefficients. They improved the model of Farrell
22 and Fieldhouse and suggested a model that could
measure efficiency with several inputs and outputs. This is known as the
CCR model.
Consider an impact coefficient (weight) \(v_{i}(i=1,2,\ldots,\ m)\)for each input \(x_{\text{ij}}(i=1,2,\ldots.,m)\) and an impact
coefficient (weight) \(w_{i}(i=1,2,\ldots,\ m)\) for each
output\(\text{\ y}_{\text{rj}}(j=1,2,\ldots,s)\). We can calculate the
efficiency of each DMU using Model 1.