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.