Efficiency of \(\mathbf{\text{DMU}}_{\mathbf{o}}\) =\(\mathbf{\ }\frac{\mathbf{\text{sum}}\mathbf{\ }\mathbf{\text{weighted}}\mathbf{\ }\mathbf{\text{outputs}}\mathbf{\ }\mathbf{\text{of}}\mathbf{\ }\mathbf{\text{DMU}}_{\mathbf{o}}}{\mathbf{\text{sum}}\mathbf{\ }\mathbf{\text{weighted}}\mathbf{\ }\mathbf{\text{inputs}}\mathbf{\ }\mathbf{\text{of}}\mathbf{\ }\mathbf{\text{DMU}}_{\mathbf{o}}}\) (1)
Subject to: \(\mathbf{\ }\frac{\mathbf{\text{sum}}\mathbf{\ }\mathbf{\text{weighted}}\mathbf{\ }\mathbf{\text{outputs}}\mathbf{\ }\mathbf{\text{of}}\mathbf{\ }\mathbf{\text{DMU}}_{\mathbf{j}}}{\mathbf{\text{sum}}\mathbf{\ }\mathbf{\text{weighted}}\mathbf{\ }\mathbf{\text{inputs}}\mathbf{\ }\mathbf{\text{of}}\mathbf{\ }\mathbf{\text{DMU}}_{\mathbf{j}}}\mathbf{\ }\mathbf{\leq}\mathbf{1\ \ \ \ \ \ \ }\mathbf{j}\mathbf{=1,2,}\mathbf{\ldots}\mathbf{,\ }\mathbf{n}\)
\(\mathbf{v}_{\mathbf{i}}\mathbf{\geq}\mathbf{0\ \ \ \ \ ,\ \ \ \ }\mathbf{u}_{\mathbf{r}}\mathbf{\geq}\mathbf{0}\) \(\mathbf{i=1,2,}\mathbf{\ldots}\mathbf{,\ m}\) ; \(\mathbf{j}\mathbf{=1,2,}\mathbf{\ldots}\mathbf{,}\mathbf{s}\)