# Efficiency of Public R&D Management Agency and Its Improvement toward Open Innovation
## 2 Research Background and Methodology
### Data Entvelopment Analysis  
The data envelopment analysis (DEA) model was used to analyze the efficiency of R&D agencies. DEA is an analysis technique mainly used to measure the efficiency of research subjects in various fields [15]. The DEA model, first proposed by [PERSON], [PERSON] (1978) [16], is based on the concept of [PERSON] (1957) [17] of relative efficiency. This is a method of measuring the efficiency value of the analysis target by deriving the empirical efficiency frontier by considering multiple input and output factors at the same time, and then comparing it with other DMUs (decision-making units). Here, DMU refers to the object to be analyzed, and in this study, R&D agencies correspond to this. The DEA model can be divided into the CCR [16] and BCC [18] models according to the assumption of the scale effect and be classified as an input- or output-based models according to the purpose of the efficiency measurement. If there are n DMUs, and each DMUj (j = 1,2,..., n) has m inputs (i = 1,2,..., m) and s outputs (r = 1, 2,..., s), the input-based CCR model and the output-based CCR model are as shown in Equations (1) and (2) below. Unlike the CCR model, a constraint of \(\sum_{j=1}^{n}\lambda_{j}=1\) is added in the BCC model. This assumes variable scale returns and means the convexity of the BCC model. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Number of Agencies** & **R\&D Management Agency** \\ \hline \multicolumn{3}{c}{National Research Foundation of Korea (NRF)} \\  & & Institute for Information and Communications Technology Promotion (IITP) \\ Main Purpose & & Korea Evaluation Institute of Industrial Technology (KEIT) \\ (Management of & 8 EA & Korea Institute of Energy Technology Evaluation and Planning (KETEP) \\ R\&D Projects) & Korea Technology and Information Promotion Agency for SMEs (TIPA) \\  & & Korea Institute of Marine Science and Technology Promotion (KIMST) \\  & & Korea Agency for Infrastructure Technology Advancement (KAIA) \\  & & Korea Institute of Planning and Evaluation for Technology in Food, Agriculture and Forestry (IPET) \\ \hline \multicolumn{3}{c}{Korea Institute for Advancement of Technology (KIAT)} \\  & & Korea Health Industry Development Institute (KHIDI) \\  & & Korea Environmental Industry and Technology Institute (KEITI) \\ Supplementary Tasks & & Korea Creative Content Agency (KOCCA) \\ (Management of & 9 EA & Korea Copyright Commission \\ R\&D Projects) & Korea Sports Promotion Foundation \\  & & Korea Meteorological Institute \\  & & Korea Foundation of Nuclear Safety \\  & & Korea Forestry Promotion Institute (KOFPI) \\ \hline \multicolumn{3}{c}{Source: [PERSON] et al. (2021) [10].} \\ \end{tabular}
\end{table} 
Table 1: Current status of R&D management agencies (2020). Input-based CCR model:  
\[ \begin{array}{c}\text{Min}\theta\\ \text{s.t. }\theta\text{x}_{\text{i}}\geq\sum\
olimits_{\text{j=1}}^{n}\text{x}_{ \text{ij}}\lambda_{\text{j}}\quad\text{i}=1,2,\...\,\ \text{m},\\ \text{y}_{\text{r}}\leq\sum\
olimits_{\text{j=1}}^{n}\text{y}_{\text{ji}} \lambda_{\text{j}}\quad\text{r}=1,2,\...\,\ \text{s},\\ \lambda_{\text{j}}\geq 0,\quad\text{j}=1,2,\...\,\ \text{n}.\end{array}  \tag{1}\]  
Output-based CCR model:  
\[ \begin{array}{c}\text{Max}\varphi\\ \text{s.t. }\text{x}_{\text{i}}\geq\sum\
olimits_{\text{j=1}}^{n}\text{x}_{ \text{ij}}\lambda_{\text{j}}\quad\text{i}=1,2,\...\,\ \text{m},\\ \varphi\text{y}_{\text{r}}\leq\sum\
olimits_{\text{j=1}}^{n}\text{y}_{\text{ji}} \lambda_{\text{j}}\quad\text{r}=1,2,\...\,\ \text{s},\\ \lambda_{\text{j}}\geq 0,\quad\text{j}=1,2,\...\,\ \text{n}.\end{array}  \tag{2}\]  
Input-based BCC model:  
\[ \begin{array}{c}\text{Min}\theta\\ \text{s.t. }\theta\text{x}_{\text{i}}\geq\sum\
olimits_{\text{j=1}}^{n}\text{x}_{ \text{ij}}\lambda_{\text{j}}\quad\text{i}=1,2,\...\,\ \text{m},\\ \text{y}_{\text{r}}\leq\sum\
olimits_{\text{j=1}}^{n}\text{y}_{\text{ji}} \lambda_{\text{j}}\quad\text{r}=1,2,\...\,\ \text{s},\\ \lambda_{\text{j}}\geq 0,\quad\text{j}=1,2,\...\,\ \text{n}.\end{array}