The previous article depicts the analysis and interpretation of the Input oriented multi-staged **constant returns to scale (CRS)**. Output oriented multi-staged * Constant returns to scale data envelopment analysis (CRS-DEA)* is, however, based on a different principle. It says that “an inefficient unit is made efficient through the proportional increase of its outputs, while the inputs proportions remain unchanged” (Coelli, 2008). The output variables are either increased or decreased irrespective of the input variables (Total Capital and Deposits).

## Efficiency based on Output oriented *CRS-DEA*

Bank 7 and 8 are efficient with values of 1.000 amongst the 10 sample banks. Bank 7 and 8 are only Banks that has an efficient or proportional Total Loans and Profit. Interpretation for the Banks indicates the need to improve Total Loans and Profits by either decreasing or increasing the Total Loans and Profits levels. 86% for Bank 1, 89% for 2, 68% for Bank 3 and so on for other Banks.

The above figure, shows the trend of case banks in the case of efficient of output oriented analysis.

## Summary of slacks

Next, in the analysis is the summary of slacks. As mentioned before, the summary of slacks represents the value which shows the discrepancy in the constant or proportional change of Output and Input variables. The analysis, indicated that all the Banks except for 7 and 8, has slacks that caused a proportional change of Output and Input variables. Interpretation indicates that Bank 1 with the proportionality of Total Loans and Profit (output variables) either decreased or increased by 914837.979 to become efficient. Similarly, Bank 6 has to improve its efficiency by increased or decreased Total Loans and Profit by 38976.844. For the rest of the inefficient Banks, similar interpretations are to be made.

## Summary of Peers

Interpretation indicates that Bank 1 must either follow the input-output variables of 7^{th} and 8^{th} Bank. Similarly, Banks 2 and 3 can only follow the proportional input-output variables (Total Capital: Deposits: Total Loans: Profits) of 7^{th} Bank. So, as to become efficient given the values of the output variables. This is either because the 2^{nd} and the 3^{rd} Bank do not have the estimated constant Total Capitals and Deposits to follow 8^{th} Bank’s organizational performance model. Again, peer weights of Bank show that the Bank 1 can either follow 44% of the 8^{th} Bank’s values or follow 179% of the 7^{th} Bank’s value. Similarly, Bank 2 can follow 53% of the output variables of Bank 7 to become efficient.

However, Bank 7 and 8 as the benchmarked Bank or reference Bank whose output-input proportionality can be followed to become efficient, has been benchmarked or referred 8 and 5 times respectively.

## Summary of Targets

In case of summary of targets, the Loans and Profit targets (output targets) remain the same for efficient organizations.

For example, Bank 7 and 8 have the same targets, while other banks have targeted total loans and profits (output variables).

Interpretations indicate that Bank 1 with a constant input of Total Capital (225906.000) and Deposits (815884.021) gives efficiently proportional Total Loans of 13202282.048 and Profit of 1822748.739.

The graph shows the percentage of difference change. In this case, between the actual loans and total profits and the projected loans and total profits for the banks to become efficient. For bank 4 it needs to change its loans and total profits by 85% to become efficient. Similarly, for other banks 0% change shows that the banks are efficient and need not change their values.

## Radial movement, slack movement and projected value

Individual bank wise efficiency results (firm by firm results) are the outcome of choosing the ‘Multi-stage’ form of analysis (Coelli, 2008).

Interpretations indicate that the adjusted proportionality of input and output are 11332022.048 and 1564534.739 for the 1^{st} firm. However, there is slack movement in the 2^{nd} bank along with radial movements of 1299187.687 and 478733.944 of 1157187.536. This shows that with a change or improvement of 1157187.536, Bank 2 can become efficient. This is by achieving the projected value of 2614082.223. Thus, for every radial and slack movement, the proportionality of input and output variables is represented as projected value (Gang & Zhenhua, 2014). Thus, the projected values show the actually perceived variables for proportional input and output values. This can help make an organization efficient.

Furthermore, Bank 10 indicates that for projected Total Capital of 883.818 and Deposits of 5311.000 (inputs). Consequently, the bank will have Loans of 94834.447 and Total Profit of 1592.692 to become efficient. In the upcoming articles **Variable Returns to Scale (VRS) **data envelopment analysis for the same case banks will be discussed.

#### References

- Coelli, T. J. (2008). A Guide to DEAP Version 2.1: A Data Envelopment Analysis (Computer) Program. CEPA Working Papers, 1–50. Retrieved from https://absalon.itslearning.com/data/ku/103018/publications/coelli96.pdf.
- Gang, C., & Zhenhua, Q. (2014). MaxDEA Pro 6.3 Manual. Beijing Realworld Research and Consultation Company Ltd, 1–71.

Multi stage CRS analysis and interpretation of input orientation | Slacks based measure or SBM analysis in DEA |

### Avishek Majumder

#### Latest posts by Avishek Majumder (see all)

- Use of Psychoanalytic theory and Pavlovian theory by online marketers - August 14, 2019
- Supply chain costs management models - August 12, 2019
- Quantitative and qualitative forecasting techniques in logistics management - August 6, 2019

plse send me sir research papers on these all areas

Dear Raja,

Thank you for writing. The research papers for all these topics are easily available. Use the keywords Data envelopment analysis, efficiency, and industry name (that you choose to work on).

Hi,

I’m a student that has just started using DEAP.

I am trying to identify the technical efficiency of a 16 train companies for which I have 4 year panel data for 1 output and 3 inputs. The malmquist summary output gives values for technical change, technical effiency change etc but no technical efficiency value . I would be very grateful for advice / help . Thanks

The technical change value indicates the extent of improvement required for the efficiency change. This would reflect the efficiency change required by the training companies. But, it still you need the technical efficiency value you can use the free version of MAX DEA software.