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Open AccessArticle
Peer-Review Record

A Unified Approach to Efficiency Decomposition for a Two-Stage Network DEA Model with Application of Performance Evaluation in Banks and Sustainable Product Design

Sustainability 2019, 11(16), 4401;
Reviewer 1: Anonymous
Reviewer 2: Anonymous
Sustainability 2019, 11(16), 4401;
Received: 16 July 2019 / Revised: 6 August 2019 / Accepted: 7 August 2019 / Published: 14 August 2019

Round 1

Reviewer 1 Report

The article is a proposal to reconcile the approach to decomposition of efficiency obtained in the two-stage DEA model. The need to reconcile different approaches to efficiency decomposition comes from discrepancies obtained by different researchers with different assumptions, which may lead to confusion among scientists. The authors identify three main methods of efficiency decomposition, which are subject to detailed analysis. Authors of the article presents special cases of three main methods of efficiency decomposition, as well as a generalization of efficiency decomposition based on their own model.

General comments:

1. In the first part of the article there were no comments on the relationship between the efficiency decomposition and efficiency aggregation. This commentery would allow a better positioning of the article in the subject literature (eg Chiang Kao, 2016).

2. The article should be shorter. Many transformations are very detailed. On the one hand, it allows you to better understand the transformations, but on the other hand it requires a lot of attention to understand the whole article. Maybe you should consider transferring some of them to the attachment?


Detailed comments:

1. line 141 (and below) the weights "w" for intermediate measures do not have to be the same for the 1-stage efficiency and 2-stage efficiency. This is an assumption that should be introduced / commented (eg see references [1] and [5]).

2. line 190 - the space designation of the objective function (efficiency space) appears for the model (3), which is stored in lines 163-166. It is worth introducing this symbol when defining the model (3).

3. line 227- what is marked by the point P? Is this the same point as in Figure 1? The text is a bit unclear about it.

4. Tables 1 - 4 should be better explained. Some abbreviations have not been provided (BG model, R-B model). The lower and upper bound efficiency should also be marked in accordance with the indications from lines 127-135. This would make it easier to understand the results.

5. Can you comment on such a high efficiency of almost all DMUs in both stages obtained in table 5 for the CCR model? Is the full efficiency of 8 DMUs out of 11 DMUs (Stage 1) important for this case?

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The article addresses an interesting topic of investigates the efficiency decomposition in the two-stage network DEA model. In scientific literature three major methods for efficiency decomposition have been proposed: uniform efficiency decomposition, Nash bargaining game decomposition and priority decomposition. The presented paper attempts to reconcile differences of the methods by redefining the fairness of efficiency decomposition based on efficiency rank and develops a rank-based model with two parameters.

The scientific problem is presented in clear way. I think the goal of the paper has been reached. The authors briefly introduces the two-stage DEA process, proves the continuity of the Pareto front to developing the proposed new model and simplifying uniform efficiency decomposition model, redefines fairness and develops a rank-based model for efficiency decomposition. After that the authors present the relations between the different methods. At the end of the manuscript there presented two empirical tests to illustrate the new model.

The presented manuscript is full of mathematic calculation to prove and redefine fairness based on efficiency rank and develop a rank-based efficiency decomposition approach.

As was mentioned at the end of the article is presented two tests from banking and car industry. At this moment, I would suggest to add more explanation why the authors  choise such different sectors to test the model. In additional, I would like to propose both examples present in the same way, because the second test is shorter and in some way not clear.

After that I suggest to expand the conclusions, because at this moment this is like a summary of the research. It would be better to add additional information from the empirical tests, also better explain the novel of the manuscript and the proposed model (rank-based model) (because more than 2/3 of conclusion rewrite the abstract).

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

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