Development of Integrated Linear Programming Fuzzy-Rough MCDM Model for Production Optimization

Round 1

Reviewer 1 Report

The topic is interesting but I have some question and suggestion to improve the article: 

(1) Is there any new on the method  ? The LPP and used MCDM are known, so where is the new contribution.

(2) Motivation is not clear. The motivation and novelties should be clearly written briefly in introduction section. 

(3) The data source is not clearly mention. Briefly cite it.

(4) By which software the LPP is solved should be mention, same for MCDM also. 

(5) Figure number 3 and 4 are very tough to understand. Draw in a scientific manner. 

(6) There should be more remarks, note, axioms. Explain the important figure briefly.

(7) The algorithm of the methods should be written. Pseudo code for the method may be added. 

(8) Add managerial insights before conclusion section. Write how your research is important for society or any organizations. 

(9) Integration of LPP and MCDM method should be explain briefly. 

Author Response

Reviewer 1:

Thank you very much for the useful suggestions. We accepted all of the suggestions and we are sure that this will improve the quality and contribute to a better understanding of the paper.

The topic is interesting but I have some question and suggestion to improve the article:

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Comment 1: Is there any new on the method? The LPP and used MCDM are known, so where is the new contribution.

Reply: Contributions are clearly noted in the introduction section. Also, novelty is apparent. Extension of the CRADIS method is the first time represented in our paper. Novelty contributions are manifested through the introduction and material and methods sections.

The following can be identified as special contributions to this paper:

1) Formation of a novel integrated model consisting of linear programming, IMF SWARA method and Rough CRADIS approach.

2) Extending the CRADIS approach with Rough Numbers (R-CRADIS) and presenting it for the first time in the literature, which is an enrichment of the entire field that treats multi-criteria problems.

3) Solving the special case of linear programming obtaining multiple optimal solutions and integration with a MCDM model in order to achieve the desired optimum.

4) Carrying out a sensitivity analysis, based on which decision-makers can make decisions in real time by looking at the real needs of the company and market requirements at any moment, and by considering the simulated values of criteria and obtaining new optimal solutions.

Comment 2: Motivation is not clear. The motivation and novelties should be clearly written briefly in introduction section.

Reply: The following has been added in introduction.

Motivation and objectives of the paper can be manifested through the following. When applying LP for the optimization and management of production processes in this special case, several potential solutions are obtained instead of one which is usually the case. In order to determine one solution that is optimal under the given circumstances and taking into account various factors, the integration with a novel MCDM model was carried out. Also, the aim is to develop a model ensuring managers make real-time decision-making

Comment 3: The data source is not clearly mention. Briefly cite it.

Reply: The data has been created for the purpose of this study and for the purpose to explain the special case of linear programming where the optimal solutions represent a multi-solution.

Comment 4: By which software the LPP is solved should be mention, same for MCDM also.

Reply: Thank you for suggestion. We have added it below Figure 1 and above Table 2.

Comment 5: Figure number 3 and 4 are very tough to understand. Draw in a scientific manner.

Reply: Figure 4 has been replaced, while in Figure 3 we have added axis titles in order to better understanding.

Comment 6: There should be more remarks, note, axioms. Explain the important figure briefly.

Reply: All Figures are explained in the text. Axioms and more remarks are not necessary for such type of study and developed methodology.

Comment 7: The algorithm of the methods should be written. Pseudo code for the method may be added.

Reply: As the first we have shown the algorithm of the whole reseach on Figure 1. All stages of the research have been explained in materials and method section below this Figure. After that we shown all steps important for this study. Especially attention is on algorithm of newly developed Rough CRADIS method. In such circumstances, pseudo code will be redundant, but we can create it if you insist.

Figures 1. Research methodology

Comment 8: Add managerial insights before conclusion section. Write how your research is important for society or any organizations.

Reply: A new 4.3. subsection has been added.

4.3. Limitations and managerial implications

Limitations of the proposed research can be observed from linear programming and MCDM methodology. From the aspect of linear programming number of variables can represent limitations, while the developed Rough CRADIS model can be applied for group decision-making only, which is the second limitation.

It is very important to note that sensitivity analysis enables real-time decision-making since the decision-maker has at his disposal a set of 40 formed scenarios in which the criteria change their original values. This means that in real time, if it is more important for the company to satisfy the requirements of the market with product B rather than A, it can precisely determine from the obtained results what quantity of product it needs. The same is the case with the use of own resources, which are presented in the paper as criteria.

Comment 9: Integration of LPP and MCDM method should be explain briefly.

Reply: Integration of LPP and MCDM methodology has been explained in introduction and material and methods section.

Reviewer 2 Report

A sufficient amount of literature review is discussed. The conclusion is well well-written that shows the main contribution to the manuscript.

The authors should add and highlight the objective in the Introduction.

The limitations of the proposed methodology should be written.

The comparative analysis of the proposed methodology with existing techniques should be revised.

Please label all equations, figures, and tables in a sequence with label and ref commands to increase the readers' interest.

Author Response

Reviewer 2:

Thank you very much for the useful suggestions. We accepted all of the suggestions and we are sure that this will improve the quality and contribute to a better understanding of the paper.

A sufficient amount of literature review is discussed. The conclusion is well well-written that shows the main contribution to the manuscript.

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Comment 1: The authors should add and highlight the objective in the Introduction.

Reply: Motivation and objectives are added in introduction:

Motivation and objectives of the paper can be manifested through the following. When applying LP for the optimization and management of production processes in this special case, several potential solutions are obtained instead of one which is usually the case. In order to determine one solution that is optimal under the given circumstances and taking into account various factors, the integration with a novel MCDM model was carried out. Also, the aim is to develop a model ensuring managers make real-time decision-making.

Comment 2: The limitations of the proposed methodology should be written.

Reply: Limitations has been added before conclusion section.

Limitations of the proposed research can be observed from linear programming and MCDM methodology. From the aspect of linear programming number of variables can represent limitations, while the developed Rough CRADIS model can be applied for group decision-making only, which is the second limitation.

Comment 3: The comparative analysis of the proposed methodology with existing techniques should be revised.

Reply: Added information: obtained results were compared with four other Rough MCDM methods: Rough WASPAS [11], Rough SAW [12], Rough ARAS [13] and Rough MARCOS [14].

Each high-quality paper should have sensitivity analysis and comparative analysis in order to verify the proposed model and to determine its stability. Each used method has its advantages as has been shown in the part of the methodology section.

Comment 4: Please label all equations, figures, and tables in a sequence with label and ref commands to increase the readers' interest.

Reply: We have improved it, we have added axis titles in all Figures.

Reviewer 3 Report

The manuscript "Development of Integrated Linear Programming Fuzzy-Rough MCDM model for Production Optimization" deals with a novel integrated methodology for decision-making processes. The authors have represented a special case of linear programming and integration with multicriteria decision-making models. The manuscript has the quality and represents a very good study with a strong and new proposed methodology. The authors are very familiar with the fields. Contributions to the paper are:

- Development of Rough CRADIS method for evaluation and ranking alternatives.

- The paper has excellent structure with a clear explanation. Introduction section cover motivation, significance, and background. Also, contributions are well explained. 

- Provided diagram of research flow with an extensive explanation. That is practically graphical abstract.

- Developed methodology has been provided in detail.

- Good definition of the problem.

- Good explanation of variants and used criteria.

- Performed sensitivity analysis with changing criteria weights.

- Performed comparative analysis.

- Calculated SCC and WS coefficients.

The paper has great potential and can be accepted after the following minor corrections:

- Line 138. No need for red color.

- Equations 9 and 10. I agree that is well known what is B and C, but should be defined. Please correct.

- Line 170. The numbering of the equation isn't with margin.

- You have used rough numbers, while the initial decision-making matrix represents equal L an U numbers. Please add an explanation.

Author Response

Reviewer 3:

Thank you very much for the useful suggestions. We accepted all of the suggestions and we are sure that this will improve the quality and contribute to a better understanding of the paper.

The manuscript "Development of Integrated Linear Programming Fuzzy-Rough MCDM model for Production Optimization" deals with a novel integrated methodology for decision-making processes. The authors have represented a special case of linear programming and integration with multicriteria decision-making models. The manuscript has the quality and represents a very good study with a strong and new proposed methodology. The authors are very familiar with the fields. Contributions to the paper are:

- Development of Rough CRADIS method for evaluation and ranking alternatives.

- The paper has excellent structure with a clear explanation. Introduction section cover motivation, significance, and background. Also, contributions are well explained.

- Provided diagram of research flow with an extensive explanation. That is practically graphical abstract.

- Developed methodology has been provided in detail.

- Good definition of the problem.

- Good explanation of variants and used criteria.

- Performed sensitivity analysis with changing criteria weights.

- Performed comparative analysis.

- Calculated SCC and WS coefficients.

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The paper has great potential and can be accepted after the following minor corrections:

Comment 1: Line 138. No need for red color.

Reply: Thank you. Corrected.

Comment 2: Equations 9 and 10. I agree that is well known what is B and C, but should be defined. Please correct.

Reply: Definition of B and C has been added.

Comment 3: Line 170. The numbering of the equation isn't with margin.

Reply: Thank you. Corrected.

Comment 4: You have used rough numbers, while the initial decision-making matrix represents equal L an U numbers. Please add an explanation.

Reply: The initial decision-making matrix represents equal low and upper numbers because it represents the difference in satisfying the set restrictions for each criterion separately which is essential for managers while having no influence on the application of the rough model.

Round 2

Reviewer 1 Report

The paper is now acceptable.