Optimal Segmentation over a Generalized Customer Distribution

Round 1

Reviewer 1 Report

Thank you for sending me for review the paper “Optimal Segmentation over a generalized customer distribution”; Manuscript no.: axioms-1159999.

Essentially the paper attempt to implement Nash equilibrium under generic distribution in consumer preference. This kind of optimization problem is known methodology and has been used to solve various types of problems. But, the authors presented a new point of view of this problem and I am giving them a support in this direction. From my point of view, its quality and originality is enough to be published. I will try to justify my opinion, given as:

¾     Similarity index is 12%, which is acceptable for academic and scientific writing.

¾     Abstract and Introduction section should be revised. Introduction section should be better updated with motivation behind this study, research gap, novelty and contributions of the work. As a part of this I suggest authors to add more recent published papers (published in last two-three years). I suggest to add and discuss more papers published in recent two three years, like Giri, B. C., & Dey, S. (2020). Game theoretic models for a closed-loop supply chain with stochastic demand and backup supplier under dual channel recycling. Decision Making: Applications in Management and Engineering, 3(1), 108-125.
¾     The motivation towards the proposed work is not clear.
¾     Why someone should use your proposed work in practice, and what are the advantages of your work in comparison with others.
¾     The conclusion writing should be improved. Please rewrite the Conclusion section by adding more advantages, limitations and the future research direction of the proposed work.
¾     The notations used should be rechecked.

Author Response

Response to Reviewer 1 Comments

Point 1:. Essentially the paper attempt to implement Nash equilibrium under generic distribution in consumer preference. This kind of optimization problem is known methodology and has been used to solve various types of problems. But, the authors presented a new point of view of this problem and I am giving them a support in this direction. From my point of view, its quality and originality is enough to be published. I will try to justify my opinion, given as:

Response 1: Thank you for your encouragement. All issues and comments have been addressed in this revision.

Point 2:. Similarity index is 12%, which is acceptable for academic and scientific writing.

Response 2: Thank you for the work.

Point 3:.Abstract and Introduction section should be revised. Introduction section should be better updated with motivation behind this study, research gap, novelty and contributions of the work. As a part of this I suggest authors to add more recent published papers (published in last two-three years). I suggest to add and discuss more papers published in recent two three years, like Giri, B. C., & Dey, S. (2020). Game theoretic models for a closed-loop supply chain with stochastic demand and backup supplier under dual channel recycling. Decision Making: Applications in Management and Engineering, 3(1), 108-125.

Response 3:

We have revised the manuscript according to suggested.

In the revision, motivation is reinforced for better exposition. Research gap, novelty, and contributions had also been revised for a clear explanation. Two recently published papers had been added for better suitability of the work. We added to the text to explain that the dual-channel competition with price sensitivity leads to low profit for a supply chain [a], and cost-sharing contracts resolve channel conflict in asymmetric Nash bargaining products [b].

A dual-channel closed-loop supply chain is considered for waste recycling, and it is also observed that when the recyclability degree of wastes increases, the expected total profit increases for the whole supply chain.

Higher price sensitivity of customer demand leads to lower profit for the chain members [a]. Two different coordination contract mechanisms, namely, all unit quantity discount along with franchise fee and revenue sharing contracts, are proposed to resolve channel conflict, and asymmetric Nash bargaining product is used for a particular profit split.

It reveals that the retailer denies the manufacturer’s warranty cost-sharing proposal for a better payoff [b].

 

Refernce

[a]Giri, B. C., & Dey, S. (2020). Game theoretic models for a closed-loop supply chain with stochastic demand and backup supplier under dual channel recycling. Decision Making: Applications in Management and Engineering, 3(1), 108-125.

[b]Panda, S., Modak, N. M., & Cárdenas-Barrón, L. E. (2020). Does extended warranty depict competitive advantage to a retailer in a retail-e-tail channel supply chain. Computers & Industrial Engineering, 149, 106770.

 

Point 4:.The motivation towards the proposed work is not clear.

Response 4:

In the revision, we have rewritten the motion for better exposition to this paper.

In a conventional setup of spatial competition problems, consumers are assumed to prefer each variation of products in the market equally, and the strategic choices of firms may be strongly influenced by the particular choice of the transportation cost function. Even though there have been many studies in the past, many solutions have been proposed to this problem. The location problems are analyzed under a restricted function form, and no generic result has been concluded. This study offers a further understanding of the competition analysis on a generic consumer distribution.

 

Point 5:.Why someone should use your proposed work in practice, and what are the advantages of your work in comparison with others.

Response 5:

This study offers an advantage for the marketing manager. This study offers a further understanding of the competition analysis on a generic consumer distribution. This study demonstrates the existence of subgame perfect Nash equilibrium under generic distribution in consumer preference. We find that competition intensity is affected by the signs of local change rates of the consumer distribution at the endpoints of consumer segments.

 

Point 6:.The conclusion writing should be improved. Please rewrite the Conclusion section by adding more advantages, limitations and the future research direction of the proposed work.

Response 6:

We rewrote the conclusion to convey the advantages, limitations, and future research of the proposed work.

We suggest that a company should implement a minimal or maximal differentiation principle if endpoints of consumer density function change in the same direction with the central point.

Conversely, a company should implement a constant differentiation principle if the directions are opposite.

This study offers an advantage for the marketing manager. We clearly resolve the debate between differentiation and imitation for rival products. We successfully explained why some companies are profitable in selling imitative products, but other companies fail in following competitors.

 

Point 7:.The notations used should be rechecked..

Response 7:

We have rechecked all the notations we used. Some minor conflicts had been corrected.

Author Response File: Author Response.docx

Reviewer 2 Report

• The introduction is not clear and very less literature is used. Follow these instruction: The introduction should briefly place the study in a broad context and highlight why it is important. It should define the purpose of the work and its significance, including specific hypotheses being tested. The current state of the research field should be reviewed carefully and key publications cited. Please highlight controversial and diverging hypotheses when necessary. Finally, briefly mention the main aim of the work and highlight the main conclusions. Keep the introduction comprehensible to scientists working outside the topic of the paper.
• Authors should further clarify and elaborate novelty in their contribution.
• What are the limitations of the present work?

• What are some key issues that present study has addressed?

Author Response

Response to Reviewer 2 Comments

 

Point 1:. The introduction is not clear and very less literature is used. Follow these instruction: The introduction should briefly place the study in a broad context and highlight why it is important. It should define the purpose of the work and its significance, including specific hypotheses being tested.

 

Response 1:

In this paper, a dual-channel closed-loop supply chain is considered for waste recycling, and it is also observed that when the recyclability degree of wastes increases, the expected total profit increases for the whole supply chain.

Higher price sensitivity of customer demand leads to lower profit for the chain members. Two different coordination contract mechanisms, namely, all unit quantity discount along with franchise fee and revenue sharing contracts, are proposed to resolve channel conflict, and asymmetric Nash bargaining product is used for a particular profit split.

In a conventional setup of spatial competition problems, consumers are assumed to equally prefer each variation of products in the market, and the strategic choices of firms may be strongly influenced by the particular choice of the transportation cost function. Even there have been many studies in the past, many solutions have been proposed on this problem, the location problems are analyzed under a restricted function form and no generic result has been concluded. This study offers a further understanding of the competition analysis on a generic consumer distribution.

 

Point 2:.The current state of the research field should be reviewed carefully and key publications cited. Please highlight controversial and diverging hypotheses when necessary.

Response 2:

Thanks for this comment. We have once again reviewed the current state of the research field and critical publications cited.

 

Point  3:.Finally, briefly mention the main aim of the work and highlight the main conclusions.

Response 3:

The main aim of the work and the main conclusion have been added into this revision. In this text, a dual-channel closed-loop supply chain is considered for waste recycling, and it is also observed that when the recyclability degree of wastes increases, the expected total profit increases for the whole supply chain.

We suggest that a company should implement a minimal or maximal differentiation principle, if endpoints of consumer density function change in the same direction with the central point.

Conversely, a company should implement a constant differentiation differentiation principle, if the directions are opposite.

 

 

Point 4:.Keep the introduction comprehensible to scientists working outside the topic of the paper.

Response 4:

We have revision the introduction and kept the comtext comprehensible to general public. Thank you for the suggestion.

 

Point 5:.Authors should further clarify and elaborate novelty in their contribution.

Response 5:

This study sheds new light on the necessity of considering the preference distribution of the consumer population. We show the condition in which the subgame perfect Nash equilibria exist when the consumer distribution function is arbitrary. Our analysis confirms that having SPNE is impossible for uniform distribution. We further provide two necessary conditions to characterize the equilibria, and suggest that the market can be bisected according to the local rates of the density function and the competition strategy. Finally, we conclude that companies should move against their rivals' actions according to the signs of local change rates of the density function at the endpoints of market segments.

 

Point 6:.What are the limitations of the present work?

Response 6:

The limitation of the present work has been added to the Conclusion section. Although this study has relaxed the restricted function form of competitive strategies and offered a further understanding of the competition analysis on a generic consumer distribution, the location problems still have ample research topics for further analytic.

 

Point 7:.What are some key issues that present study has addressed?

Response 7:

In a conventional setup of spatial competition problems, consumers are assumed to prefer each variation of products in the market equally. The strategic choices of firms may be strongly influenced by the particular choice of the transportation cost function. Even there have been many studies in the past, many solutions have been proposed on this problem, the location problems are analyzed under a restricted function form and no generic result has been concluded. This study offers a further understanding of the competition analysis on a generic consumer distribution.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors have addressed the point of my concern. I am happy with their corrections. Hence, I would like to recommend this manuscript to be published.

Reviewer 2 Report

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