Round 1

Reviewer 1 Report

Very interesting topic and quality presentation. In Introduction you have some old data (from the 90s and 2000s) which could be renewed. Moreover, it would add more value to your paper if you don't focus only on Americans since last mile is common issue all over the world. And this term is not only related to public transport, car users might also use BSS if available near by parkings.

You have a quality literature review. Methods and results are clearly described.

Also, there are some technical errors.

There is a strange column break on Page 8, please fix.

On page 10 there is link error "Error! Reference source not found.", and on the end of same page there is a page break before two words are "big instances.", but please move this words to page 10).

Please format cell values in Table 3 (number should have same decimal spaces, etc.)

 

Author Response

Reviewer 1

1. Very interesting topic and quality presentation. In Introduction, you have some old data (from the 90s and 2000s) which could be renewed. Moreover, it would add more value to your paper if you don't focus only on Americans since the last mile is a common issue all over the world. And this term is not only related to public transport, but car users might also use BSS if available nearby parking’s. You have a quality literature review. Methods and results are clearly described. Also, there are some technical errors. There is a strange column break on Page 8, please fix it. On page 10 there is a link error "Error! Reference source not found.", and at the end of the same page there is a page break before two words are "big instances.", but please move these words to page 10). Please format cell values in Table 3 (numbers should have the same decimal spaces, etc.)

 

• We fixed the Error! Reference source not found and make the manuscript one column for easy to read also we made our talk general for all over the world.

Reviewer 2 Report

The subject of the article is well-formulated, interesting, important and topical for thinking through the prism of Sustainable Develpement, it also carries significant research potential. Also preceding the scientific considerations, the Abstract has the correct formal construct (consists of one paragraph) and contains both the purpose of the text (BSS imbalance), the proposed research methodology (balancing the load of BSS stations, thanks to the extension of the proprietary heuristics based on the deferred acceptance algorithm - algorithm for finding the shortest Hamilton cycle). Keywords reflect the ideas of the main areas of scientific cognition. The article has a good methodological and formal structure and the way of organizing the entire text, in the form of: IMRaD - Introduction, Methods, Results and Discussion. The conducted literature review (Related work) and the presented methods (Methods) confirm the fact that the Authors proved that the analysis of literature sources is correct, up-to-date and has a utilitarian character (it is the basis for theoretical considerations and the construction of data aggregation instruments and the basis for model creation). Therefore, they rightly identify three types of rebalancing BSS bike distribution: static, dynamic, and incentivized, specifying the modeling techniques used in the research process, i.e. Black Hole Algorithm (BHA), Deferred Acceptance Algorithm (DAA) and The 2-opt Local Search Algorithm. Finally, the formulated algorithm was tested using randomly generated instances, each consisting of 90 stations (with three subnets, the balance problem was solved in less than 3 minutes, according to the authors). However, another research challenge would be not only to balance the system, because the availability of bicycles at stations depends on many determinants, which are shaped by the demand side (e.g. preferences of cyclists, the specifics of the trip and time of day and year) but also the supply side ( e.g. system design and operation, bike pool management and quick response possibility). These suggestions address further scientific challenges. At this stage, it should be considered that the presented article meets the requirements for this type of publication both in terms of technical (structure, correctness and logic of statements, legibility of graphic presentations) and methodological (adopted research approach, skillful definition of the goal, applied research methods, analysis and verification of the obtained results, formulated conclusions).

Author Response

Reviewer  2

1. The subject of the article is well-formulated, interesting important and topical for thinking through the prism of Sustainable Development, it also carries significant research potential. Also preceding the scientific considerations, the Abstract has the correct formal construct (consists of one paragraph) and contains both the purpose of the text (BSS imbalance). the proposed research methodology (balancing the load of BSS stations, thanks to the extension of the proprietary heuristics based on the deferred acceptance algorithm- algorithm for finding the shortest Hamilton cycle). Keywords reflect the ideas of the main areas of scientific cognition. The article has a good methodological and formal structure and the way of organizing the entire text, in the form of IMRaD - Introduction, Methods, Results and Discussion. the conducted literature review (Related work) and the presented methods (Methods) confirm the fact that the Authors proved that the analysis of literature sources is correct, up-to-date and has a utilitarian character (t is the basis for theoretical considerations and the construction of data aggregation instruments and the basis for model creation). Therefore, they rightly identify three types of rebalancing BSS bike distribution: static, dynamic, and incentivized, specifying the modelling techniques used in the research process, ie. Black Hole Algorithm (BHA). Deferred Acceptance Algorithm (DAA) and the 2-opt Local Search Algorithm. finally, the formulated algorithm was tested using randomly generated instances, each consisting of 90 stations (with three subnets, the balance problem was solved in less than 3 minutes, according to the authors). However, another research challenge would be not only to balance the system, because the availability of bicycles at stations depends on many determinants, which are shaped by the demand side (e.g., preferences of cyclists, the specifics of the trip and time of day and year) but also the supply side ( e.g. system design and operation, bike pool management and quick response possibility). These suggestions address further scientific challenges. At this stage, it should be considered that the presented article meets the requirements for this type of publication both in terms of technical (structure, correctness and logic of statements, legibility of graphic presentations) and methodological (adopted research approach, skilful definition, the goal, applied research methods, analysis, and verification the obtained results, formulated conclusions).

- We considered dealing with BBS with constraints into our future work 

Reviewer 3 Report

This paper investigates the rebalancing method for BSS. The topic is interesting. An algorithm with three stage based on BHA, DAA and 2-opt local search algorithm is proposed. The simulation experiments are carried out to verify the proposed method. The main concerns are listed as follows:

1. In the Abstract, it is suggested to involve some numerical results from the research to verify the effectiveness of the proposed method.
2. It is not clear that how to get the information regarding the projected daily demand in Section I.
3. What is the gap between the proposed method and existing literature? It is suggested to summarize the novelty of this study in Section II by comparative analysis of literature.
4. It is suggested to reorganize and combine the Section III and Section IV to improve the related description. For example, the serial number of equations should be perfectly given. The description regarding the methods (Section III) should be condensed.
5. The equation (2) and (5) presented in Section V are not complete and confusing. Please check them and give a revision.
6. The results regarding the comparison with another heuristic are not detailed. Why choose the BHA as the reference algorithm to verify the proposed method? In fact, the BHA is one of the components for the proposed algorithm.
7. In Section VII, it is suggested to give the description regarding the deficiencies and related future works, which is generally presented in the conclusion and useful to further clarify the work.

Author Response

Reviewer  3

1. In the Abstract, it is suggested to involve some numerical results from the research to verify the effectiveness of the proposed method

• We added some numerical results in our abstract section

2. It is not clear that how to get the information regarding the projected daily demand in Section I.

• The prediction of the demand is out of the scope of this paper. In this paper, we assume the demand is given and we propose an algorithm to rebalance the BSS and satisfy the demand as possible

3. What is the gap between the proposed method and existing literature? It is suggested to summarize the novelty of this study in Section ll by comparative analysis of literature.

• Table 2 and Table 4 shows the best-known cost for several instances and the cost of our solution. The advantage of our solution is that modelling the rebalancing problem as a game and allowing each player to have his own preference list will enable us to solve the problem even if each player has his own objective function

4. It is suggested to reorganize and combine Section lIl and section IV to improve the related description. For example, the serial number of equations should be perfectly given. The description regarding the methods (Section Il) should be

• Thank you for your suggestion. We see that the current organization is good. We reviewed the equations and fixed the numbering

5. The equations (2) and (5) presented in Section V are not complete and confusing. Please check them and give a revision.

• The equations are numbered

These two equations are the cost functions

5. The results regarding the comparison with another heuristic are not detailed. Why choose the BHA as the reference algorithm to verify the proposed method? In fact, the BHA is one of the components of the proposed algorithm.

We compared the proposed algorithm with BHA for the sake of completeness. We should highlight that in the proposed algorithm we used BHA to cluster the BSS and divide it into smaller subnetworks. Where in the comparison “We used the black hole to partition the whole network as explained in subsection 5.1 (i.e. Network Clustering Using the BHA). Then for each subnetwork, we use BHA to minimize the total travelling distances () and total residuals ( and hence find a good solution to rebalance subnetwork .”

6. In Section VIl, it is suggested to give the description regarding the deficiencies and related future works, which is generally presented in the conclusion and useful to further clarify the work.

• We added our proposed algorithm’s limitation and our future work at the end of the conclusion

Round 2

Reviewer 3 Report

Thanks for the authors’ responses to the earlier comments. In the previous comments, I hope the authors can improve the literature review by comparative analysis. The authors present their argument to the recommendations and do not make related revisions in the paper. The main reasons for such responses lie in that the results from Table 2 and Table 4 evaluate the proposed method. I do agree with the authors’ explanation that the results demonstrate the advantage of the proposed method. However, I still think the revision is useful to improve the paper. This is because the comparative analysis of literature aims to highlight the novelty of this study, especially from the aspect of problem situation, which is critical to guide readers to understand the value of this research. Moreover, it is useful to give a clear description regarding the demand. Although the demand in this paper is assumed as the given information, it is useful to add some description related to its acquirement. For example, in real-world situation, which institution can provide the demand information?

Author Response

Thank you so much for your comments, we improved the manuscript according. 

Also, we fixed reference 5.

 

Author Response File: Author Response.docx