A Discrete Cooperative Control Method for Production Scheduling Problem of Assembly Manufacturing System

Round 1

Reviewer 1 Report

With the sharp decrease in resource utilization of the complex production process, integrated scheduling methods are urgently needed in assembly manufacturing industries. To this end, this paper presents an integrated scheduling with jobs processing and assembly sequence (ISJPAS) problem where jobs and assemblies can be processed simultaneously. As the first contribution to this work, we develop a mixed integer nonlinear programming model (MINLP) that aims at minimizing maximum completion time and determining the earliness and tardiness of jobs and resulting inventory time. The structured property of the optimal scheduling solution is analyzed with regard to job sequencing and assembly sequencing. The NP-hard nature of the problem is proved, which gives upper and lower bounds on the optimal solution. Second, an efficient discrete assembly time and arrival time control (DAATC) method based on continuous time variable control models. From a modified set of benchmark problems, the proposed method is tested by comparing four assembly association level in real applications. The comparisons indicate the potentiality of our method to satisfy the due date. Lastly, discussion, relevance of practical applications, and several future research avenues are emphasized.

The following issues need to be noted:

1. The structure of related work can be further optimized.

2. What are the basis for adopting these assumptions?

 

3. What are the limitations and practical value of the method?

There are some grammatical errors and the language needs to be polished.

Author Response

Dear Editor and Reviewers,

Thank you for your review of our manuscript " A discrete cooperative control method for production scheduling problem on assembly manufacturing system" with Manuscript Number sustainability-2531678. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our research.

We have carefully revised the manuscript according to the suggestions of reviewers, along with some minor grammatical changes. We prepared two documents, named "Manuscript_Revised_1" and "Manuscript_Revised_1 with Marks". In " Manuscript_Revised_1 with Marks", the revised parts were marked with the function "insert a comment". It should be noted that due to the lengthy title of the original manuscript, we have streamlined the title to 'An adaptive balance optimization algorithm and its engineering application'. The main correction in the paper and the responses to reviewers’ comments are as flowing:

Reviewer 1:

First of all, please allow us to express our sincere gratitude for your rigorous and professional review comments, which have greatly helped us to improve the quality of the manuscript.

1. Response to comment: The structure of related work can be further optimized.

Response: Thank you for this important comment. We optimized the structure of the related work in the paper. And, the related work has been divided into two parts.

2. Response to comment: What are the basis for adopting these assumptions?

Response: First of all the assumptions of the mathematical model for the integrated scheduling with jobs processing and assembly sequence (ISJPAS) problem are based on the flexible job shop scheduling problem and the assembly job shop scheduling problem. And references to the findings of the above mentioned literatures [3,17,18, 19, 20]” to clarify. Then the proposed discrete assembly time and arrival time control (DAATC) method is presented which is based on the real-time distributed arrival time control (DATC) systems and on the literature [9,10,11,42, 43,44,45].

3. Response to comment: What are the limitations and practical value of the method?

Response: 1 limitation: this method takes a long time to solve large-scale problems and data and does not result in an exact solution.

2. practical value: The assembly manufacturing system is an integrated discrete production system where various manufacturing operations are simultaneously and independently processed, then the jobs are collected and transported to assembly lines arranged in the assembly shop for "factory assembly operations". Specifically, the production process is divided into two stages. The different processing time and process path of each job also leads the assembly-associated jobs exist in significant scheduling collaboration difficulties. This method is intended that the coupling constraints between the production shop and the assembly shop are explained to contribute to the further development of such assembly manufacturing systems.
3. Response to comment: There are some grammatical errors and the language needs to be polished.

Response: We apologize for the poor language of our manuscript. We worked on the manuscript for a long time and the repeated addition and removal of sentences and sections obviously led to poor readability. We have now worked on both language and readability and have also involved native English speakers for language level have been substantially improved.

 

We appreciate for Editors/Reviewers’ warm work earnestly and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestions.

Sincerely Yours,

Xiao Wang, Mei Liu, Peisi Zhong, Chao Zhang, Dawei Zhang.

[email protected] (Peisi Zhong)

August 24, 2023

Reviewer 2 Report

I am very thankful for reviewing this manuscript and it was my pleasure to assist you with my suggestions. I have read for reviewing assessment and my suggestions have been given in the following points: This work is not strongly motivated by current need of production scheduling problem on assembly manufacturing system, and the paper is not felt to carry the significant new knowledge required to justify publication at the international level. How MINLP helps to find the earliness and tardiness of jobs and resulting inventory time? Considering the long history of NP-hard nature of the problem which seems to give only upper and lower bounds on the optimal solution, expand the model and elaborate the problem with infinite cases. Novelty is missing in abstract section. How can you solve industry problem considering this model? Add research questions and gaps. There is a significant lack of relevant literature references so need some more literature; in order to motivate the researchers in the subject. Add theoretical and practical implications. Limitations and future work should be added in the conclusions section. Mention some application based work that can be applied to today’s rapidly changing environment. Need to improve the English language and general communication.

see the comment.

 

Author Response

Dear Editor and Reviewers,

Thank you for your review of our manuscript " A discrete cooperative control method for production scheduling problem on assembly manufacturing system" with Manuscript Number sustainability-2531678. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our research.

We have carefully revised the manuscript according to the suggestions of reviewers, along with some minor grammatical changes. We prepared two documents, named "Manuscript_Revised_1" and "Manuscript_Revised_1 with Marks". In " Manuscript_Revised_1 with Marks", the revised parts were marked with the function "insert a comment". It should be noted that due to the lengthy title of the original manuscript, we have streamlined the title to 'An adaptive balance optimization algorithm and its engineering application'. The main correction in the paper and the responses to reviewers’ comments are as flowing:

Reviewer 2:

First of all, please allow us to express our sincere gratitude for your rigorous and professional review comments, which have greatly helped us to improve the quality of the manuscript.

1. Response to comment: How MINLP helps to find the earliness and tardiness of jobs and resulting inventory time?

Response: Thank you for this important comment. First of all, the earliness of the job refers to the value of the completion time before the delivery date. And, the tardiness represents the deviation between the completion time and the delivery time. Inventory time means the deviation between the machining completion time and the assembly start time. We use these objectives to determine the machines that will process the job and the sequence in which they will be processed.

2. Response to comment: Considering the long history of NP-hard nature of the problem which seems to give only upper and lower bounds on the optimal solution, expand the model and elaborate the problem with infinite cases.

Response: Analyzing the upper and lower bounds of the optimal solution begins with an analysis of the theory of the problem model, including the structure of the optimal solution. Furthermore, the results of the algorithms in solving the problem can be compared by upper and lower bounds on the effectiveness of the algorithms. The ratio of result to the lower bound can be obtained directly.

3. Response to comment: Novelty is missing in abstract section.

Response: We describe the innovation and novelty of the paper in detail in paragraph 4 of the first section (introduction). (on p.2)

4. Response to comment: How can you solve industry problem considering this model? Add research questions and gaps.

Response: We need to build collaborative manufacturing models and systems that enable synchronized production and assembly practices. We added the research questions (integrated scheduling with jobs processing and assembly sequence (ISJPAS) problem) in the first paragraph of the first section of the article and the advantages of using this research methodology (discrete assembly time and arrival time control (DAATC) method) in the third paragraph of the first section.

5. Response to comment: Limitations and future work should be added in the conclusions section.

Response: We are paying a lot of attention to this question. And it is explained in detail in the discussion section. (p.20-21)

6. Response to comment: Need to improve the English language and general communication.

Response: We apologize for the poor language of our manuscript. We worked on the manuscript for a long time and the repeated addition and removal of sentences and sections obviously led to poor readability. We have now worked on both language and readability and have also involved native English speakers for language level have been substantially improved.

We appreciate for Editors/Reviewers’ warm work earnestly and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestions.

Sincerely Yours,

Xiao Wang, Mei Liu, Peisi Zhong, Chao Zhang, Dawei Zhang.

[email protected] (Peisi Zhong)

August 24, 2023

Author Response File: Author Response.pdf

Reviewer 3 Report

The current manuscript presents a discrete cooperative control method for production scheduling case study of a manufacturing system. The manuscript is well written and organized. The data is thorough and informative. However, some minor issues should be considered as follows:

 - The term "NP-hard" should be defined in more detail.

- The discussion should be supported with references to justify the obtained analysis.

- The conclusion should be focused to present the main results, contributions, and novelty of the proposed method. A pullet points style is highly recommended to be applied.  

moderate change is required.

Author Response

Dear Editor and Reviewers,

Thank you for your review of our manuscript " A discrete cooperative control method for production scheduling problem on assembly manufacturing system" with Manuscript Number sustainability-2531678. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our research.

We have carefully revised the manuscript according to the suggestions of reviewers, along with some minor grammatical changes. We prepared two documents, named "Manuscript_Revised_1" and "Manuscript_Revised_1 with Marks". In " Manuscript_Revised_1 with Marks", the revised parts were marked with the function "insert a comment". It should be noted that due to the lengthy title of the original manuscript, we have streamlined the title to 'An adaptive balance optimization algorithm and its engineering application'. The main correction in the paper and the responses to reviewers’ comments are as flowing:

Reviewer 3:

First of all, please allow us to express our sincere gratitude for your rigorous and professional review comments, which have greatly helped us to improve the quality of the manuscript.

1. Response to comment: The term "NP-hard" should be defined in more detail.

Response: Thank you for this important comment. We describe and define NP-hard in detail in first line of first paragraph on page 2. (p2)

2. Response to comment: The discussion should be supported with references to justify the obtained analysis.

Response: The authors have reconsidered and modified the recommendations provided. Discussion section has added references, with references to the work of Wu (reference 7), Prabhu (reference 9), Fattahi (reference 14), Nourali (reference 17), Zhang (reference 19) and Zhang (reference 20) (all on p. 20-21).

3. Response to comment: The conclusion should be focused to present the main results, contributions, and novelty of the proposed method. A pullet points style is highly recommended to be applied.

Response: The Results section was reworked according to the order of main contribution, novelty, and results. (p. 21)

4. Response to comment: Moderate change is required.

Response: We apologize for the poor language of our manuscript. We worked on the manuscript for a long time and the repeated addition and removal of sentences and sections obviously led to poor readability. We have now worked on both language and readability and have also involved native English speakers for language level have been substantially improved.

We appreciate for Editors/Reviewers’ warm work earnestly and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestions.

Sincerely Yours,

Xiao Wang, Mei Liu, Peisi Zhong, Chao Zhang, Dawei Zhang.

[email protected] (Peisi Zhong)

August 24, 2023

Reviewer 4 Report

This paper addressed an integrated scheduling with jobs processing and assembly sequence problem. The problem aims to optimize the makespan via optimally determining the earliness and tardiness of jobs and resulting inventory time. Generally, this paper well organized its content and presented each part clearly. However, I have some following comments which should be responded.

 

1. Mathematical model is unclear.

(1) It is confused for the symbols, e.g., what is the meaning of "ij-th machines" in P6?

(2) The definition of variables in P7 is unclear. The meaning of each subscript index should be indicated.

(3) The Model (1)-(8) is not rigorous, the ranges of some subscripts of symbols in the constraints are not indicated. Formal (8) should be written in a clear way.

 

2. The title of each subsections and the structure of Section 3 should be reconsidered.

 

3. Do the analytical upper/lower bound help for the designed method? If not, what is the meaning of obtaining such bounds?

 

4. The addressed problem is a minimization problem with objective eq. (8), then how can we evaluate the objective results of the proposed DAATC? As we do not know the real optimal objective value.

Author Response

Dear Editor and Reviewers,

Thank you for your review of our manuscript " A discrete cooperative control method for production scheduling problem on assembly manufacturing system" with Manuscript Number sustainability-2531678. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our research.

We have carefully revised the manuscript according to the suggestions of reviewers, along with some minor grammatical changes. We prepared two documents, named "Manuscript_Revised_1" and "Manuscript_Revised_1 with Marks". In " Manuscript_Revised_1 with Marks", the revised parts were marked with the function "insert a comment". It should be noted that due to the lengthy title of the original manuscript, we have streamlined the title to 'An adaptive balance optimization algorithm and its engineering application'. The main correction in the paper and the responses to reviewers’ comments are as flowing:

Reviewer 4:

First of all, please allow us to express our sincere gratitude for your rigorous and professional review comments, which have greatly helped us to improve the quality of the manuscript.

1. Response to comment: Mathematical model is unclear. (1) It is confused for the symbols, e.g., what is the meaning of "ij-th machines" in P6? (2) The definition of variables in P7 is unclear. The meaning of each subscript index should be indicated. (3) The Model (1)-(8) is not rigorous, the ranges of some subscripts of symbols in the constraints are not indicated. Formal (8) should be written in a clear way.

Response: Thank you for this important comment. (1). We reworked the mathematical modeling in Section III. And, the ij-th machines denote the machines that process the j-th workpiece of the i-th product. (2). We modified the definition of the variable which is shown in Table 1. (3) We modified Models 1-8 seriously. However the range of symbol subscripts is determined by the number of jobs and machines in the experiment. Model 8 refers to minimizing the maximum completion time of each workpiece, with references to Literature 3,17,18,19,20,21,30.

2. Response to comment: The title of each subsections and the structure of Section 3 should be reconsidered.

Response: Thanks for the helpful comments. And the author carefully considered the titles of each section. Specifically, the content and title of section III have been revised. Section 3 focuses on the mathematical model of the integrated scheduling with jobs processing and assembly sequence planning problem and the theoretical analysis of the mathematical model, which provides a theoretical foundation for the later methods to solve this problem.

3. Response to comment: Do the analytical upper/lower bound help for the designed method? If not, what is the meaning of obtaining such bounds?

Response: Analyzing the upper and lower bounds of the optimal solution begins with an analysis of the theory of the problem model, including the structure of the optimal solution. Furthermore, the results of the algorithms in solving the problem can be compared by upper and lower bounds on the effectiveness of the algorithms. The ratio of result to the lower bound can be obtained directly.

4. Response to comment: The addressed problem is a minimization problem with objective eq. (8), then how can we evaluate the objective results of the proposed DAATC? As we do not know the real optimal objective value.

Response: The experimental studies of our proposed method mainly consist of small-scale instances of arithmetic and large-scale instances of arithmetic. The main values obtained in the small-scale instances are the arrival time and the minimization of the squared difference. There is no analysis of the minimized maximum completion time because the minimized maximum completion time is easy to calculate, and the emphasis here is on highlighting lead times and tardiness. The analysis is carried out for minimizing the maximum completion time in a large-scale instance.

We appreciate for Editors/Reviewers’ warm work earnestly and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestions.

Sincerely Yours,

Xiao Wang, Mei Liu, Peisi Zhong, Chao Zhang, Dawei Zhang.

[email protected] (Peisi Zhong)

August 24, 2023

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

The paper has been significantly improved. It now appears clearer and more coherent.