Discretization-Strategy-Based Solution for Berth Allocation and Quay Crane Assignment Problem
Round 1
Reviewer 1 Report
Dear Author
Discretization-strategy-based Solution for Berth Allocation and Quay Crane Assignment Problem
Although it is an old topic, it is always important to find new solutions that optimize quay equipment allocation issues in ports.
The authors seem to carry out an adequate review of the literature with a review of older and more recent papers on the Theme and on the various developments of the Theme, although they do not then mention the following issues:
- what is the gap that you find in the literature and that will be filled with this study?
- What is the general purpose and specific objectives, as well as what hypotheses are put forward and which will be tested?
- In the chapter on the methodology, which authors have already used it in this or another aspect, what is the origin of the methodology?
There must be a table with the variables, including the units, the Origins and the type of transformation they have, as well as the authors they used previously.
In the Numerical Experiments chapter, it would be appropriate to present the means and variances of the samples used with respect to the different variables of the model.
CPLEX or CPLAX?
In the results, it remains to translate the numbers and values ​​were reached from the results values ​​that are possible to understand by the managers of the ports and terminals, namely how the application of the model translates in the saving of time on average per ship in the port in operation and on hold or in improving the capacity for the quay to receive ships per year, or in improving the occupancy rate of the quays, and how this improves in terms of results compared to other models by other authors who previously studied the problem.
Author Response
Response to Reviewer 1 Comments
We thank you, the editor and the reviewer for this revision opportunity of our manuscript jmse-1650650. During the revising process, we have taken the reviewers’ comments into careful consideration and made corresponding changes to our manuscript. We believe we have improved the quality of the paper through addressing the comments. The editor and reviewers’ comments are answered in this document, and corresponding changes are highlighted in blue in the main manuscript.
Point 1: What is the gap that you find in the literature and that will be filled with this study?
Response 1: We thank the reviewer for this comment. We have supplemented the gap in our revised manuscript. In this work, an MINLP model is presented for the BACASP. The BACASP is converted to a discrete combinatorial optimization problem via a discretization strategy, and a large neighborhood search (LNS) incorporating a specific constraint-handling technique is proposed to efficiently solve it. The main contributions of this work are three-folds and summarized as follows: 1) A discretization-strategy-based method to solve the BACASP based on its combinatorial optimization property. 2) A specific LNS algorithm is designed to solve the BACASP. Under the framework of LNS algorithm, some destroy and repair operators are designed according to the problem's characteristics to update the solution and a backtracking comparison-based (BCB) constraint-handling strategy is proposed to enhance the performance of the LNS for achieving feasible solutions of the BACASP, so as to achieve an efficient solution to the BACASP. 3) A large number of experiments are conducted to demonstrate the effectiveness of the proposed algorithm and constraint-handling strategy in solving the BACASP.Please see the text highlighted in blue on page 3, lines 114-126.
Point 2: What is the general purpose and specific objectives, as well as what hypotheses are put forward and which will be tested?
Response 2: We thank the reviewer for this comment. In our revised manuscript, we have highlighted the general purpose, specific objectives and hypotheses.
The general purpose in this work is to improve the efficiency berth and QC operation at container terminals. The specific objectives of this paper are to obtain the optimal berth allocation and QC assignment theme, so as to minimize the port stay time and delayed departure time of vessels. Please see the text highlighted in blue on page 1, lines 26-27 and page 3, lines 142-144.
Hypotheses 1,2 and 4 are presented as simplified models. Hypothesis 3 was tested in the allocation scheme. Figure 8 shows that the QC assigned to a vessel cannot serve other vessels during the berthing period of the vessel. Please see the text highlighted in blue on page 4, lines 146-151 and Figure 8 on page 15.
Point 3: In the chapter on the methodology, which authors have already used it in this or another aspect, what is the origin of the methodology?
Response 3: Thanks for this comment. We have supplemented the origin of each method and strategy in our revised manuscript. The discretization strategy was originally proposed by Cordeau et al. (2005) to solve the BAP. This work extends the discretization strategy solution of BAP to address and solve the BACASP. The related destroy operator was first proposed by Shaw for vehicle routing problems. The deep greedy repair operator was proposed by Ropke for solving vehicle routing problems. In this study, we propose a few operators suitable for the problem of interest. Please see the text highlighted in blue on page 7, lines 237-238, page 8, lines 258-259 and lines 273-275, page 9, lines 297-300.
Point 4: There must be a table with the variables, including the units, the Origins and the type of transformation they have, as well as the authors they used previously.
Response 4: Thanks for this comment. We have added Table 1 with the variables uesd in our mathematical model. The type, definition and unit of variables are added in our revised manuscript. Please see the text on page 5.
Point 5: In the Numerical Experiments chapter, it would be appropriate to present the means and variances of the samples used with respect to the different variables of the model.
Response 5: We thank the reviewer for this comment. In our revised manuscript, we have presented the means and variances of the parameters used in the large-scale samples. The mean of in the large-scale example generated in this paper is 5.4, and the variance is 1.9. The mean of the sample of is 66.4, and the variance of sample is 1119.6; The means of sample of and are 2.4 and 4.4, respectively, and the variances of sample are 0.2 and 1.9, respectively. The mean of sample of is 10.6 and the variance of sample is 30.3. The means of sample of and are 294.7 and 320.6, respectively, and the variances of sample are 26827.8 and 26934.1, respectively. Please see Table 2 on page 10.
Point 6: CPLEX or CPLAX?
Response 6: We thank the reviewer for this comment. In our revised manuscript, we have changed “CPLAX” in Table 4 to “CPLEX”. Please see the text highlighted in blue on page 14, Table 5.
Point 7: In the results, it remains to translate the numbers and values ​​were reached from the results values ​​that are possible to understand by the managers of the ports and terminals, namely how the application of the model translates in the saving of time on average per ship in the port in operation and on hold or in improving the capacity for the quay to receive ships per year, or in improving the occupancy rate of the quays, and how this improves in terms of results compared to other models by other authors who previously studied the problem.
Response 7: We thank the reviewer for this comment. In our revised manuscript, the analysis of the stay time of vessel in port, delayed departure time of vessel and berth occupancy rate has been added. Please see the text highlighted in blue on pages 14-16. We have compared the best solution obtained by the LNS algorithm and GA-RM, and the results are shown in Table 7 and Figure 7. In addition, we have supplemented Figure 8 to show the usage of port berths and quay cranes in the allocation scheme intuitively.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper presents an average level of Quality of Presentation and Scientific Soundness. However, the results and conclusions are clearly presented.
The structure of the paper stays according to the scientific paper schedule (IMRAD). Literature review and state-of-the-art (SOTA) also are correctly prepared.
In the opinion of the reviewer, the paper is interesting and solves current maritime research problems.
The main disadvantage is the lack of limitations in discretization strategy and the insufficient part of the discussion and references list.
Good luck, Reviewer
Author Response
Response to Reviewer 2 Comments
We thank you, the editor and the reviewer for this revision opportunity of our manuscript jmse-1650650. During the revising process, we have taken the reviewers’ comments into careful consideration and made corresponding changes to our manuscript. We believe we have improved the quality of the paper through addressing the comments. The editor and reviewers’ comments are answered in this document, and corresponding changes are highlighted in blue in the main manuscript.
Point 1: The main disadvantage is the lack of limitations in discretization strategy and the insufficient part of the discussion and references list.
Response 1: We thank the reviewer for this comment. In our revised manuscript, we have supplemented the limitations of discretization strategy. Please see the text highlighted in blue on page 7, lines 247-264.
In the result section, we have added a discussion about port resource utilization. The analysis of the stay time of vessel in port, delayed departure time of vessel and berth occupancy rate has been added. Please see the text highlighted in blue on pages 13-15. We have compared the best solution obtained by the LNS algorithm and GA-RM, and the results are shown in Table 7 and Figure 7. In addition, we have supplemented Figure 8 to show the usage of port berths and quay cranes in the allocation scheme intuitively.
We have added references to the studies related to the BAP, BACASP and discretization strategy. Please see the text highlighted in blue on pages 2-3, and added references [7-8], [11-12], [16-17] and [23-25].
Author Response File: Author Response.pdf
Reviewer 3 Report
The authors are advised to check entire paper again for proper referencing. For example, immediately it becomes apparent that the first sentence requires referencing: "Maritime container transportation is one of the most important modes of transport in international trade, and about 80 percent of the global trade volume is carried out by sea and ports around the world"."
The authors are advised to announce the abbreviations first time they use them or make a list as already done. For example, abbreviation QC is first used several times, and then announced as "quay cranes". Similar approach should be used for all such occurences. There is no need to explain abbreviations twice; first in the paper and then at the end.
Please check all referencing, for example, references [7] and [8] seem to be missing while meaning of reference [? ] is uncertain.
Paragraph 3. should be titled "Methodology".
If possible, during text editing, remove text "vessels at berth k and Bnk represent the latest service vessel on berth k, where the vessels are B1, B2, · · · , Bnk." prior to Algorithm 1.
Subparagraphs of the main paragraphs should be announced briefly. After main paragraphs 2., 3. etc., please state briefly in one sentence, what the subparagraphs 2.1, 2.2.. 3.1, 3.2... etc. are about.
Text "Taking berth k as an example, berth k occupies the right half of the left
berth and the left half of the right berth. The discretization strategy formally divides the berth segment, and the continuous docking of vessels has no effect actually. Figure 2 (b) is the berthing sequence of berth k." should be moved after Figure 2., in order to explain the figure, and not end the subparagraph with figure.
Please insert line space prior to "(2) Random destroy operator" and after (1) and (2) in the same subparagraph 3.2.2. Destroy operators.
Authors are advised to do the same for other paragraphs, namely 3.2.3 etc.
Please adjust Algorithm 2 table to fit the page format, as for Algorithm 1 and not use entire width of the paper.
Please align "go to Step 6." with word "If" of the previous line.
Please separate "Figure 3" explanation from the algorithm prior to it.
Please move text "The overlap is eliminated by delaying the berthing start time of the vessel and pushing back the berthing position of the vessel, and the influence of the two methods on the value of the objective function is calculated. Finally, the BCB strategy compares the objective function value increments and chooses a way to make the increments smaller to eliminate the overlap." after Figure 3.
Should 3.2.5 be titled Acceptance Criterion or Criteria? Please use equal reasoning in this subparagraph.
Can the authors please state how quickly the results are produced after C program is run (immediate, seconds, minutes), and acknowledge does the computer have regular or SSD hard drive.
Are the results run for 20 times, or the analysis is run 20 consecutive times? Please adjust accordingly.
The authors claim that "a certain parameter combination is selected based on the best average result of the testing instances." Please describe in more details which exactly is this parameter combination? "Certain" is vague and inadequate definition.
Table 1 is not announced.
There seems to be an error in writing here: "Figure 4. The comparison results of related destroy operator (Re), random destroy operator (Ra), ..."
Authors are advised to split Figure 4 to two Figures, Figure 4 and Figure 5 and adjust width formatting accordingly.
Please adjust font family and size in tables to be similar; it seems that Table 2 uses other fonts than Table 1.
There also seems to be ty** error: "Table 2 statistics the results of WRS test,"? Also, please move a portion of text after Table 2, and do not split sentence with a table.
Please announce Table 3.
Please expand the Conclusion. There is a claim "It saves 60% time of the scheduling time.", where in the paper is this visible - please claim this were applicable in previous paragraphs, and just state in the Conclusion that time saving is identified.
Please state in the Conclusion what are possible future venues/possibilities of this type of research.
Author Response
Response to Reviewer 3 Comments
Point 1: The authors are advised to check entire paper again for proper referencing. For example, immediately it becomes apparent that the first sentence requires referencing: "Maritime container transportation is one of the most important modes of transport in international trade, and about 80 percent of the global trade volume is carried out by sea and ports around the world"."
Response 1: We thank the reviewer for this comment. We have added a citation where appropriate in our revised manuscript and checked the reference format of the revised manuscript. Please see the text highlighted in blue on page 1, line 21 and page 2, line 50.
Point 2: The authors are advised to announce the abbreviations first time they use them or make a list as already done. For example, abbreviation QC is first used several times, and then announced as "quay cranes". Similar approach should be used for all such occurences. There is no need to explain abbreviations twice; first in the paper and then at the end.
Response 2: We thank the reviewer for this comment. We have removed the repeated abbreviation QCs and added abbreviation QC where it is first used. Relevant parts have been revised. Please see the text highlighted in blue on page 1, line 24.
Point 3: Please check all referencing, for example, references [7] and [8] seem to be missing while meaning of reference [? ] is uncertain.
Response 3: We thank the reviewer for this comment. We have checked the reference format of the revised manuscript. Please see the text highlighted in blue on page 1, line 21 and page 2, line 51.
Point 4: Paragraph 3. should be titled "Methodology".
Response 4: We thank the reviewer for this comment. We have changed the title of Paragraph 3 to “Methodology” in our revised manuscript. Please see the text highlighted in blue on page 6, line 198.
Point 5: If possible, during text editing, remove text "vessels at berth k and Bnk represent the latest service vessel on berth k, where the vessels are B1, B2, · · · , Bnk." prior to Algorithm 1.
Response 5: We thank the reviewer for this comment. We have deleted this content “Let be the number of vessels at berth and represent the latest service vessel on berth, where the vessels are .” in the revised manuscript.
Point 6: Subparagraphs of the main paragraphs should be announced briefly. After main paragraphs 2., 3. etc., please state briefly in one sentence, what the subparagraphs 2.1, 2.2.. 3.1, 3.2... etc. are about.
Response 6: We thank the reviewer for this comment. We have added relevant descriptions in the revised manuscript, and briefly introduced the subsections of Section 2 and 3.
The problem description section is divided as follows. Subsection 2.1 describes the nation and subsection 2.2 introduces the problem model. Section 3 describes the solution method for the BACASP. The framework of solution method is presented in subsection 3.1. The main techniques of the method are described in subsection 3.2. Please see the text highlighted in blue on page 3, lines 128-129 and page 6, lines 199-201.
Point 7: Text "Taking berth k as an example, berth k occupies the right half of the left berth and the left half of the right berth. The discretization strategy formally divides the berth segment, and the continuous docking of vessels has no effect actually. Figure 2 (b) is the berthing sequence of berth k." should be moved after Figure 2., in order to explain the figure, and not end the subparagraph with figure.
Response 7: We thank the reviewer for this comment. We have moved the text “Take berth as an example, berth occupies the right half of the left berth and the left half of the right berth. The discretization strategy formally divides the berth segment, and the continuous docking of vessels has no effect actually. Figure 2(b) is the berthing sequence of berth .” after Figure 2. Please see the text highlighted in blue on page 7, lines 245-247.
Point 8: Please insert line space prior to "(2) Random destroy operator" and after (1) and (2) in the same subparagraph 3.2.2. Destroy operators. Authors are advised to do the same for other paragraphs, namely 3.2.3 etc.
Response 8: We thank the reviewer for this comment. We have changed the line space of the subparagraph 3.2.2 and 3.2.3. Please see the text highlighted in blue on page 8, lines 256, 267, 272 and 285.
Point 9: Please adjust Algorithm 2 table to fit the page format, as for Algorithm 1 and not use entire width of the paper.
Response 9: We thank the reviewer for this comment. We have modified the format of Algorithm 2 in the revised manuscript. Please see the Algorithm 2 on page 8.
Point 10: Please align "go to Step 6." with word "If" of the previous line.
Response 10: We thank the reviewer for this comment. We have modified the format of "Go to Step 6" in Step 4. Please see the text highlighted in blue on page 9, line 310.
Point 11: Please separate "Figure 3" explanation from the algorithm prior to it.
Response 11: We thank the reviewer for this comment. We have moved the description of Step 5 of the BCB algorithm after Figure 3 to separate Figure 3 from the algorithm. In addition, we have explained Figure 3, which shows the setting method of berthing position. This method corresponds to Step 3 of the BCB algorithm. Please see the text highlighted in blue on page 9, lines 315-322 and page 10, lines 323-324.
Point 12: Please move text "The overlap is eliminated by delaying the berthing start time of the vessel and pushing back the berthing position of the vessel, and the influence of the two methods on the value of the objective function is calculated. Finally, the BCB strategy compares the objective function value increments and chooses a way to make the increments smaller to eliminate the overlap." after Figure 3.
Response 12: We thank the reviewer for this comment. We have moved the relevant text in the revised manuscript to an appropriate location. Please see the text highlighted in blue on page 9, lines 315-322 and page 10, lines 323-324.
Point 13: Should 3.2.5 be titled Acceptance Criterion or Criteria? Please use equal reasoning in this subparagraph.
Response 13: We thank the reviewer for this comment. We have revised the title of subsection 3.2.5 and unified the text in our revised manuscript. Please see the text on page 10, lines 325.
Point 14: Can the authors please state how quickly the results are produced after C program is run (immediate, seconds, minutes), and acknowledge does the computer have regular or SSD hard drive.
Response 14: We thank the reviewer for this comment. We have shown the run time of each instance with different scales in our revised manuscript. The run time of small-scale instances are shown in Figure 5 and Table 5. We have also supplemented the run time of large-scale instances, as shown in Table 7. Please see the Figure 5 on page 12, Table 5 on page 14 and Table 7 on page 15.
The computer drive used in our experiment is a regular drive, not an SSD.
Point 15: Are the results run for 20 times, or the analysis is run 20 consecutive times? Please adjust accordingly.
Response 15: We thank the reviewer for this comment. In our revised manuscript, we changed “run for 20 times” to “run 20 consecutive times”. Please see the text highlighted in blue on page 10, lines 351-352 and page 10, line 360.
Point 16: The authors claim that "a certain parameter combination is selected based on the best average result of the testing instances." Please describe in more details which exactly is this parameter combination? "Certain" is vague and inadequate definition.
Response 16: We thank the reviewer for this comment. We have added the range of parameters in Table 3 in our revised manuscript. A parameter combination is a combination of parameters in this range. When the parameter changes within the range, the most appropriate quantity is selected according to the influence of the variation of the parameter combination on the solution. Afterwards, a certain parameter combination is selected based on the best average result of the testing instances. Please see the text highlighted in blue on page 10, lines 352-356.
Point 17: Table 1 is not announced.
Response 17: We thank the reviewer for this comment. We have cited Table 3 (which was as Table 1 in the original manuscript) where appropriate the revised manuscript. Table 3 shows the parameters of the LNS algorithm. Please see the text highlighted in blue on page 10, line 356.
Point 18: There seems to be an error in writing here: "Figure 4. The comparison results of related destroy operator (Re), random destroy operator (Ra), ... "
Response 18: We thank the reviewer for this comment. In our revised manuscript, we have revised this sentence.
Figure 4 shows the average and the best objective values of the solution obtained by different combinations of destroy-repair operators. Figure 5 depicts the standard deviation of solutions and CPU times by different combinations of destroy-repair operators. Different operators are represented by related destroy operator (Re), random destroy operator (Ra), deep greedy repair operator (Gr) and slack sorted repair operator (Sl). Please see the text highlighted in blue on page 10, line 366 and page 11, lines 367-370.
Point 19: Authors are advised to split Figure 4 to two Figures, Figure 4 and Figure 5 and adjust width formatting accordingly.
Response 19: We thank the reviewer for this comment. In our revised manuscript, we have split Figure 4 to Figure 4 and Figure 5 and adjusted the widths and formatting accordingly. Figure 4 is the average and the best objective values of the solution obtained by different combinations of destroy-repair operators. Figure 5 depicts the standard deviation and CPU time of the solution obtained by different combinations of destroy-repair operators. Different operators are represented by the related destroy operator (Re), random destroy operator (Ra), deep greedy repair operator (Gr) and slack sorted repair operator (Sl). Please see Figure 4 on page 11 and Figure 5 on page 12.
Point 20: Please adjust font family and size in tables to be similar; it seems that Table 2 uses other fonts than Table 1.
Response 20: We thank the reviewer for this comment. We have adjusted font family and size in Table 4 (which was Table 2 in the original manuscript) in the revised manuscript. Please see Table 4 on page 12.
Point 21: There also seems to be ty** error: "Table 2 statistics the results of WRS test,"? Also, please move a portion of text after Table 2, and do not split sentence with a table.
Response 21: We thank the reviewer for this comment. We have changed the text "Table 2 statistics the results of WRS test," to "Table 4 shows the WRS test of different combinatorial operators,". Please see the text highlighted in blue on page 12, line 390. In addition, we have put Table 4 on the same page as the text description.
Point 22: Please announce Table 3.
Response 22: We thank the reviewer for this comment. We have cited Table 5 (which as Table 3 in the original manuscript) where it is mentioned in the revised manuscript. Table 5 shows the comparison results of the LNS algorithm and CPLEX solver for solving the BACASP. Please see the text highlighted in blue on page 13, lines 419-422.
Point 23: Please expand the Conclusion. There is a claim "It saves 60% time of the scheduling time.", where in the paper is this visible - please claim this were applicable in previous paragraphs, and just state in the Conclusion that time saving is identified.
Response 23: We thank the reviewer for this comment. We have supplemented the calculation of this data in our revised manuscript. It can be seen from the data of CPU times by different operator combinations in subsection 4.3.1. For example i07 in Figure 5, the CPU time of the Re-Gr operator is 79.6s, and the CPU time of the Re-Sl operator is 31.9s. Compared with the Gr operator, the Sl operator saves of the computing time. Please see the text highlighted in blue on page 16, lines 491-492 and page 11, lines 376-379.
Point 24: Please state in the Conclusion what are possible future venues/possibilities of this type of research.
Response 24: We thank the reviewer for this comment. We have stated possible future directions for this type of research. This study has opened up several directions for future research. First, this study mainly focuses on the BACASP in a certain environment, but there are some uncertain factors in port such as unscheduled vessels and breakdown of QCs, which deserves further investigations. Second, although the LNS has been confirmed to be able to achieve high-quality solutions for the BACASP, the gap between the obtained solution and the optimal solution is unknown. As such, it will be interesting to develop accurate and efficient exact methods, such as branch-and-price and branch-and-cut, to achieve optimal solutions for the BACASP. Please see the text highlighted in blue on page 16, lines 499-506.
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
The authors have accepted all the comments, congratulations.
