Joint Optimization of Multi-Period Empty Container Repositioning and Inventory Control Based on Adaptive Particle Swarm Algorithm

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

-

Author Response

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Reviewer 2 Report

Comments and Suggestions for Authors

Improve the explanation of Fig. 1 and fix it.

Define each acronym only once at its first usage.

Fix the typo, lexical and gramma errors.

Define each constant/variable/parameter of each Equation.

Include a benchmarking comparison with similar methodologies.

 

 

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

This paper presents a relevant contribution to the maritime container logistics literature. The integration of adaptive PSO with heuristic-driven joint optimization is both original and useful for practitioners. However, before publication, the manuscript must undergo moderate language improvements and refinement of result presentation.

I would recommend that the authors either (1) offer a theoretical or empirical justification for not pursuing exact optimization techniques, or (2) demonstrate that even small instances are not easily solvable using mathematical solvers. Such clarification would strengthen the methodological rigor and help readers better understand why the APSO-based heuristic approach is the preferred or necessary solution path.

The introduction provides an adequate contextual background regarding the importance of empty container repositioning in maritime logistics. It successfully highlights the economic burden of repositioning and motivates the need for a joint inventory-repositioning framework. Consider condensing repeated information on the supply chain dynamics and better framing the gap in existing literature. 

The literature review is comprehensive and categorically organized, but some citations lack critical analysis or positioning. Try to contrast previous models more explicitly and connect them with your contributions.

The use of a joint optimization model incorporating (s,S) inventory strategy and APSO (Adaptive Particle Swarm Optimization) is well justified. The framework aligns logically with the problem statement, which seeks to balance cost-efficiency in container repositioning and inventory control.

The mathematical model is detailed and correctly formulated, incorporating both cost and operational constraints. The APSO algorithm is well described, including pseudo-code, flowcharts, parameter settings, and velocity/position update rules. The integration of heuristic rules into APSO tailored for maritime logistics is a strong contribution.

The numerical results are adequate and demonstrate the algorithm’s effectiveness, especially through convergence plots and cost breakdowns. The sensitivity analysis adds great value, particularly the insights on how rental cost and maximum inventory capacity impact the total cost. Nonetheless, the presentation of results (e.g., Tables 3–5) can be improved for clarity. Try summarizing key patterns with fewer tables or highlighting results visually (e.g., bar or line charts) instead of long tabular formats.

The conclusion ties back to the problem and reiterates the significance of the joint optimization framework. It acknowledges limitations (e.g., deterministic assumptions, lack of multi-agent behavior), which is appreciated. You may consider expanding future work prospects, perhaps suggesting how this model could scale with real-time IoT data or port-level cooperative strategies.

The English could be improved to more clearly express the research.

Author Response

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Reviewer 4 Report

Comments and Suggestions for Authors

The authors study multi-period empty container repositioning and inventory control in maritime logistics. A corresponding optimization model is formulated, and a metaheuristic is proposed. Numerical results are provided.

The paper is of some interest and fits the scope of the journal, English is good. However, the presentation is poor and must be improved. I recommend major revision considering the following comments:

General comments:

1. It is not clear why the mathematical model in Section 4 is formulated. This model is neither used, nor referenced any further. From this point of view Section 4 is useless.
2. You may use the model from Section 4 to justify the use of the metaheuristic. But in this case, you need to compare a solution obtained by solving the mathematical model by an exact method with a solution obtained by your heuristic. At least for small/median problem instances. Please note that the model (1)-(18) is (or at least can be transformed to) a mixed integer linear programming problem. There are a lot of efficient exact solution techniques and solvers for this class of problems.
3. No computational comparison is provided with other known techniques. If there are no previous results, please state it clearly. If the previous results are available, please demonstrate numerically that your approach is more efficient.

Specific comments:

1. Line 278 “Methematical Model”, please correct.
2. To improve the presentation in subsection 4.2, I recommend forming several separate tables for sets, parameters and variables used in the model.
3. In the model (1)-(18) not all constraints are equations. So, in the description of the model in lines 359-371 it is better using the word “constraint” or “expression” instead of “equation”.
4. Definitions of the variables XX and z in (15),(16) are just the same. Is it correct?
5. Typically, binary indicator variables XX (z) are introduced by a linear inequality between XX and W to explicitly present the logical condition stated in (15), (16).
6. Line 358, “as integer”. Please correct.
7. Line 541. “the optimal empty container transportation plan is shown in Table 5”. As far as I understand, Table 5 presents a solution obtained by your heuristic. Are you sure that this solution is optimal to your model (1)-(18)?

Author Response

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Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Define each acronym only once at its first usage.

Review and if it is the case, correct the logic of algorithms shown in Figures  2 & 3.

Improve the English language style of the paper

Define each constant/variable/parameter of each Equation.

Improve the visual quality of Tables 1,2,3,4.

Improve the visual presentation correcting the size of the letters in some sections of the proposal

Include more examples to test and compare the proposal vs similar technologies.

 

 

 

 

 

 

 

 

Comments on the Quality of English Language

Improve the English language style of the paper

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

The revised manuscript has significantly improved in both structure and technical clarity. The authors have responded thoughtfully and thoroughly to all major concerns raised in the previous round of review. Specifically, they have provided a compelling justification for using an adaptive heuristic method, enhanced the presentation of results through clearer figures, and strengthened the theoretical positioning in the literature.

Their newly added discussion on integrating IoT and port collaboration mechanisms into future work enhances the practical relevance of the study.

I still believe that there are literature not taken into consideration in the area of near real-time solutions for container port optimization systems and in the how they interact with Port Community Systems or Smart Port Digital systems.

While minor language improvements could still enhance readability, the manuscript now meets the expectations of scholarly rigor and relevance for publication in JMSE.

Author Response

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Reviewer 4 Report

Comments and Suggestions for Authors

The authors revised the paper responding to some questions. However, there are still many questions concerning the correctness and necessity of the main mathematical model (1)-(18):

1. In Table 3 the authors declare variables Q as “The quantity of empty container….”. We may assume that these variables must be declared as integer and nonnegative. However, in the problem (1)-(18) these variables are unrestricted. Similarly, variables Ldt.
2. On the contrary, quantities q in Table 2 are introduced as parameters. However, in the problem (1)-(18) these values are considered as variables, see line 349.
3. Suppose that the variables Q and Ldt mentioned above have been declared nonnegative integers. In this case the problem (1)-(18) is a bilinear mixed integer problem. All nonlinearities are products of binary and integer variables. Corresponding bilinear term can be easily linearized (see, e.g. the paper Transformation and Linearization Techniques in Optimization: A State-of-the-Art Survey. Mathematics, 2022, https://doi.org/10.3390/math10020283 and the references therein). So, the main model can be transformed by the well-known techniques to a (large-scale) mixed integer linear optimization problem. The latter can be solved by commercial software at least for moderate dimensions. This way the need for the model (1)-(18) can be justified. It can be used to compare results obtained by metaheuristic and exact approaches.
4. However, the authors can apply metaheuristic approach instead. In this case it is not clear, why do they need the model (1)-(18), since it is not used/referenced any further. In this case the whole section 4 is useless and must be eliminated since its results are not used to construct the metaheuristic.
5. In Section 5, lines 433-437 the authors declare “it should be emphasized that in the research on optimizing decision-making for empty container repositioning problems, heuristic rules related to surplus container quantity, shortage container quantity, and empty container inventory threshold control have not yet been integrated into the adaptive particle swarm algorithm, which means that there are no previous results we can use for reference.” From this we can only conclude that there are no previous particle swarm algorithms to solve the problem. But as far as we can see from Section 2 there are other approaches to solve this problem. Why not compare your results with those mentioned in Section 2?
6. All in all, the quality of results obtained by the proposed metaheuristic must be evaluated. Either comparing with the exact solution, or by comparing with other known approaches (not necessarily with the particle swarm approach).

Author Response

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Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

The paper lacks of novelty

Include a benchmarking comparison with similar methodologies.

 

Author Response

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Reviewer 4 Report

Comments and Suggestions for Authors

The authors corrected the main model according to my comments. At least, now there are no serious errors in mathematical formulations.

Author Response

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