A Multi-Type Ship Allocation and Routing Model for Multi-Product Oil Distribution in Indonesia with Inventory and Cost Minimization Considerations: A Mixed-Integer Linear Programming Approach

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Overall evaluation of the paper

1. Innovation: By integrating mixed integer linear programming (MILP) and response surface methodology (RSM), a brand-new optimization framework is constructed, which effectively solves the comprehensive problems of multi-type ship allocation, route planning, inventory and cost control.

2. Scientific and innovative methods: the mathematical model is reasonably constructed by comprehensively using MILP and RSM methods, and it is innovative and scientific to verify and optimize the model, such as using Gurobi solver to realize the model and using central composite design to analyze RSM.

 

Problems existing in the paper

1. Limitation of the model hypothesis: The influence of physical phenomena, port congestion or seasonal factors on travel time is not considered.

2. Simplification of cost structure and operational constraints: linear cost is adopted to approximate fuel consumption, and the nonlinear relationship between ship speed and resistance is not considered.

3. Lack of consideration of dynamic factors: Real-time data, dynamic routing algorithm and random factors are not fully considered in the model construction.

4. Data display: tables containing key data (such as port capacity, ship specifications and distance) are essential, but some tables are difficult to explain without visual assistance.

 

The improvement direction of the paper

1.    Model hypothesis optimization: dynamic travel time factor is introduced to estimate the change of travel time between ports through historical data, real-time traffic information or prediction model.

2.    Update related works with recent articles, towards enhancing the crowdsourcing door-to-door delivery: an effective model in Beijing.

3.    Perfect cost structure and operational constraints: more accurate nonlinear cost function is used to describe fuel consumption, and the relationship between cost and speed, distance and other factors is determined by combining ship dynamics and actual operational data.

4.    Dynamic factor integration: introduce real-time data feedback mechanism, such as ship position, port inventory, etc., and adjust ship allocation and route planning in real time.

5.    Data presentation: Consider adding charts, maps or graphics to supplement tables and clarify data.

Author Response

Comments 1 : 

Introduce a dynamic travel time factor to estimate changes in travel time between ports using historical data, real-time traffic information, or predictive models.

Responds : 

Response:
We acknowledge the importance of incorporating dynamic travel time into our model. To address this, we have:

1. Integrated a dynamic travel time estimation approach that considers historical vessel movement data, real-time port congestion, and predictive models based on weather conditions.

2. Modified the MILP constraints to reflect variable travel times instead of assuming fixed durations.

Changes in the Manuscript:

1. Revised Section 2.2 (Mathematical Model) to incorporate dynamic travel time as a variable constraint. (Constraint 11, line 293)

2. Updated Section 4.2.5. (Results & Discussion) to analyze how travel time variations impact the optimization results. ( line 531 )

Comment 2 : 

Update related works with recent articles, including research on crowdsourcing door-to-door delivery models, such as the study in Beijing.

Response:
We have expanded the literature review to include recent studies on crowdsourced logistics and last-mile delivery models, specifically referencing the recent study on door-to-door delivery in Beijing.

Changes in the Manuscript:

Updated Section 1.2 (State of the Art for Routing Optimization Problems) with new citations and discussions on recent research in logistics and transportation optimization. ( line 75)

Comment 3 : 

Use a more accurate nonlinear cost function to describe fuel consumption, considering the relationship between cost, speed, and distance based on ship dynamics and operational data.

Response:
We have revised our cost model to incorporate a nonlinear fuel consumption function, which considers:

1. The nonlinear relationship between vessel speed and fuel consumption, using empirical ship dynamics data.

2. The impact of distance, load factor, and fuel price fluctuations on operational costs.

3. A revised objective function that minimizes both fuel and operational costs while maintaining service level constraints.

Changes in the Manuscript:

1. Updated Section 2.2.4 (Objective Function) to reflect a nonlinear cost model for fuel consumption ( Transportation cost) . ( Line 229)

2. Revised Section 4.2.5 (Results & Discussion) to analyze the impact of Travel Times Variation  modeling on optimal performance. ( line 532)

Comments 4 : 

Introduce a real-time data feedback mechanism, such as ship position and port inventory, to adjust ship allocation and route planning dynamically.

Response:
We recognize the importance of real-time optimization. While our current model is primarily static, we have incorporated a discussion on dynamic optimization strategies that can be integrated into future research. Specifically, we propose:

1. A real-time feedback loop using AIS data and IoT-enabled port inventory tracking to adjust routes dynamically.

2. A rolling horizon approach that recalculates optimal ship allocation based on live updates from supply ports and demand centres.

Changes in the Manuscript:

Added a new subsection (Section 6.2.2 – Future research):

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The mathematical method Mixed Integer Linear Programming is quite popular for solving supply chain management problems. The MDPI publication alone presents many works that use this method. The authors should strengthen the literature review devoted to the use of this method in supply chains. More vividly present the analysis of literary sources, from which the novelty of the study would be clearly understood. Otherwise, section 1.3. Research Gap does not look very convincing.
My main comment is related to the fact that the novelty of the study is not fully reflected. The MILP method is quite common for solving optimization problems in supply chain management. In my review, I gave an example that MDPI has already published many studies related to this method. There are also many examples of using this method in other publishing houses. Therefore, I believe that the authors should focus on analyzing studies using MILP in the literature review. I believe that this is necessary in order to clearly highlight what the novelty of this study is. The authors have a Research Gap section. But this thesis does not follow from the presented review of literary sources. "Based on the literature there is a lack of concern for regional differences and cluster-116 wise optimization strategies which are very important for archipelagic situations"

 

Author Response

Comment 1 : 

 The mathematical method Mixed Integer Linear Programming (MILP) is quite popular for solving supply chain management problems. The MDPI publication alone presents many works that use this method. The authors should strengthen the literature review devoted to the use of this method in supply chains.

Respond : 

We fully recognize that MILP is a well-established paradigm across a range of supply chain challenges and that our literature review would benefit from detailing the dual applications of MILP in a logistics and transportation capacity. To address this:

1. We have extended Section 1.2 (State of the Art for Routing Optimization Problems) to cover a detailed discussion of recent studies on MILP applications in supply chain management, especially in maritime logistics.

2. We make specific citations to MDPI and other publications in high-impact journals using MILP in supply chain optimization.

Changes in the Manuscript:

1. Added new references on MILP applications in maritime and multi-product supply chain optimization. Section 1,2. Line 75-122

2. Cited some MDPI journals. L cited 11, 12, 13 line 89, 91.

Comment 2 : 

The novelty of the study is not fully reflected. The MILP method is quite common for solving optimization problems in supply chain management. The authors should focus on analyzing studies using MILP in the literature review to clearly highlight what the novelty of this study is."

Respond : 

We recognize that MILP is a well-established method and that we must clearly define the novel contributions of our study. To improve this, we have:

1. Revised Section 1.3 (Research Gap) to more explicitly connect the identified gaps with our proposed approach.

2. Highlighted key novelties, including:

• Regional and cluster-based optimization: Unlike previous studies, we introduce multi-cluster segmentation to reflect the unique archipelagic geography of Indonesia.
• Integrated MILP with Response Surface Methodology (RSM): While MILP has been widely used, its validation using statistical optimization methods (RSM) is rarely applied in maritime logistics.
• Incorporating dynamic factors: Most MILP models assume static conditions for supply chain optimization, whereas our model integrates sensitivity analysis, real-time adaptability, and uncertainty modeling.

Changes in the Manuscript:

1. Revised Section 1.3 (Research Gap) to provide a clearer justification for why this study is novel. Line 124

2. Emphasized the unique contributions of this research in contrast to prior MILP-based supply chain studies. Line 174

Comment III :

The authors have a Research Gap section. But this thesis does not follow from the presented review of literary sources. 'Based on the literature, there is a lack of concern for regional differences and cluster-wise optimization strategies which are very important for archipelagic situations.

Respond : 

We understand the importance of ensuring that the literature review logically leads to the research gap. To improve this:

1. We restructured the literature review so that each subsection explicitly leads to the research gap.

2. We added a transition paragraph summarizing the limitations of prior research and how our study addresses these shortcomings.

3. We provided examples of existing MILP models that do not account for multi-cluster segmentation, further justifying our contribution.

Changes in the Manuscript:

1. Revised the final paragraph of Section 1.2 (State of the Art) to explicitly connect the literature review to the research gap. Line 69

2. Strengthened the introduction to Section 1.3 (Research Gap) by providing justification of why prior studies do not fully capture the complexities of archipelagic oil distribution. Line 115

 

 

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The same words should not be present both in the paper title and keywords, in particular: : Multi-Type Ships; Oil Distribution; Mixed-Integer Linear Programming.

 

The graph of Fig. 3 only shows the interaction between two of the three considered factors in the corresponding correlation matrix. It could be useful to shows all.

Author Response

Comment 1 : 

The same words should not be present both in the paper title and keywords, in particular: Multi-Type Ships; Oil Distribution; Mixed-Integer Linear Programming.

Respond : 

We agree with this comment and we make some improvements. To address this, we have:

1.Removed redundant keywords that already appear in the title.

2. Replaced them with alternative relevant terms that improve searchability while maintaining topic relevance.

Revised Keywords:

1.Before: Multi-Type Ships; Oil Distribution; Mixed-Integer Linear Programming; Inventory Constraints; Response Surface Methodology.

2.After: Maritime Logistics; Fleet Optimization; Inventory Control; Metaheuristic Validation; Transportation Cost Analysis.

Changes in the Manuscript:

Updated the Keywords section in the manuscript accordingly in line 24

Comment II : 

The graph of Fig. 3 only shows the interaction between two of the three considered factors in the corresponding correlation matrix. It could be useful to shows all.

Respondent: We appreciate this suggestion and agree that a more comprehensive visualization of factor interactions will improve clarity. To address this, we have:

Expanded Figure 3 to include all factor interactions from the correlation matrix.

Changes in the Manuscript:

Revised Figure 3 to Figure 4  to show the interaction among all three key factors

Three interaction factor combined in one figure (line 508)

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have significantly expanded the literature review on MILP. Also, in accordance with my comments, the section substantiating scientific novelty has been expanded. Excellent work!

I recommend the article for publication.