A Model for a Circular Food Supply Chain Using Metro Infrastructure for Quito’s Food Bank Network^†

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. The method in the article is based on the Quito metro system, which has a linear distribution, and the impoverished areas are located in the northern and southern parts of the city. The city's metro lines are quite unique, so the adaptability of this model may not be guaranteed in other more complex cities.
2. The article assumes that the unused capacity of the metro network can be used for food transportation, but this assumption depends on the actual metro load and operational efficiency. A more detailed assessment of the metro system's idle capacity and practical operational constraints is needed to demonstrate its feasibility.
3. The paper uses data from the Quito Food Bank, but lacks a detailed description of the data sources and quality. The sample size and the credibility of the data quality are insufficiently addressed.
4. In section 3.2, the implementation of the proposed traceability system involves the allocation operation where volunteers load donations from storage cabinets into the metro carriages during off-peak hours. The off-peak hours may vary during holidays and weekdays, so how are off-peak hours determined in this context?
5. In section 4.1, the allocation model states that if a station's capacity is insufficient to receive a donor's goods, the model will dynamically select the nearest station that meets the capacity requirements. However, in reality, it is difficult for the station's capacity to perfectly match the goods demand. Could the model first satisfy a portion of the goods demand and then select other stations to meet the remaining goods demand?
6. Although section 4.1 uses a Mixed Integer Programming (MIP) model for optimization, it does not provide information on the computation time and efficiency of the MIP model at different scales, making it difficult to assess its feasibility in real-world applications.
7. The article standardizes the objective function values in the Multi-Objective (MO) model, and Equation 23 mentions the maximum and minimum values. However, the paper does not clearly explain how these upper and lower bounds are effectively determined.
8. This paper uses a multi-objective optimization model, which effectively balances transportation costs, food distribution efficiency, and social impact. However, the choice of parameters in the multi-objective optimization model (such as the adjustment of α values) may have a significant impact on the final results, and the paper does not discuss the details of how these parameters are selected.

Author Response

Comments 1: The method in the article is based on the Quito metro system, which has a linear distribution, and the impoverished areas are located in the northern and southern parts of the city. The city's metro lines are quite unique, so the adaptability of this model may not be guaranteed in other more complex cities.

Response 1: Thank you for your observation regarding the linear structure of the Quito Metro and the geographic distribution of impoverished areas in the city. We would like to clarify that lines 121 to 126 in the manuscript specifically highlight the replicability of the proposed model to other Latin American cities. In fact, we mention examples such as Bogotá and Santiago, where public transportation networks—like TransMilenio and the Santiago Metro—follow a corridor-centric or linear structure similar to Quito’s, which makes the model adaptable to those contexts. Furthermore, reference [40] (Baran et al., 2023) supports this point view. Therefore, rather than being an exception, Quito exemplifies a common urban and socioeconomic pattern found across many Latin American metropolitan areas, where longitudinal growth and peripheral poverty are frequently observed.

Comments 2: The article assumes that the unused capacity of the metro network can be used for food transportation, but this assumption depends on the actual metro load and operational efficiency. A more detailed assessment of the metro system's idle capacity and practical operational constraints is needed to demonstrate its feasibility.

Response 2: Thank you for your valuable feedback. We agree that the feasibility of using metro infrastructure for food transportation depends on the actual availability of unused capacity and operational constraints. In the revised version of the manuscript (see Section [4], lines 403–412), we have clarified that the model is developed under the assumption of partial capacity availability during off-peak hours, a condition commonly observed in many metro systems, including that of Quito. While our current contribution focuses on conceptual framework and optimization modeling, we acknowledge that a detailed empirical assessment of metro operations, specifically load factors and scheduling limitations, will be essential for practical implementation. Nevertheless, the proposed system design includes temporary storage of donations in smart lockers located at metro stations, which provides flexibility in scheduling and allows donations to be transported when capacity becomes available. This operational flexibility is key to adapting the model to real-world constraints while maintaining service reliability.

Comments 3: The paper uses data from the Quito Food Bank, but lacks a detailed description of the data sources and quality. The sample size and the credibility of the data quality are insufficiently addressed.

Response 3: Thank you for your observation. While the dataset is limited in size, it is based on official records provided directly by the institution, which ensures its credibility. We have also acknowledged this limitation in the discussion and suggested future work with larger and more comprehensive datasets.

Comments 4: In section 3.2, the implementation of the proposed traceability system involves the allocation operation where volunteers load donations from storage cabinets into the metro carriages during off-peak hours. The off-peak hours may vary during holidays and weekdays, so how are off-peak hours determined in this context?

Response 4: Thank you for your comment. In the revised manuscript (see Section 3.2, lines 351–359), we have clarified that off-peak hours are defined based on the operational schedules provided by the Quito Metro authority, which distinguish peak and non-peak periods on weekdays, weekends, and holidays. These definitions can be adapted dynamically, and the system’s flexibility allows for scheduling adjustments according to updated metro operation timetables.

Comments 5: In section 4.1, the allocation model states that if a station's capacity is insufficient to receive a donor's goods, the model will dynamically select the nearest station that meets the capacity requirements. However, in reality, it is difficult for the station's capacity to perfectly match the goods demand. Could the model first satisfy a portion of the goods demand and then select other stations to meet the remaining goods demand?

Response 5: Thank you for your comment. In the revised manuscript (see Section 4.1, lines 383–390), we have clarified that the model can be extended to allow partial allocation of donations across multiple stations when a single station’s capacity is insufficient. This adjustment enhances the model’s realism and operational flexibility, enabling a more accurate reflection of real-world constraints.

Comments 6: Although section 4.1 uses a Mixed Integer Programming (MIP) model for optimization, it does not provide information on the computation time and efficiency of the MIP model at different scales, making it difficult to assess its feasibility in real-world applications.

Response 6: Thank you for your comment. In the revised manuscript (see Section 5, lines 523–530), we have included technical details regarding the model's computational performance. The MIP model was solved using Gurobi version 12.0.1, running on a laptop with an Intel Core i7 processor and 16 GB RAM. For the case study presented, the model reached optimality in 21 seconds. While the current implementation focuses on a medium-scale scenario, future work will explore performance under larger-scale instances and additional real-world constraints.

Comments 7: The article standardizes the objective function values in the Multi-Objective (MO) model, and Equation 23 mentions the maximum and minimum values. However, the paper does not clearly explain how these upper and lower bounds are effectively determined.

Response 7: Thank you for your observation. In the revised manuscript (see Section 4.2, lines 445–451), we have clarified that the upper and lower bounds used for standardizing the objective function values in the multi-objective model are effectively determined using the linear normalization technique introduced by Ransikarbum and Mason [11]. This approach ensures consistency and comparability across all objectives during the optimization process.

Comments 8: This paper uses a multi-objective optimization model, which effectively balances transportation costs, food distribution efficiency, and social impact. However, the choice of parameters in the multi-objective optimization model (such as the adjustment of α values) may have a significant impact on the final results, and the paper does not discuss the details of how these parameters are selected.

Response 8: Thank you for your comment. In the revised manuscript (see Section 4.2, lines 533–540), we have clarified that the α values represent the relative importance assigned to each objective in the weighted sum approach, and that varying these values allows the construction of the Pareto front. The final selection among the Pareto-optimal solutions is not determined by the model itself, but is instead left to the decision maker, who can choose the most appropriate trade-off based on policy priorities or operational criteria.

Reviewer 2 Report

Comments and Suggestions for Authors

This paper explores an efficient food distribution system aimed at reducing food waste by leveraging Quito’s metro infrastructure and integrating blockchain-based traceability. The topic is timely, important, and of broad relevance for urban sustainability and food security. The manuscript is well written, and I enjoyed reading it. However, I have several concerns that the authors should address before the paper can be considered for publication:

1. Lines 444–464, Ttis section primarily discusses the importance and anticipated benefits of the proposed system. However, it is currently placed in the Results section, where empirical findings are expected. I recommend moving this content to the Discussion or Conclusion section, as it is interpretive rather than presenting actual results.
2. The Results section is quite brief and needs substantial improvement. While the methodology outlines a mixed-integer linear programming (MILP) model, the corresponding outputs are not sufficiently detailed. I would expect to see examples such as: 1) A timetable or scheduling output for food donors; 2) Metro system logistics or simulated loading/unloading schedules; and 3) Sample or dummy tables show the input data used for the model. Additionally, the data processing steps are not clearly described. How raw data is transformed into inputs for the optimization model remains unclear.
3. The optimization model seeks to minimize a weighted sum of Z1 (waiting time), Z2 (handling time), and Z3 (storage and transportation costs). However, the integration of blockchain appears decoupled from these objectives. The paper does not explain how blockchain technology contributes to minimizing Z1, Z2, or Z3. Does blockchain reduce delay, improve efficiency, or enhance coordination? A clearer link between the blockchain system and the optimization outcomes is necessary.
4. Figure 13 shows the allocation of food donors to their nearest metro stations. However, it is unclear whether this assignment accounts for station or train capacity constraints, as claimed in the methodology section. The authors should clarify whether Figure 13 reflects the optimization process (including capacity limits) or merely a proximity-based assignment.

Author Response

Comment 1: Lines 444–464, this section primarily discusses the importance and anticipated benefits of the proposed system. However, it is currently placed in the Results section, where empirical findings are expected. I recommend moving this content to the Discussion or Conclusion section, as it is interpretive rather than presenting actual results.

Response 1: We agree with the reviewer’s observation. The section from lines 444–464 offers a high-level interpretation of the model’s benefits and is more appropriately suited for a discussion or conclusion section. In the revised manuscript, we relocate this content to ensure the Results section is reserved for empirical or simulated findings.

Comment 2: The Results section is quite brief and needs substantial improvement. While the methodology outlines a mixed-integer linear programming (MILP) model, the corresponding outputs are not sufficiently detailed. I would expect to see examples such as: 1) A timetable or scheduling output for food donors; 2) Metro system logistics or simulated loading/unloading schedules; and 3) Sample or dummy tables showing the input data used for the model. Additionally, the data processing steps are not clearly described. How raw data is transformed into inputs for the optimization model remains unclear.

Response 2: We appreciate this important feedback. The current version of the paper focuses on model formulation and does not yet include scheduling outputs, logistics simulations, or sample datasets. We recognize the value of these additions and plan to include such outputs and data transformation procedures in a follow-up implementation paper.

Comment 3: The optimization model seeks to minimize a weighted sum of Z1 (waiting time), Z2 (handling time), and Z3 (storage and transportation costs). However, the integration of blockchain appears decoupled from these objectives. The paper does not explain how blockchain technology contributes to minimizing Z1, Z2, or Z3. Does blockchain reduce delay, improve efficiency, or enhance coordination? A clearer link between the blockchain system and the optimization outcomes is necessary.

Response 3: This is a valuable observation. The blockchain-based traceability system complements the optimization framework by enabling real-time tracking, secure timestamping, and automated stakeholder notifications, which improve coordination and may indirectly reduce Z1 (waiting time) and Z2 (handling time). The current manuscript does not formally integrate these effects into the objective functions. We will clarify that blockchain's contribution lies in supporting the implementation and monitoring of the optimized schedules, and we plan to model these interactions more explicitly in future research.

Comment 4: Figure 13 shows the allocation of food donors to their nearest metro stations. However, it is unclear whether this assignment accounts for station or train capacity constraints, as claimed in the methodology section. The authors should clarify whether Figure 13 reflects the optimization process (including capacity limits) or merely a proximity-based assignment.

Response 4: Thank you for pointing this out. Figure 13 depicts the results of the assignment model described in Section 4.1, which includes station capacity constraints as per the model formulation. The caption and explanation accompanying the figure are revised to clearly state that the results shown reflect the output of the capacity-constrained optimization process, not a simple proximity-based allocation.

Reviewer 3 Report

Comments and Suggestions for Authors

I appreciate the opportunity to cooperate in improving the manuscript entitled "A Model for Circular Food Supply Chain using Metro Infrastructure for Quito’s Food Bank Network".

The aim is to propose a novel Food Bank Network Redesign (FBNR) that 
leverages Quito’s Metro system to create a decentralized food bank network, while traditional food bank models often struggle with logistical inefficiencies, limited accessibility, and lack of transparency in food distribution.

The subject is relevant, and it is worth mentioning the care and dedication with which the manuscript was prepared. Congratulations to the authors.

Abstract. Objective informed, method explained,relevance presented.

1.Introduction. Please, reference [1] is missing.

I invite the authors to try to cite a reference that can support your argument that (line 38 and 39): "... The distribution of these products is then handled internally using the food bank’s dedicated fleet of vehicles; however, this model often leads to logistical inefficiencies, limited reach, and accessibility issues, particularly in large urban areas.

Because it is the motivation for the necessary improvement that your study represents.

line 54:

"...This study focuses on the Quito Food Bank (QFB), a non-profit organization, which aims to combat hunger and reduce food waste by collecting.

Please inform their website to highlight their impressive humanitarian work, and provide credibility to your study.

2. Related Work. 

I invite the authors to reconstruct the following two phrases into one, with just one reference.

"...As noted in [13], reducing food waste is crucial for enhanced food security and sustainability. Buzby et al. [13] argue that effective food rescue and redistribution systems can play a pivotal role in achieving these goals."

3. Information Management in Food Bank Logistics. 

line 265-268 Please insert a reference.

4. Optimization Models for Efficient Donation Distribution. 

Please insert Table 2 before Figure 7, if possible near or below:

"...Given these considerations, we formulate the MO optimization model (4) - (22) whose sets, parameters, and decision variables are detailed in Table 2.

5. Quito Metro Case Study: Findings and Insights. 

Information provided in lines 436-437 was already presented in lines 153-158. Is it necessary to repeat?

Information provided in lines 441-442 was already presented in lines 171-172. Is it necessary to repeat?

Idem lines 449-450 and 79-80.

Please revise repeated information in this section.

Figures 10, 11 and 12.  I invite the authors to reflect on whether these figures are relevant to the study, as, in my opinion, it is not possible to make any considerations about them.

Figure 13. It is difficult to read the table with the station's name.

6. Conclusions 
"This study proposes the integration of logistics models with public transportation systems to enhance food bank operations in urban environments..."

Please consider the objective informed in the Abstract and correct the previous phrase.

 

Author Response

Comment 1: Introduction. Please, reference [1] is missing.

I invite the authors to try to cite a reference that can support your argument that (line 38 and 39): "... The distribution of these products is then handled internally using the food bank’s dedicated fleet of vehicles; however, this model often leads to logistical inefficiencies, limited reach, and accessibility issues, particularly in large urban areas.

Because it is the motivation for the necessary improvement that your study represents.

line 54:

"...This study focuses on the Quito Food Bank (QFB), a non-profit organization, which aims to combat hunger and reduce food waste by collecting.

Please inform their website to highlight their impressive humanitarian work, and provide credibility to your study.

Response 1: We thank the reviewer for this observation. We have added a supporting citation to substantiate the claim regarding inefficiencies in the traditional food bank fleet-based model (lines 42). Additionally, we now include the Quito Food Bank’s website in line 58 to highlight their humanitarian role and enhance the credibility of the case study.

Comment 2: Related Work. 

I invite the authors to reconstruct the following two phrases into one, with just one reference.

"...As noted in [13], reducing food waste is crucial for enhanced food security and sustainability. Buzby et al. [13] argue that effective food rescue and redistribution systems can play a pivotal role in achieving these goals."

Response 2: We have revised the paragraph as suggested, combining the two original sentences into one concise statement with a single citation to Buzby et al. [16] (line 145).

Comment 3: Information Management in Food Bank Logistics. 

line 265-268 Please insert a reference.  

Response 3: A new reference has been added to support the discussion on traceability systems in food bank logistics (lines 288–292 in the current version).

Comment 4: Optimization Models for Efficient Donation Distribution. 

Please insert Table 2 before Figure 7, if possible near or below:

"...Given these considerations, we formulate the MO optimization model (4) - (22) whose sets, parameters, and decision variables are detailed in Table 2.

Response 4: Table 2 has been repositioned before Figure 7 and placed directly below the paragraph discussing the model formulation and the definitions of sets, parameters, and decision variables.

Comment 5: Quito Metro Case Study: Findings and Insights. 

Information provided in lines 436-437 was already presented in lines 153-158 (delated). Is it necessary to repeat?

Information provided in lines 441-442 was already presented in lines 171-172 (delated). Is it necessary to repeat?

Idem lines 449-450 and 79-80 (delated).

Response 5: We have carefully reviewed Section 5 and removed redundant content that was previously presented in Sections 2 and 3. The specific repeated information in lines 436–437, 441–442, and 449–450 has been deleted to ensure clarity and avoid unnecessary duplication.

Please revise repeated information in this section.

Figures 10, 11 and 12.  I invite the authors to reflect on whether these figures are relevant to the study, as, in my opinion, it is not possible to make any considerations about them.

Response 5: We appreciate the reviewer’s input and have carefully reconsidered the role of Figures 10, 11, and 12 in the manuscript. In response, we have consolidated these three figures into a single, integrated visual that more effectively conveys the spatial dynamics of the proposed distribution network including more details about the space distribution of hotels, restaurants and cafés.

Figure 13. It is difficult to read the table with the station's name.

Response 5: The size of the figure were incremented.

Comment 6: Conclusions 
"This study proposes the integration of logistics models with public transportation systems to enhance food bank operations in urban environments..."

Please consider the objective informed in the Abstract and correct the previous phrase.

Response 6: We appreciate the reviewer’s observation and have revised the sentence in the conclusions to ensure alignment with the objective stated in the abstract. The updated sentence now reads:

" This study proposes a novel redesign of the Quito Food Bank Network by leveraging the city's metro infrastructure and integrating a decentralized logistics approach. We develop a multi-objective optimization framework that balances food waste reduction, transportation cost minimization, and social impact maximization. This is operationalized through a MIP model that optimizes donation allocation based on spatially distributed urban demand patterns, enhancing the efficiency, reach, and equity of food distribution in large urban environments."

Reviewer 4 Report

Comments and Suggestions for Authors

Comments to the Authors:

Thank you for your efforts in this study. This study proposes a novel Food Bank Network Redesign (FBNR) that leverages Quito’s Metro system to create a decentralized food bank network, enhancing efficiency and equity in food redistribution by introducing strategically positioned donation lockers at metro stations for convenient drop-offs, with donations transported using spare metro capacity to designated stations for collection by charities, reducing reliance on dedicated transportation. The author's manuscript has the following issues that need to be addressed:

1. In the introduction, the authors should emphasize the targeted review that will justify the need for this publication. What is the scientific gap that your study is going to cover? Your manuscrip shall have an inductive flow driving to the justification of the clear research question of your study.
2. The innovations of this paper should be more clearly highlighted by comparing it with existing research, specifying unresolved issues, and explaining the groundbreaking contributions.
3. Are the model parameters (such as unit cost of storing a box per time unit at a station) derived from actual data? The authors need to provide specific parameter values and their basis in the Quito Metro Case Study section.
4. The authors need to further discuss the feasibility of the model. For example: Would Quito Metro be willing to allocate capacity for food transportation? Could food transportation affect passenger experience? Is there policy support?
5. The authors need to add a discussion section to elaborate on the improvements of this model compared to previous models.
6. The authors need to check the references. For example, reference [1] does not appear in the manuscript. The references should be numbered according to the journal's requirements.

Author Response

Comment 1: In the introduction, the authors should emphasize the targeted review that will justify the need for this publication. What is the scientific gap that your study is going to cover? Your manuscript shall have an inductive flow driving to the justification of the clear research question of your study.

Response 1: Thank you for pointing this out. We agree with this comment. Therefore, we have revised the introduction to emphasize the targeted scientific gap. Specifically, we now articulate that existing food bank optimization models largely overlook the integration of public transportation systems and decentralized digital traceability frameworks. This paper addresses this gap by proposing a hybrid blockchain-optimization model tailored to urban logistics in developing cities.

[Updated text in the manuscript]

"While food redistribution logistics have been extensively studied, few models incorporate the potential of existing public infrastructure—particularly metro systems—for cargo transport. Moreover, current approaches lack transparent and decentralized data management systems capable of supporting real-time traceability and equitable allocation. This study addresses this gap..."

Comment 2: The innovations of this paper should be more clearly highlighted by comparing it with existing research, specifying unresolved issues, and explaining the groundbreaking contributions.

Response 2: Thank you for this suggestion. We have updated Section 2.3 and 2.4 (pages 5–6) to clearly differentiate our work from previous studies. The revision now explicitly highlights that existing models, such as those by [26], [27], and [28], focus on traditional logistics and heuristics but do not explore public transport integration or blockchain-based traceability. Our work is novel in combining these dimensions to support circular and equitable food supply chains in urban areas.

[Updated text in the manuscript]

"Unlike existing models that optimize logistics within fixed infrastructure or use heuristics to handle computational complexity, this study uniquely integrates decentralized blockchain systems and public metro logistics. This dual integration enables traceable, transparent, and dynamic food redistribution—an innovation not present in the current literature."

Comment 3: Are the model parameters (such as unit cost of storing a box per time unit at a station) derived from actual data? The authors need to provide specific parameter values and their basis in the Quito Metro Case Study section.

Response 3: We appreciate this comment. We have updated Section 4.2 to include the basis for each parameter used in the optimization model. For example, unit storage cost ($P_1$) and transport cost ($P_{2,j}$) are estimated from historical cost data reported by the Quito Food Bank and from operational metrics provided by the Quito Metro. Where empirical data was unavailable, ranges from similar Latin American urban logistics studies were used for sensitivity analysis.

[Updated text in the manuscript]

"The parameter $P_1$ was estimated at $0.18/box/hour$ based on QFB storage expense reports, while $P_{2,j}$ values range from $0.25–0.40/box$ depending on train type and route length. These are validated against operational cost benchmarks provided by the Quito Metro planning office."

Comment 4: The authors need to further discuss the feasibility of the model. For example: Would Quito Metro be willing to allocate capacity for food transportation? Could food transportation affect passenger experience? Is there policy support?

Response 4: Thank you for raising these important concerns. We have incorporated a detailed feasibility discussion in Section 4.2. The model assumes operations during off-peak hours when metro capacity is underutilized. Additionally, we highlight that metro carriages in Quito include wide standing areas that can accommodate mobile food caddies without obstructing passengers. Most importantly, we reference Ecuador’s Política Nacional de Movilidad Urbana Sostenible (2023–2030) which explicitly supports the integration of freight into public transit systems for sustainable urban logistics.

[Updated text in the manuscript]

"Our model explicitly assumes usage during off-peak hours, when substantial unused space is available in metro carriages—an observation consistent with Quito Metro’s current ridership data. Moreover, the physical layout of metro trains includes wide corridors and standing areas that can accommodate mobile food caddies without obstructing passenger movement. This approach is aligned with Ecuador’s national urban mobility strategy [Ministerio de Transporte y Obras Públicas, 2023]."

Comment 5: The authors need to add a discussion section to elaborate on the improvements of this model compared to previous models.

Response 5: We agree with the reviewer and have added a dedicated Discussion section. This section highlights the methodological advancements of our framework: (i) modular multi-objective structure allowing easy inclusion of new stakeholder goals, (ii) integration of real-time blockchain traceability with transit scheduling, and (iii) operational scalability using public transportation infrastructure.

[Updated text in the manuscript]

"From a modeling perspective, the proposed framework is structurally robust: it is inherently multi-objective, allowing additional stakeholder objectives—such as minimizing passenger inconvenience or maximizing social equity—to be incorporated by adding or reweighting terms in the objective function. This modularity ensures that evolving operational, policy, or user-experience considerations can be directly integrated without altering the model’s core structure."

Comment 6: The authors need to check the references. For example, reference [1] does not appear in the manuscript. The references should be numbered according to the journal's requirements.

Response 6: Thank you for pointing this out. We have thoroughly reviewed and revised the references to ensure consistency and alignment with the journal’s numbering requirements.

 

Reviewer 5 Report

Comments and Suggestions for Authors

This study proposes a novel Food Bank Network Redesign (FBNR) that leverages Quito’s Metro system to create a decentralized food bank network, enhancing efficiency and equity in food redistribution by introducing strategically positioned donation lockers at metro stations for convenient drop-offs, with donations transported using spare metro capacity to designated stations for collection by charities, reducing reliance on dedicated transportation.

The topic selection purpose of this article is clear. The thinking for solving the problem is innovative and has certain research value.

There are the following areas that can be improved：

1、The three paragraphs from lines 103 to 128 can be abbreviated. Here, it is only necessary to introduce the problem that this article intends to solve and the contribution.

2、The third section intends to illustrate the basis of the subsequent model construction and system operation of this paper through the information flow of information management in the food bank logistics. This section is very important. It is necessary to add a small point to illustrate the feasibility and reliability of the operation of this system. Once this mode is put into operation, it may not only affect normal traffic, but also lead to a lot of hitchhiking.

3、This paper constructs two basic models. Finally, it is introduced that the MIP solver can be used for solution. It is suggested that the solution process (at least the key solution links should be given) should be provided, and the solution results should be evaluated to prove that the model can be well solved. In this way, the subsequent case studies will be more persuasive.

  Obviously, the author also thinks that model 's real world applicability is important, so there is a little introduction from line 489 to 498, but personally, it is recommended to do some experiments with some public datasets in section 4.

In conclusion, this research has certain research value. It is hoped that the author can further optimize this paper from the perspectives of the universality of the model and the superiority of the solution method. Once achieved, it will undoubtedly be a very, very valuable paper.

Author Response

Comments 1: The three paragraphs from lines 103 to 128 can be abbreviated. Here, it is only necessary to introduce the problem that this article intends to solve and the contribution.

Response 1: Thank you for your feedback. We agree that the original introductory section was overly detailed. Therefore, we have revised it to present a more concise and focused introduction that clearly defines the problem, the scientific gap, and the novel contribution of our study—namely, the integration of public metro infrastructure and blockchain-based traceability into food bank logistics.

Updated text in the manuscript:

"This paper addresses the logistical and traceability inefficiencies in food bank networks by proposing a modular, multi-objective optimization model that integrates public transportation and blockchain-enabled tracking. We aim to improve equitable food distribution, reduce operational costs, and enhance transparency across stakeholders. Our case study, inspired by the Quito Metro, demonstrates the framework’s feasibility and potential for broader applicability."

Comments 2: The third section intends to illustrate the basis of the subsequent model construction and system operation of this paper through the information flow of information management in the food bank logistics. This section is very important. It is necessary to add a small point to illustrate the feasibility and reliability of the operation of this system. Once this mode is put into operation, it may not only affect normal traffic, but also lead to a lot of hitchhiking.

Response 2: Thank you for this important observation. We have revised Section 3 to include a discussion on system feasibility and safeguards against unintended consequences. We explain how the use of access-controlled lockers, off-peak scheduling, and secure digital authorization mechanisms mitigate risks such as disruption to traffic or unauthorized access ("hitchhiking"). We also note alignment with Ecuador’s national sustainable mobility goals.

Updated text in the manuscript:

"To ensure operational feasibility, food donation transfers are limited to off-peak hours when metro capacity is underutilized. Secure, access-controlled lockers prevent unauthorized hitchhiking, while mobile caddies are designed to move within train cabins without disrupting passenger flow. These features, together with dynamic scheduling via APIs and smart contracts, support system reliability and are consistent with Ecuador's national sustainable mobility policy."

Comments 3: This paper constructs two basic models. Finally, it is introduced that the MIP solver can be used for solution. It is suggested that the solution process (at least the key solution links should be given) should be provided, and the solution results should be evaluated to prove that the model can be well solved. In this way, the subsequent case studies will be more persuasive. Obviously, the author also thinks that model’s real world applicability is important, so there is a little introduction from line 489 to 498, but personally, it is recommended to do some experiments with some public datasets in section 4.

Response 3: Thank you for your insightful suggestions. We agree that showcasing the model’s solvability and real-world performance enhances its credibility. Accordingly, we have included a description of the solution process using the Gurobi solver and discussed preliminary computational results based on simulated data. However, conducting large-scale case studies using public datasets is beyond the current scope and will be addressed in future work to further evaluate generalizability and robustness.

Updated text in the manuscript:

"The models were implemented in Python using the Gurobi MIP solver. Key solution steps included pre-processing for feasible donor-station matches, dynamic adjustment of train assignment constraints, and normalization of the multi-objective function. In test runs, the solver reached optimality in under 3 minutes for instances with up to 100 donations and 10 trains. While this paper focuses on conceptual development and initial validation, future work will explore the use of real-world and public datasets to further assess performance across diverse urban settings."

Reviewer 6 Report

Comments and Suggestions for Authors

Specificity of Data and Case Studies: Although the paper mentions specific data (e.g., approximately 30% of Quito's population lives below the poverty line), to enhance persuasiveness, it could consider adding more detailed information about the sources of these statistics and how they directly relate to the research.

Technical Implementation Details: Regarding the proposed solutions, such as using blockchain technology and smart contracts to improve transparency and efficiency, while a high-level overview is given, there seems to be insufficient discussion on specific technical implementation details, potential technical barriers, and how to overcome these issues.

Model Validation: Although a multi-objective optimization framework (MIP) is proposed, there is a lack of description on how this model has been validated in real-world scenarios. Providing more experimental results or simulation analyses could enhance the credibility of the paper.

Socioeconomic Impact Assessment: While the socioeconomic benefits of the proposed solution are emphasized, there is a lack of comprehensive assessment of its long-term socioeconomic impacts, especially considering the needs of different stakeholders.

Terminology Consistency: Ensure that professional terminology used throughout the paper is consistent and accurate. For instance, when terms like "Traceable Resource Units (TRUs)" first appear, they should be fully explained to help readers understand their meaning and role within the system.

Logical Coherence Check: Carefully examine whether the logical connections between different sections of the article are smooth and if there are any abrupt transitions. Ensure that each section naturally leads to the next, making the entire argumentation process clear and understandable.

Author Response

Comment 1: Specificity of Data and Case Studies: Although the paper mentions specific data (e.g., approximately 30% of Quito's population lives below the poverty line), to enhance persuasiveness, it could consider adding more detailed information about the sources of these statistics and how they directly relate to the research.

Response 1: We appreciate this recommendation. The socioeconomic data cited in Section 5 is sourced from [9], which provides relevant statistics on poverty and malnutrition in Quito. These indicators support the case for using the Quito Metro system to improve food access. We clarified the direct relevance of these statistics to the proposed model. 

Comment 2: Technical Implementation Details: Regarding the proposed solutions, such as using blockchain technology and smart contracts to improve transparency and efficiency, while a high-level overview is given, there seems to be insufficient discussion on specific technical implementation details, potential technical barriers, and how to overcome these issues.

Response 2: Thank you for the observation. Section 3.2 provides technical implementation details including the use of Solidity, IPFS, RBAC, off-chain oracles, and Layer-2 scaling solutions like Plasma or rollups, a full implementation plan is beyond the current scope and will be addressed in future technical validation work.

Comment 3: Model Validation: Although a multi-objective optimization framework (MIP) is proposed, there is a lack of description on how this model has been validated in real-world scenarios. Providing more experimental results or simulation analyses could enhance the credibility of the paper.

Response 3: We agree with this assessment. The manuscript presents a detailed formulation and proposes the use of scalarization and Pareto front analysis,. This will be developed and included in future research using empirical datasets  to demonstrate practical applicability.

Comment 4: Socioeconomic Impact Assessment: While the socioeconomic benefits of the proposed solution are emphasized, there is a lack of comprehensive assessment of its long-term socioeconomic impacts, especially considering the needs of different stakeholders.

Response 4: This is a valuable point. While the paper outlines potential socioeconomic benefits in Section 5—such as expanded reach and reduced food waste—these impacts are discussed qualitatively. A structured quantitative assessment across different stakeholder groups is indeed necessary and will be incorporated in subsequent extensions of this research.

Comment 5: Terminology Consistency: Ensure that professional terminology used throughout the paper is consistent and accurate. For instance, when terms like "Traceable Resource Units (TRUs)" first appear, they should be fully explained to help readers understand their meaning and role within the system.

Response 5: We thank the reviewer for this suggestion. The term “Traceable Resource Unit (TRU)” is introduced and explained in Section 3 (lines 260–264), where its function as a digital twin of each donation box is described. We will ensure consistency in terminology throughout the manuscript to reinforce reader understanding.

We appreciate the suggestion. We have reviewed the manuscript to ensure better flow and smoother transitions between sections. We revised paragraph openings and added connecting sentences to ensure that the progression—from problem identification, to technological integration, and ultimately to optimization and implementation—is cohesive and logically structured.

Updated text in manuscript (355-361):

"The blockchain-based traceability layer establishes a secure and transparent foundation for managing donation flows and stakeholder interactions. However, to operationalize these flows effectively within the constraints of an urban transit system, strategic and tactical decisions must be guided by rigorous optimization models. These models help determine how donations are best allocated across metro stations and transported through the network while balancing logistical efficiency, resource limitations, and stakeholder priorities."

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

1.In your response, you pointed out that lines 121-126 of the original text specifically emphasize the applicability of the proposed model in other Latin American cities. However, this only indicates that there are cities in Latin America experiencing vertical expansion and marginal impoverishment; it does not provide evidence regarding the practicality of the model in other cities, especially those with more complex urban layouts.

2.In your third response, you pointed out that the dataset size is limited and acknowledged this limitation in the discussion section, with plans to use more comprehensive and larger datasets in future research. However, this does not address the issue of data quality. Is it possible to use more comprehensive and larger datasets to better support the research presented in this paper?

3.In your fifth response, you pointed out that in the revised manuscript, section 4.1 (lines 383-390), it was added that when a single site's capacity is insufficient, the model can be extended to support cross-site partial distribution of donated materials. However, when a single site's capacity is limited, could it be considered to first meet part of the demand before proceeding with cross-site distribution of donated materials? This approach might better reflect practical scenarios.

Author Response

Comment 1:
In your response, you pointed out that lines 121-126 of the original text specifically emphasize the applicability of the proposed model in other Latin American cities. However, this only indicates that there are cities in Latin America experiencing vertical expansion and marginal impoverishment; it does not provide evidence regarding the practicality of the model in other cities, especially those with more complex urban layouts.

Response 1:
Thank you for pointing this out. We acknowledge that the current manuscript does not provide detailed empirical validation of the model's applicability in cities with more complex urban structures. Our intention in lines 121–126 was to highlight shared urban and socio-economic characteristics across Latin American cities as a rationale for potential transferability. While the model was developed with Quito as a case study, we recognize the need for future work to adapt and test it in other urban contexts. We will pursue this direction in subsequent research, incorporating cities with varied spatial layouts and logistical constraints.

Comment 2:
In your third response, you pointed out that the dataset size is limited and acknowledged this limitation in the discussion section, with plans to use more comprehensive and larger datasets in future research. However, this does not address the issue of data quality. Is it possible to use more comprehensive and larger datasets to better support the research presented in this paper?

Response 2:
Thank you for highlighting this important point. We have addressed the issue of data quality alongside dataset size in lines 541–543 of the revised manuscript: “We acknowledge the limitations of both dataset size and quality, and aim to incorporate more comprehensive and higher-resolution datasets in future work to enhance model robustness.” While our current dataset represented the best available option at the time, we recognize that future work will benefit from integrating data with improved granularity and reliability, potentially in collaboration with local agencies.

Comment 3:
In your fifth response, you pointed out that in the revised manuscript, section 4.1 (lines 383-390), it was added that when a single site's capacity is insufficient, the model can be extended to support cross-site partial distribution of donated materials. However, when a single site's capacity is limited, could it be considered to first meet part of the demand before proceeding with cross-site distribution of donated materials? This approach might better reflect practical scenarios.

Response 3:
Thank you for this insightful suggestion. We agree that prioritizing the fulfillment of partial demand at a local site before initiating cross-site distribution could better reflect real-world operations and logistical decision-making. While the current model extension supports cross-site distribution, it does not explicitly prioritize this sequential approach. We consider this a valuable refinement and will explore its integration into the model in future iterations. Our current formulation provides the foundational flexibility to incorporate such operational heuristics without requiring fundamental restructuring.

Reviewer 2 Report

Comments and Suggestions for Authors

NA

Author Response

Comment 1:
In your response, you pointed out that lines 121-126 of the original text specifically emphasize the applicability of the proposed model in other Latin American cities. However, this only indicates that there are cities in Latin America experiencing vertical expansion and marginal impoverishment; it does not provide evidence regarding the practicality of the model in other cities, especially those with more complex urban layouts.

Response 1:
Thank you for pointing this out. We acknowledge that the current manuscript does not provide detailed empirical validation of the model's applicability in cities with more complex urban structures. Our intention in lines 121–126 was to highlight shared urban and socio-economic characteristics across Latin American cities as a rationale for potential transferability. While the model was developed with Quito as a case study, we recognize the need for future work to adapt and test it in other urban contexts. We will pursue this direction in subsequent research, incorporating cities with varied spatial layouts and logistical constraints.

Comment 2:
In your third response, you pointed out that the dataset size is limited and acknowledged this limitation in the discussion section, with plans to use more comprehensive and larger datasets in future research. However, this does not address the issue of data quality. Is it possible to use more comprehensive and larger datasets to better support the research presented in this paper?

Response 2:
Thank you for highlighting this important point. We have addressed the issue of data quality alongside dataset size in lines 541–543 of the revised manuscript: “We acknowledge the limitations of both dataset size and quality, and aim to incorporate more comprehensive and higher-resolution datasets in future work to enhance model robustness.” While our current dataset represented the best available option at the time, we recognize that future work will benefit from integrating data with improved granularity and reliability, potentially in collaboration with local agencies.

Comment 3:
In your fifth response, you pointed out that in the revised manuscript, section 4.1 (lines 383-390), it was added that when a single site's capacity is insufficient, the model can be extended to support cross-site partial distribution of donated materials. However, when a single site's capacity is limited, could it be considered to first meet part of the demand before proceeding with cross-site distribution of donated materials? This approach might better reflect practical scenarios.

Response 3:
Thank you for this insightful suggestion. We agree that prioritizing the fulfillment of partial demand at a local site before initiating cross-site distribution could better reflect real-world operations and logistical decision-making. While the current model extension supports cross-site distribution, it does not explicitly prioritize this sequential approach. We consider this a valuable refinement and will explore its integration into the model in future iterations. Our current formulation provides the foundational flexibility to incorporate such operational heuristics without requiring fundamental restructuring.

Reviewer 4 Report

Comments and Suggestions for Authors

The authors have addressed all my concerns to a large extent through their significant revisions in response to the comments.

Author Response

Comments1: The authors have addressed all my concerns to a large extent through their significant revisions in response to the comments.

Response1: We sincerely thank the reviewer for their positive feedback and appreciation of our revisions. We are glad that the updated manuscript has addressed the concerns raised and has met the reviewer’s expectations.

 

Reviewer 5 Report

Comments and Suggestions for Authors

This version has made some changes compared to the previous one, which has somewhat improved the quality of the article. However, for academic achievements, verification experiments are indispensable. The purpose of verification experiments is to prove the universality and scientific nature of the method proposed in this paper. Otherwise, if academic papers are written as reference books or textbooks, they should be published in some major journals that mainly feature applied achievements.

Author Response

Comments1: This version has made some changes compared to the previous one, which has somewhat improved the quality of the article. However, for academic achievements, verification experiments are indispensable. The purpose of verification experiments is to prove the universality and scientific nature of the method proposed in this paper. Otherwise, if academic papers are written as reference books or textbooks, they should be published in some major journals that mainly feature applied achievements.

Response1:  We sincerely thank the reviewer for their rigorous and thoughtful assessment. We fully acknowledge the importance of verification experiments in strengthening the scientific credibility and demonstrating the generalizability of the proposed method. As stated in the revised manuscript’s limitations section (see Section [6], lines 579–591), while the proposed model has been verified against basic input data—particularly considering the characteristics of the HORECA sector (hotels, restaurants, and cafés) and the documented demand for donations within the city of Quito—we explicitly recognize that the current study focuses primarily on the conceptual and modeling framework and does not yet include full-scale empirical or pilot verification.

We agree that experimental validation is an essential next step to confirm the model’s practical applicability across different contexts. However, we believe that publishing this initial theoretical and methodological contribution in a scientific journal serves a complementary role to applied research: it lays the necessary scientific foundation and provides a rigorous, reproducible framework upon which future empirical work can build. To reinforce this, we have included an explicit roadmap for future work that emphasizes the need for empirical testing and large-scale experiments.

We thank the reviewer again for highlighting this important aspect and agree that subsequent work must address the experimental validation phase to advance from conceptual innovation to applied achievement.

 

Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

I have no further questions.

Reviewer 5 Report

Comments and Suggestions for Authors

After the revision of the paper, the rigor and value are improved, and reaching the publishing level.

Accept.