PCSY-D-25-00013

A green vehicle routing methodology for assessing optimal fleet mix and cost/emissions tradeoffs given environmental policy incentives

PLOS Complex Systems

Dear Dr. Wilson,

Thank you for submitting your manuscript to PLOS Complex Systems. After careful consideration, we feel that it has merit but does not fully meet PLOS Complex Systems's publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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Kind regards,

Keith Burghardt, Ph.D.

Academic Editor

PLOS Complex Systems

Keith Burghardt

Academic Editor

PLOS Complex Systems

Hocine Cherifi

Editor-in-Chief

PLOS Complex Systems

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Additional Editor Comments:

Overall, I recommend major revision. More robustness analysis is needed, namely the time windows (R1), and other sensitivity analysis (R2,R4), as well as how indicators/predicted variables change over space and/or time. R2 mentions a related issue about the number of assumptions linked to the model. I also agree with R1 and R4’s clarifying suggestions. This includes adding more visualizations where appropriate. On top of grammar, I suggest addressing R4’s suggestion to clarify the main achievements, such as your model/finding uniqueness.

R1 suggests 3 papers to cite: only cite whichever that seem most relevant. If you find that not all are relevant, you do not need to cite all of them. In addition, disregard R3 (the “minor revision” recommendation). If any of those changes seem reasonable to you, feel free to add them, but you do not need to make a rebuttal to their suggestions.

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Reviewers' Comments:

Reviewer's Responses to Questions

Comments to the Author

1. Does this manuscript meet PLOS Complex Systems’s publication criteria?>

Reviewer #1: Yes

Reviewer #2: Partly

Reviewer #3: Yes

Reviewer #4: Yes

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2. Has the statistical analysis been performed appropriately and rigorously?-->?>

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: N/A

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3. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)??>

The PLOS Data policy

Reviewer #1: Yes

Reviewer #2: No

Reviewer #3: Yes

Reviewer #4: No

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4. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: Yes

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Reviewer #1: This study develops a novel bi-objective green vehicle routing problem to help firms make decisions in this context. The methodology minimizes both total transportation costs and GHG emissions, analyzing policy impacts on fleet mix and routing. However, the quality of the paper needs to be further improved to fit the requirements of the journal. In my opinion, a major revision is needed for this manuscript, and the detailed comments are listed below:

• The reason for excluding time windows in the model needs to be strengthened to be more persuasive. Authors might add references to support how much more computational resources are needed if time windows are included in the model.

• The paper should include more recently published journals to substantiate the points stated in Section 2. For instance, there should be more discussion about how the environmental factors are considered in different vehicle routing approaches. However, there are not enough examples to support this discussion. Therefore, I would like to suggest the authors cite the following papers to improve the quality of the paper further

o Design of Flexible Vehicle Scheduling Systems for Sustainable Paratransit Services. Sustainability, 2020.

o Green vehicle routing and dynamic pricing for scheduling on-site services. International Journal of Production Economics, 2022.

o Green vehicle-routing problem of fresh agricultural products considering carbon emission. International Journal of Environmental Research and Public Health, 2022.

• Since the equations of the mathematical model spans across several pages, it would be easier for readers to understand what the objective functions and constraints are referring if the description is put right above the equations instead of putting them in a table at the end of the section.

• Improvements are needed for grammar, style, and choice of words. The manuscript should be proofread thoroughly before submission. It is recommended that the authors should justify the text for a better presentation.

Therefore, I don’t think this manuscript is suitable for publication at this moment.

Reviewer #2: This paper proposes a bi-objective routing model for green vehicles. The intent is to evaluate trade-offs between GHG emissions in relation to ETS, subsidies and taxes. It employs a Pareto frontier analysis. The analysis then provides policy recommendations on an optimal fleet mix. The explicit modelling of carbon taxes, ETS and subsidies is a benefit in this approach.

Challenges with this analysis are in a number of assumptions linked to the development of new technological frontiers, market competition between technologies and cost of alternative forms of energy. All of these will be critical considerations for corporate actors engaged in logistics and policy makers assessing the feasibility of alternative policy instruments.

Furthermore, a number of concerns are linked to the utility of this model:

the behaviour of firms has not been realistically modelled;

what is the model robustness to extreme shocks/disruptions or extreme scenarios?

linear charging for HGEVs does not seem a realistic assumption;

as acknowledged, 'economic policy is fluctuating', it has not been demonstrated how can a model like the one proposed stabilise policy, or indeed if this is desirable.

Reviewer #3: very interesting paper, i am very much pleased to read in general. some comments may help to improve the paper.

warm regards.

Comments

1. Mathematical Model Complexity and Validation

• The mathematical formulation in Section 3 is comprehensive but lacks validation. The authors should include:

o A small numerical example demonstrating the model's functionality

o Computational complexity analysis

o Discussion of solution methods (exact vs. heuristic approaches)

o Comparison with existing GVRP formulations to highlight novelty

2. Empirical Application Missing

• The authors acknowledge this limitation (lines 556-559), but the paper would be significantly strengthened by:

o At least a proof-of-concept case study using synthetic data

o Sensitivity analysis demonstrating how the Pareto frontier changes under different policy scenarios

o Computational experiments showing scalability

3. Policy Parameter Ranges

• While Section 4 provides extensive ranges for policy parameters, the paper lacks:

o Discussion of how these parameters interact

o Analysis of which combinations are most likely/effective

o Regional variations in policy implementation

4. Literature Review Gaps

• The review of multi-objective GVRP (Table 1) is helpful

o Should clarify the specific gap this work fills beyond "considering all three policies"

Moderate Comments

5. Model Assumptions

• Several assumptions need justification:

o Why is charging limited to 80% (line 388)?

o The assumption of zero acquisition cost for existing CFVs (line 314) may not reflect reality if vehicles need replacement

o Grid emissions factor (μ) is treated as constant but varies by time and location

6. Objective Function Design

• The carbon cap constraint (equation 16) uses annualization, but:

o The rationale for this approach needs clarification

o How does this handle seasonal variations in operations?

o What if the firm operates multiple distinct route sets?

7. Methodological Clarity

• The paper promises a "Pareto frontier sensitivity analysis" but doesn't provide:

o Specific algorithms for generating the Pareto frontier

o Methods for handling the bi-objective nature

o Metrics for comparing Pareto frontiers

Minor Comments

8. Presentation and Structure

• Abstract is too long (395 words) - consider condensing

• Table 2 notation could be organized more systematically (group by type)

• Some equations (especially in Appendix A) could be simplified for readability

9. Writing and Clarity

• Lines 92-96: This paragraph is too dense - break into clearer points

• Section 2.1.2 on solution methodologies seems tangential to the main contribution

• The discussion section (Section 5) reads more like a conclusion - need deeper analysis

Recommendations for Improvement

1. Add Computational Study: Even with synthetic data, demonstrate the model's behavior under different policy scenarios

2. Strengthen Contribution Claims: More clearly articulate what's novel beyond integrating three policies - is it the formulation, the analysis approach, or the policy insights?

3. Develop Solution Methodology: Provide specific algorithms or approaches for solving the bi-objective model

4. Include Managerial Insights: Add a section translating the technical results into actionable insights for both policymakers and fleet managers

5. Consider Uncertainty: Discuss how uncertainty in policy parameters, demand, or energy prices could be incorporated

Decision Recommendation

Minor Revision Required: While the paper addresses an important and timely topic with a comprehensive mathematical model, it may requires strengthening through empirical validation, clearer methodological contributions, and more actionable insights. The theoretical framework is solid, but without computational experiments or case studies, the practical value may remain unclear.

Reviewer #4: SPECIFIC COMMENTS:

The paper is a potentially interesting paper about public policy in the form of carbon taxes, emissions trading systems (ETSs), and subsidies for heavy goods electric vehicles (HGEVs), and their benefits. Specifically authors look into assessing optimal fleet mix and cost/emissions tradeoffs given environmental policy incentives.

In the following I will refer to Multi-Objective GVRP (moGVRP)

Comments are below.

-- How is your model and/or findings unique (or common/universal) and is that the main achievement? in other words, what is the generalizabilty of your results and consistency with other results? It seems like you did not validate your model based on any real-world patterns, then one may question the validity of your findings....

-- in none of the figures there is a probabilistic assessment that is performed, where probability density functions (pdfs) characterize the distribution of information, that is the uncertainty, and that can be used for inferring the causal linkages between the predictors and predictands.

-- I think you shouild make many more visualizations of your results.

Generic comments are provided below to perhaps try to find some sort of generalizabilty and depth of results through quantification, whether possible. Further quantification may be done in the future but the statement of limitations and possibilities is an important aspect of scientific publication.

GENERAL COMMENTS:

(1) Eco-STOCHASTICITY/VARIABILITY of PATTERNS (eco-variability attribution via and systemic uncertainty decomposition for causal attribution): To address the model/data Uncertainty-Sensitivity coupling, global sensitivity and uncertainty analysis (GSUA, aka systemic information decomposition) should be done to identify key determinants of model/data variability (including the GVRP) and universal determinants across geographies. You do not quite perform a one-factor-at-a-time sensitivity analysis, nor a non-linear sensitivity analysis to capture the variables' interactions (high-order interactions that underping the function of any complex system) that can be predominant in defining patterns' variability. See Pianosi et al. (2016) for an extensive discussion about this topic and how data should be used for GSUA using a simple variance-based approach. Entropy approaches of GSUA (Servadio and Convertino, 2018) bounded to predicted patterns, are also available when the pdfs are too complex to make the variance meaningful. The attribution of uncertainty can lead to the quantification of ecological stress (as change into the systemic function considered. e.g. GVRP features' change) attributable to different environmental causes or unknown factors.

I also think the paper should pinpoint which site has the highest and lowest uncertainty (uncertainty sources and sinks), uncertainty/information baseline and thresholds (regular and anomalous patterns), type of tipping points, and whether the degree of uncertainty is attributable to env determinants. Maximum GVRP gradients (as preferential information flow networks as in Servadio and Convertino, 2018) should have the lowest uncertainty.

(2) eco-STABILITY and eco-STATE CONTROL via OPTIMAL Network CORE (prediction of optimal causal controls): How indicators/predicted variables (i.e. GVRP pattern/network indicators or values) change over space and/or time, conditional to optimal or desired outcomes (e.g. related to GVRP optimal ranges that are not identified in your paper), is critical for mapping site-/time-specific and universal patterns and shifts (Sugihara G et al (2012)), and more importantly environment-ecological controls that are Pareto-optimal (Shoval, O. et al, 2012 and ParTi model). The stability (and universality) of ecological patterns over predictors' gradients and their critical change, should be quantified because that can define potential stable states over which the predictands (causal factors) are relatively stable or approaching a transition. These calculations can be done by doing inverse modeling via MonteCarlo filtering over the pdfs of GVRP.

RECOMMENDATION:

I suggest accepting the paper after Moderate/Major Revisions. The paper is interesting, but I think the findings are quite dependent on the model construction considered; and uniqueness, limitations, and uncertainty should be stated or addressed more explictily. GSUA should be conducted to identify complex non-linear dependencies of the model and that can support the inference of optimal controls for the GVRP patterns.

REFERENCES:

Servadio, J. & M. Convertino. (2018). Optimal information networks: Application for data-driven integrated health in populations. Science Advances, 4(2)

Pianosi et al. (2016)

Sensitivity analysis of environmental models: A systematic review with practical workflow

Environmental Modelling & Software

Volume 79, May 2016, Pages 214-232

Packages for GSUA

https://safetoolbox.github.io/Documentation.html

Sugihara G et al (2012)

Detecting Causality in Complex Ecosystems

https://www.science.org/doi/10.1126/science.1227079

Shoval, O. et al. Evolutionary trade-offs, Pareto optimality, and the geometry of phenotype space. Science 336(6085), 1157–1160 (2012).

Pareto Task Inference (ParTI) https://www.weizmann.ac.il/mcb/alon/download/pareto-task-inference-parti-method

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

Reviewer #4: No

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A green vehicle routing methodology for assessing optimal fleet mix and cost/emissions tradeoffs given environmental policy incentives

PCSY-D-25-00013R1

Dear Dr. Wilson,

We're pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you'll receive an e-mail detailing the required amendments. When these have been addressed, you'll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Kind regards,

Keith Burghardt, Ph.D.

Academic Editor

PLOS Complex Systems

Additional Editor Comments (optional):

I want to thank the authors for their revision. I personally disagree with R6 as exploring phase transitions, Pareto-optimal frontiers (also mentioned by an earlier reviewer), etc., is out of scope. I would argue a model to improve operations of a complex system is well aligned with complex systems science. I acknowledge the reviews have diverged in each review, but they have come from new reviewers each time.

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

Reviewer #4: All comments have been addressed

Reviewer #5: All comments have been addressed

Reviewer #6: All comments have been addressed

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publication criteria?>

Reviewer #4: Yes

Reviewer #5: Yes

Reviewer #6: No

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3. Has the statistical analysis been performed appropriately and rigorously?-->?>

Reviewer #4: Yes

Reviewer #5: N/A

Reviewer #6: N/A

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4. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)??>

The PLOS Data policy

Reviewer #4: Yes

Reviewer #5: Yes

Reviewer #6: Yes

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5. Is the manuscript presented in an intelligible fashion and written in standard English?<br/><br/>PLOS Complex Systems does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.-->?>

Reviewer #4: Yes

Reviewer #5: Yes

Reviewer #6: Yes

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Reviewer #4: I believe that the authors have addressed all reviewers' comments. Global sensitivity and uncertainty analyses is still missing, however the data size would is relatively limited and would make it difficult to run a proper GSUA.

Reviewer #5: The authors prepared a revised version of their original manuscript addressing the previous comments. The improvements are significant with additional discussions and a better structure including Appendixes. I have no further comments at this time.

Reviewer #6: This paper presents a bi-objective green vehicle routing model that incorporates multiple policy instruments and charging infrastructure investment over a multi-period planning horizon, offering practical relevance for sustainable logistics. However, as a submission to a complex systems journal, the work falls short of making a meaningful methodological contribution. The authors introduce high-dimensional, discrete decision variables and multi-period dynamics that inherently generate combinatorial complexity, yet they treat this complexity merely as a computational obstacle rather than as a core feature of a complex system worthy of analytical exploration. There is no substantive investigation into emergent system behaviors—such as phase transitions in Pareto-optimal frontiers, nonlinear interactions among policy parameters, or scale-dependent trade-offs between strategic investment and operational routing. Furthermore, the paper does not propose new analytical or computational paradigms suited for such coupled strategic–operational problems across temporal scales. Given these limitations, the manuscript reads more as a competent applied operations research study than as a research article advancing complex systems science. I therefore recommend rejection.

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Reviewer #4: None

Reviewer #5: No

Reviewer #6: No

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