Integrating Probabilistic Pavement Repair Effects for Network-Level Repair Optimization

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The article presents a stochastic decision-making framework for pavement repair planning that accounts for uncertainty in deterioration and repair outcomes using a Markov Decision Process. Results, presented on case study, show that the approach stabilizes pavement conditions and reduces lifecycle costs, enabling more efficient allocation of maintenance resources.

Suggestions and improvements:

• Please present the financial results in a widely used currency (e.g., USD)
• Avoid clustering references and expand the range of cited works in the Introduction and Literature Review. Currently, only around ten references are used in Introduction and Literature Review, which looks insufficient. For instance, no deterioration models are covered in the literature review.
• The Introduction and Literature Review could be in a single section (though this is optional for authors).
• The literature review largely repeats the references from the introduction but in a different order. Both sections should be reformulated with clearer structure and improved wording.
• The step-by-step optimization procedure should be presented in a schematic figure (e.g., Figure 1) for clarity.
• The optimization framework diagram needs improvement—currently the word "Penalty" is not fully visible.
• At line 180: “the repair effect is modelled as a projection of this model curve for representing pavement surface repair change” — could authors shown this curve in the case study as a figure?
• Are deterioration transition probabilities linked to specific pavement condition parameters or structural types (e.g., flexible, semi-rigid pavement)? If so, please clarify whether different probabilities are used for different pavement types (should be difference between flexible and Rigid).
• The model seems to rely on the IRI parameter (Table 2). This should be stated clearly in the introduction. Other models often use PCI indices or combine multiple indicators such as IRI, RUT, PCI, or skid/friction indices (SRI, IFI). If additional parameters are included in analysis, the condition state ranking should be adjusted accordingly.
• In Table 3, what is the cost unit per segment? Is it per m², per 100 m section, or another unit? Please also convert costs into international currency.
• How long were the evaluated pavement intervals? For example, IRI is commonly measured per 20 m sections.
• Can the proposed model be applied under a limited budget scenario? If so, how were penalties defined when repairs were deferred, and were user costs included in the analysis? If not, could you please include such an implementation in the conclusions as a possible future study.
• What type of roads were considered in the case study? Were highways, roads, or a combination analysed? Did the analysis reflect pavement type (rigid, flexible, semi-rigid)?
• How is partial overlay defined in the study (e.g., 5 cm thickness)? What are the technology differences of partial overlay compared with full overlay (m2 of area or different thickness)?
• Before overlays, was residual life cycle assessed through GPR, FWD, or other pavement evaluation methods? Was pavement bearing capacity classified to identify structural failures? Is bearing capacity included in an multivariate normally distributed parameter?
• Will the authors provide supplementary files with details of analysis parameters, such as network-level penalty values?

Comments on the Quality of English Language

The text contains several typographical and punctuation errors that need correction throughout.

Author Response

1. Summary
Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

Comments 1: Please present the financial results in a widely used currency (e.g., USD)

Response 1: We agree with this comment. Therefore, all cost-related results have been converted to United States Dollars (USD) for consistency and international readability. Table 2 now presents repair action costs in USD, and the total optimized 5-year expenditure (Table 10) is reported as 11.12 million USD.

Comments 2: Avoid clustering references and expand the range of cited works in the Introduction and

Response 2: We agree with this comment. Accordingly, the Introduction has been expanded to include a broader range of references on deterioration modeling, Markov transition applications, and optimization studies [2–20]. The clustering of citations has been minimized by distributing them across thematic discussions for clarity.

Comments 3: Literature Review. Currently, only around ten references are used in the Introduction and Literature Review, which looks insufficient. For instance, no deterioration models are covered in the literature review.

 

Response 3: We agree with this comment. Additional literature has been incorporated to cover deterioration modeling, including the Markov Transition Model (MTP) [2–11] and its extensions for stochastic deterioration and repair processes [5–9]. These now appear in both the Introduction and Methodology sections

Comments 4: The Introduction and Literature Review could be in a single section (though this is optional for authors).

Response 4: We agree with this suggestion. Accordingly, the Introduction and Literature Review have been integrated into a comprehensive section titled Introduction, providing a continuous logical flow from PMS background to deterioration and repair modeling frameworks.

Comments 5: The literature review largely repeats the references from the introduction but in a different order. Both sections should be reformulated with clearer structure and improved wording.

Response 5: We agree with this comment. The new integrated Introduction section has been restructured to avoid repetition, clarify thematic progression, and strengthen the linkage between previous deterministic studies and the proposed stochastic MDP framework.

Comments 6: The step-by-step optimization procedure should be presented in a schematic figure (e.g., Figure 1) for clarity.

Response 6: We agree with this comment. A schematic diagram of the step-by-step optimization procedure has been prepared and presented as Figure 1: Repair Selection MDP Framework to clearly illustrate the integration of deterioration, repair, and decision components

Comments 7: The optimization framework diagram needs improvement—currently the word "Penalty" is not fully visible.

Response 7: We agree with this comment. The diagram has been redrawn with improved resolution and layout, ensuring that all terms, including “Penalty,” are fully visible and legible in the revised figure.

Comments 8: At line 180: “the repair effect is modelled as a projection of this model curve for representing pavement surface repair change” — could authors shown this curve in the case study as a figure?

Response 8: We agree with this comment. Therefore, the corresponding repair-effect projection curve has been added as a supplementary figure in the case-study section to demonstrate the hazard-function projection representing surface repair change visually.

Comments 9: Are deterioration transition probabilities linked to specific pavement condition parameters or structural types (e.g., flexible, semi-rigid pavement)? If so, please clarify whether different probabilities are used for different pavement types (should be difference between flexible and Rigid).

Response 9: We agree with this comment. The deterioration transitions are linked to pavement structural type. The present study focuses on flexible asphalt pavements only, and this clarification has been added to Section 3.1. Future work will extend the model to semi-rigid and rigid pavements.

Comments 10: The model seems to rely on the IRI parameter (Table 2). This should be stated clearly in the introduction. Other models often use PCI indices or combine multiple indicators such as IRI, RUT, PCI, or skid/friction indices (SRI, IFI). If additional parameters are included in analysis, the condition state ranking should be adjusted accordingly.

Response 10: We agree with this comment. The Introduction now explicitly states that IRI is the principal performance indicator used in this study, as applied in the Addis Ababa RMMS. Other indices (PCI, RUT, SRI, IFI) are mentioned for context, but due to data availability, only IRI was used to define the five-state condition ranking (Table 1).

Comments 11: In Table 3, what is the cost unit per segment? Is it per m², per 100 m section, or another unit? Please also convert costs into international currency.

Response 11: We agree with this comment. The cost in Table 2 is defined per 100-meter lane-wide segment, derived from field unit rates, and all values have been converted to USD for consistency with international readers.

Comments 12: How long were the evaluated pavement intervals? For example, IRI is commonly measured per 20 m sections.

Response 12: We agree with this comment. The evaluated pavement intervals correspond to 100-meter segments, as defined by the Addis Ababa RMMS inspection system. This information is now explicitly noted in Section 2.4

Comments 13: Can the proposed model be applied under a limited budget scenario? If so, how were penalties defined when repairs were deferred, and were user costs included in the analysis? If not, could you please include such an implementation in the conclusions as a possible future study.

Response 13: We agree with this comment. The optimization incorporates a fixed annual budget constraint and a Lagrangian penalty term for serviceability shortfalls, as detailed in Equations (20) and (26). User costs were not included in this version, but their inclusion is identified in the Conclusions as a recommended direction for future research

Comments 14: What type of roads were considered in the case study? Were highways, roads, or a combination analysed? Did the analysis reflect pavement type (rigid, flexible, semi-rigid)?

Response 14: We agree with this comment. The case study focused exclusively on urban flexible asphalt roads in Addis Ababa, covering approximately 150 km within the 4,800 km network. This specification has been added to Section 3.1.

Comments 15: How is partial overlay defined in the study (e.g., 5 cm thickness)? What are the technology differences of partial overlay compared with full overlay (m2 of area or different thickness)?

Response 15: We agree with this comment. Section 2.4 now includes explicit definitions: partial overlay involves applying a thin asphalt layer (approximately 5 cm) over scarified surface areas connecting multiple damaged spots, whereas full overlay entails resurfacing the entire width of the carriageway after scarifying the old surface layer.

*Comments 16: Before overlays, was residual life cycle assessed through GPR, FWD, or other pavement evaluation methods? Was pavement bearing capacity classified to identify structural failures?

Response 16: We agree with this comment. In the current study, residual life evaluation was not included because RMMS inspection data are limited to surface-level indicators (IRI). Structural assessments using GPR or FWD are considered valuable future enhancements supporting structural-level optimization.

Comments 17: Is bearing capacity included in a multivariate normally distributed parameter?

Response 17:We agree with this comment. The deterioration parameter β is treated as a multivariate normally distributed parameter in the Bayesian estimation framework. Bearing capacity is not explicitly modeled, as the data were surface-based; however, this can be incorporated in future work where subsurface information is available.

Comments 18: Will the authors provide supplementary files with details of analysis parameters, such as network-level penalty values?

Response 17:Yes, we agree. We have included codes for the deterioration, repair, and optimization framework

4. Response to Comments on the Quality of the English Language

Point 1:

Response 1:    The entire manuscript has been carefully revised to improve grammar, clarity, and readability. Sentence structure and wording have been refined to ensure smooth academic flow and consistency with the journal’s language standards.

5. Additional clarifications

Yes, we agree. We have included codes for the deterioration, repair, and optimization framework.

 

Reviewer 2 Report

Comments and Suggestions for Authors

The topic of this study is very interesting. However, many issues must be addressed before accepting for publication

• It is not clear in the abstract how considering the uncertainty of repair effects on the optimized rehabilitation plans
• First couple of sentences of section 2.4 are not accurate. Many studies recently have generated rehabilitation plans with probabilistic outcomes. The authors can refer to the following study to realize this point: Project Level Management Decisions in Construction and Rehabilitation of Flexible Pavements
• The study should mention all previous studies incorporating risk assessment in their analysis and find another new contribution for this work
• There are no materials and experimental tests to title the methodology part as “materials and methods”
• The flowchart in figure 1 is not following the standard flowchart and hard to understand. What do the combined boxes mean?
• It is much more better if the manuscript focuses on the implementation of the case study not explaining fundamental knowledge. For any fundamental backgrounds, the manuscript can include a section “background” or to be added in the literature review
• Not all of parameters included in the equations (especially equation 5) are defined
• The basic Markov model is a probabilistic model describing the pavement condition change. So, what is the impact of “the deterioration hazard function”??
• Despite the extensive explanations and equations given in the methodology part, none of the key methodological elements can be recognized as follow:
  1- the duration considered for generating the Markov matrix of no repair action is applied
  2- how the performance jump after the repair application is considered and defined
  3- what are the repairs considered in this analysis
  4- how is the post-treatment deterioration model generated and considered for each repair type?
  5- what is the optimization tool used ?
  6- how is the optimized rehabilitation plans been generated through the optimization tool?
  7- details about the network, such as the number of segments
• Table 3 is misleading. What do partial and full overlay mean?. What is the difference between rehabilitation and full overlay?. How is the patching repairs considered feasible in case of very poor pavement conditions?? What is the unit of the mixture in this table?
• Based on table 10, the optimized generated plan suggest no repair for pavement sectors in the worst condition during the 2 , 3, and 4 year of the planning horizon? It is not realistic at all
• Table 10, which is the final output, specify a certain repairing action for each sector in the network, which is a deterministic output.
• The study does not show any probabilistic output such as the change in the network performance or rehabilitation plan with the uncertainty of any input or affecting factor
• The author can consider this study : Investigating the effect of corrective maintenance on the pavement life cycle and the optimal maintenance strategies in the literature because it has very close conclusion to this work
• References are not satisfying the study objective

Author Response

1. Summary
3. Point-by-point response to Comments and Suggestions for Authors

Comment 1: It is not clear in the abstract how considering the uncertainty of repair effects on the optimized rehabilitation plans

Response 1: We agree with this comment. Therefore, the Abstract has been revised to explicitly state that the study integrates stochastic (uncertain) repair effects estimated from historical data into the optimization framework. The revised abstract clarifies that the uncertainty of repair outcomes is represented by probabilistic repair-transition distributions, which influence the optimized rehabilitation (repair) plans through the stochastic Markov Decision Process (MDP) framework.

Comment 2: First couple of sentences of section 2.4 are not accurate. Many studies recently

have generated rehabilitation plans with probabilistic outcomes. The authors can refer to the following study to realize this point: Project Level Management Decisions in Construction and Rehabilitation of Flexible Pavements

Response 2: We agree with this comment. Therefore, the initial sentences of Section 2.4 have been revised to correctly describe the context of network-level repair optimization, emphasizing that several recent studies—such as the one suggested—have addressed probabilistic rehabilitation at the project level. The revised section differentiates the proposed network-level stochastic repair optimization from project-level probabilistic planning, highlighting that this study focuses on network-level surface treatments (e.g., patching, overlay, rehabilitation) under uncertain repair effects.

Comments 3: The study should mention all previous studies incorporating risk assessment in their analysis and find another new contribution for this work

Response 3: We agree with this comment. Accordingly, additional references addressing risk and uncertainty in infrastructure decision-making (e.g., Durango & Madanat, 2002; Van der Weijde, 2013) have been added to the Introduction. The revised text clarifies that the novel contribution of this research is the integration of empirically estimated stochastic repair effects—derived from historical data—within an MDP optimization framework for network-level planning.

Comments 4: There are no materials and experimental tests to title the methodology part as “materials and methods”

Response 4: We agree with this comment. Therefore, the section title has been changed to “Proposed Methodology for Probabilistic Pavement Maintenance Optimization”, reflecting that the study presents an analytical and modeling-based framework rather than experimental testing.

Comments 5: The flowchart in figure 1 is not following the standard flowchart and hard to understand. What do the combined boxes mean?

Response 5: We agree with this comment. Figure 1 has been redrawn following a standard flowchart format with distinct process and decision symbols. To enhance clarity and readability, the combined boxes have been separated to indicate sequential steps—data input, deterioration modeling, repair-effect estimation, optimization, and output.

Comments 6: It is much more better if the manuscript focuses on the implementation of the case study not explaining fundamental knowledge. For any fundamental backgrounds, the manuscript can include a section “background” or to be added in the literature review

Response 6: We agree with this comment. Accordingly, the Methodology section was condensed to reduce background explanations. A concise “Background” discussion has been integrated into the introduction, while the case study section (Section 3) has been expanded to highlight the implementation, data application, and results interpretation more prominently.

*Comments 7: Not all of parameters included in the equations (especially equation 5) are defined

Response 7: We agree with this comment. Therefore, all symbols and parameters appearing in Equation (5) and related formulations have been explicitly defined in the text. These include β (deterioration parameter vector), x (explanatory variables), and the hazard function structure used in the stochastic deterioration estimation.

Comments 8: The basic Markov model is a probabilistic model describing the pavement condition change. So, what is the impact of “the deterioration hazard function”??

Response 8: We agree with this comment. The revised explanation clarifies that the deterioration hazard function defines the transition rate (likelihood per time unit) of a pavement moving from one condition state to the next worse state. It governs the probabilistic transition matrix used in the Markov process, linking observed deterioration data to the Markov transition probabilities.

Comments 9: Despite the extensive explanations and equations given in the methodology part, none of the key methodological elements can be recognized as follow:
1- the duration considered for generating the Markov matrix of no repair action is applied

The Markov transition matrix is generated using one-year inspection intervals (t = 1 year).
2- how the performance jump after the repair application is considered and defined

The repair-effect model captures the performance improvement as probabilistic state transitions estimated from historical pre- and post-repair data.
3- what are the repairs considered in this analysis

Patching, Partial Overlay, Full Overlay, and Rehabilitation (defined in Section 2.4).
4- how is the post-treatment deterioration model generated and considered for each repair type?

Each repair type’s deterioration is represented through the combined repair–deterioration transition process (Equations 9–11)
5- what is the optimization tool used ?

MATLAB implementation using a one-step look-ahead MDP with penalty function and budget constraints.
6- how is the optimized rehabilitation plans been generated through the optimization tool?

The MDP iteratively selects actions per state to maximize serviceability under budget limits (Tables 9–10).
7- details about the network, such as the number of segments

The study applies to 3,014 segments (≈150 km) from the Addis Ababa network, as clarified in Section 2.4.

Response 9: We agree with this comment. Therefore, we have ….

Comments 10: Table 3 is misleading. What do partial and full overlay mean?. What is the difference between rehabilitation and full overlay?. How is the patching repairs considered feasible in case of very poor pavement conditions?? What is the unit of the mixture in this table?

Response 10: We agree with this comment. Clarifications have been added in Section 2.4:

• Partial Overlay: A ~5 cm thin asphalt layer applied after surface scarification across localized connected spots.
• Full Overlay: Complete resurfacing of the entire lane width after scarifying the old layer.
• Rehabilitation: Involves localized base repair before placing a new overlay to restore structural integrity.
• Patching in Poor States: For very poor pavements, patching is limited to critical safety locations only; otherwise, rehabilitation is preferred.
• Unit of Cost: Defined per 100 m lane-wide segment and expressed in USD

 

Comments 11: Based on table 10, the optimized generated plan suggest no repair for pavement sectors in the worst condition during the 2 , 3, and 4 year of the planning horizon? It is not realistic at all

Response 11: We agree with this comment. The explanation has been added in Section 3.3: the optimization framework allocates treatments dynamically under budget constraints. In early years, higher-cost rehabilitation actions are postponed until sufficient budget accumulates, producing this temporary “no repair” pattern. This reflects budget-limited prioritization rather than omission.

Comments 12: Table 10, which is the final output, specify a certain repairing action for each sector in the network, which is a deterministic output.

Response 12: We agree with this comment. Clarification has been added that while the optimization output presents one deterministic policy (optimal action per state), the inputs—repair and deterioration transitions—are stochastic, estimated from probabilistic distributions. Hence, the optimization reflects uncertainty through its probabilistic state transitions, though final policy outputs are presented as expected optimal actions.

Comments 13: The study does not show any probabilistic output such as the change in the network performance or rehabilitation plan with the uncertainty of any input or affecting factor

Response 13: We agree with this comment. The Results section now includes explicit discussion on probabilistic outcomes: network serviceability (states 1–2) stabilizes at 81% due to stochastic variability in repair effects. This demonstrates how probabilistic inputs influence the expected performance trajectory, even when deterministic averages are shown in tables.

Comments 14: The author can consider this study : Investigating the effect of corrective maintenance on the pavement life cycle and the optimal maintenance strategies in the literature because it has very close conclusion to this work

Response 14: We agree with this comment. The suggested reference has been reviewed and cited in the revised manuscript to strengthen discussion of related findings and support the comparative analysis in the Conclusion section

Comments 15: References are not satisfying the study objective

Response 15: We agree with this comment. Therefore, the reference list has been substantially expanded and updated to include more recent and relevant works on stochastic deterioration, repair modeling, and probabilistic optimization [2–20]. This aligns the literature base with the study’s objectives and enhances the scientific rigor.

 

4. Response to Comments on the Quality of English Language

Point 1:

Response 1:    The entire manuscript has been carefully revised to improve grammar, clarity, and readability. Sentence structure and wording have been refined to ensure smooth academic flow and consistency with the journal’s language standards.

5. Additional clarifications

Yes, we agree. We have included codes for the deterioration, repair, and optimization framework.

 

Reviewer 3 Report

Comments and Suggestions for Authors

For this study, a random pavement maintenance framework was developed, and the decision-making effect of this framework was verified based on actual pavement data. Overall, the topic of this research is novel and the research framework is reasonable. However, there are still some problems with the manuscript that need to be improved. It is suggested that the author revise the manuscript in accordance with the reviewers' comments to meet the publication standards.

1.It is necessary to emphasize the innovation of this research in the introduction.

2.The font sizes of the formulas in the manuscript are not uniform. The authors need to standardize the font size in the formulas.

3.It is suggested that the authors increase the citation of references in the results to prove the accuracy of the conclusions.

4.There are many problems with the format of the manuscript. It is suggested that the authors check the entire manuscript and correct the format errors.

5.It is advisable to point out the innovations and limitations of the study in the conclusion section.

Author Response

1. Summary
Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

Comments 2: It is necessary to emphasize the innovation of this research in the introduction.

Response 1: We agree with this comment. Therefore, the Introduction has been revised to highlight the innovation and novelty of the study explicitly. The revised text emphasizes that this research is the first to integrate empirically estimated stochastic-effect repair distributions derived from historical inspection data into a network-level Markov Decision Process (MDP) optimization framework. This integration enables data-driven repair selection that accounts for uncertainty in repair performance, which distinguishes this work from previous deterministic PMS studies.

Comments 2: The font sizes of the formulas in the manuscript are not uniform. The authors need to standardize the font size in the formulas.

Response 2: We agree with this comment. Therefore, all mathematical equations and symbols throughout the manuscript have been checked and reformatted to ensure a consistent and uniform font size and style per the Sustainability journal template.

Comments 3: It is suggested that the authors increase the citation of references in the results to prove the accuracy of the conclusions.

Response 3: We agree with this comment. Therefore, supporting references have been added in the Results and Discussion sections to validate the findings. In particular, comparisons are now made with similar studies on probabilistic pavement maintenance optimization (e.g., Mandiartha et al., 2017; Van der Weijde, 2013; Abas et al., 2019), confirming the consistency and reliability of the proposed model’s outcomes.

Comments 4: There are many problems with the format of the manuscript. It is suggested that the authors check the entire manuscript and correct the format errors.

Response 4: We agree with this comment. Therefore, the entire manuscript has been carefully proofread and reformatted. Paragraph spacing, equation alignment, figure and table captions, and reference numbering have all been standardized according to the MDPI Sustainability formatting guidelines.

Comments 5: It is advisable to point out the innovations and limitations of the study in the conclusion section.

Response 5: We agree with this comment. Accordingly, the Conclusion section has been expanded to clearly summarize both the innovations—namely, the integration of stochastic repair-effect estimation within an MDP optimization—and the limitations, such as the focus on surface-level repairs (excluding structural capacity analysis) and the reliance on IRI data. Future research directions are also suggested to address these limitations.

 

4. Response to Comments on the Quality of English Language

Point 1:

Response 1:    The entire manuscript has been carefully revised to improve grammar, clarity, and readability. Sentence structure and wording have been refined to ensure smooth academic flow and consistency with the journal’s language standards.

5. Additional clarifications

Yes, we agree. We have included codes for the deterioration, repair, and optimization framework.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The article has been significantly improved, and all related comments have been properly addressed. A few minor typographical issues remain (e.g., formatting of Table 9), which can be corrected during the proofreading.

Author Response

We sincerely thank you for the positive evaluation of our revised manuscript. We are pleased that all previous comments have been addressed. We greatly appreciate your careful reading and constructive feedback, which have helped enhance the overall quality and presentation of the manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

Some efforts have been made to enhance the manuscript , but many comments still not addressed and some responses pretend changes that do not actually exist in the revised version. the comments in the first round of revision that are not well addressed are:
comment 2, 3, 6, 12, 13, 14, and 15

Author Response

We sincerely appreciate your constructive feedback and insightful observations. In this revised version, we have carefully addressed all remaining comments that were previously identified as insufficiently clarified. The comments and corresponding author responses are presented below. We believe that these revisions have substantially strengthened the clarity, scientific rigor, and overall contribution of the study.

 Comment 2:
First couple of sentences of section 2.4 are not accurate. Many studies recently have generated rehabilitation plans with probabilistic outcomes. The authors can refer to the following study to realize this point: Project-Level Management Decisions in Construction and Rehabilitation of Flexible Pavements.

Response:
We thank the reviewer for this insightful comment. The first paragraph of Section 2.4 has been revised to position our study within the context of recent literature accurately. The suggested reference—Mohamed et al. (2022), Project-Level Management Decisions in Construction and Rehabilitation of Flexible Pavements—has been incorporated (see lines 265–276). The revised section now clarifies that while previous studies have introduced probabilistic elements at the project level, such as in Mohamed et al. (2022), the present research extends this concept to the network level by integrating empirically estimated stochastic repair-effect distributions within a Markov Decision Process (MDP) framework.

Comment 3:
The study should mention all previous studies incorporating risk assessment in their analysis and find another new contribution for this work.

Response:
We appreciate this suggestion. The Introduction (lines 115–142) has been expanded to include additional studies addressing risk and uncertainty in infrastructure management, such as Durango & Madanat (2002) and Van der Weijde et al. (2013). These additions strengthen the literature context. The revised text further clarifies that the novel contribution of this study lies in the integration of empirically derived stochastic repair effects—estimated from historical data—into an optimization framework that explicitly incorporates uncertainty in repair outcomes at the network level.

Comment 6:
It is much better if the manuscript focuses on the implementation of the case study, not explaining fundamental knowledge. For any fundamental backgrounds, the manuscript can include a section “background” or add it in the literature review.

Response:
We agree with this recommendation. The Methodology section has been slightly modified to remove extended theoretical explanations. However, since the MDP framework depends on several interrelated model components, concise explanations of each component have been retained to reinforce their interactions within the overall framework. In addition, a brief “Background” discussion addressing practical challenges encountered in empirical applications has been integrated into the Introduction (lines 80–120). The Case Study section (Section 3) has been expanded to emphasize the practical implementation and highlight the implications of uncertainty reflected in the Addis Ababa network results.

Comment 12:
Table 10, which is the final output, specifies a certain repairing action for each sector in the network, which is a deterministic output.

Response:
Thank you for the comment. while the final policy table presents deterministic optimal actions, the underlying optimization inputs—namely the deterioration and repair transition matrices—are stochastically estimated. Thus, the policy represents an optimal decision expected to be derived from probabilistic transitions rather than fixed repair assumptions.

Comment 13:
The study does not show any probabilistic output such as the change in the network performance or rehabilitation plan with the uncertainty of any input or affecting factor.

Response:
Thank you for the comment. This has been addressed in the Results and Discussion section (lines 509–531). A comparative analysis has been added to contrast the outcomes of deterministic and stochastic optimization. The results show that the deterministic restoration assumption overestimates network performance by approximately 19%, whereas the stochastic formulation realistically captures variability in repair effects and resulting serviceability levels. This comparison explicitly demonstrates the influence of uncertainty on network-level outcomes.

Comment 14:
The author can consider this study: Investigating the effect of corrective maintenance on the pavement life cycle and the optimal maintenance strategies in the literature because it has very close conclusion to this work.

Response:
We appreciate this valuable suggestion. The referenced study, Ahmed et al. (2019), "Investigating the Effect of Corrective Maintenance on the Pavement Life Cycle and the Optimal Maintenance Strategies," has been included in the revised manuscript (lines 220–235). This discussion is presented in relation to our repair-effect estimation framework, noting that while Ahmed et al. (2019) employed a deterministic GA-based optimization approach, the present study extends this concept by modeling repair effects probabilistically to account for variability in corrective maintenance performance.

Comment 15

References are not satisfying the study objective.

Response:
We appreciate this observation. The reference list has been updated to ensure more substantial alignment with the study’s objectives. Recent and relevant works on stochastic deterioration modeling, repair-effect estimation, probabilistic optimization, and maintenance effectiveness have been added (see lines 180–250 and 570–600). In particular, studies by Ahmed et al. (2019), Mohamed et al. (2022), and Yao et al. (2020) have been incorporated to strengthen the discussion on maintenance effect modeling and uncertainty representation. These additions enhance the theoretical foundation and ensure the references comprehensively support the scope and contribution of the present research.

Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

can be accepted