Optimizing Sustainable and Resilient Electric Vehicle Battery Recycling Network: Insights from Fourth-Party Logistics

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This study focuses on the resilience optimization of EVB recycling networks under the 4PL framework. Addressing industry and academic pain points such as the lack of consideration for facility disruption risks and the inefficiency of traditional solvers, it integrates multi-dimensional resilience strategies, constructs a two-stage stochastic programming model, and develops the SRDBH algorithm. The effectiveness of the model and algorithm is verified through real-world case studies. The research topic aligns with the sustainable development needs of the new energy industry, demonstrating strong theoretical innovation and engineering practicality. Specific comments are as follows: 

1. The study mentions conducting experiments based on 1024 disruption scenarios, but fails to clarify the specific logic of scenario generation. For some key parameters, the source of values is only labeled as "derived from actual enterprise operations," with no description of data distribution characteristics or outlier handling methods—this reduces the reproducibility of the research.
2. For the "budget constraint on facility fortification and backup costs" in the model, the basis for setting the total budget is not clarified, nor is the logic of budget allocation among different types of facilities discussed. The study assumes a fixed value of "96 cells per EVB," but in reality, the number of cells varies across vehicle types, and the boundary of the assumption’s impact on model results is not explained.
3. The algorithm comparison only selects CPLEX as a benchmark, without comparing it with other mainstream heuristic algorithms or dedicated algorithms in the EVBRND field published in recent years. Performance is only evaluated based on "upper-lower bound gap" and "running time," with no analysis of the algorithm’s adaptability under different network scales.
4. The management implication that "prioritize increasing C_max rather than relying on penalty mechanisms" is overly general, with no distinction between implementation differences for different enterprise types. Barriers to practical application of the model are not discussed.
5. Refine specific pathways for future research directions (e.g., "an EVBRND model integrating a carbon trading mechanism can introduce carbon quota constraints and incorporate carbon emission costs into the objective function"). Add research suggestions for "collaborative optimization of EVB echelon utilization and recycling" (e.g., considering the impact of echelon utilization centers on facility location in recycling networks) to align with current industry needs for full-lifecycle management of EVBs and expand the application scenarios of the research.

Author Response

Comments 1: "The study mentions conducting experiments based on 1024 disruption scenarios, but fails to clarify the specific logic of scenario generation. For some key parameters, the source of values is only labeled as ‘derived from actual enterprise operations,' with no description of data distribution characteristics or outlier handling methods—this reduces the reproducibility of the research."

Response:

We sincerely appreciate the reviewer's insightful comments. We acknowledge that the logic of disruption scenario generation and the data source description were not sufficiently clear in the original version. Accordingly, we have provided a more detailed explanation in the revised manuscript.

To better represent disruption situations, the following assumptions are made:

• (a). Disruptions among facilities are assumed to be independent.
• (b). The disruption probability of each facility is known.
• (c). Each facility with disruption risk has a binary state—disrupted or non-disrupted.

Assumptions (a)–(c) are commonly adopted in the existing literature. For example, Losada et al. (2012), Baghalian et al. (2013), and Fattahi et al. (2017) assumed that the facility states follow a known probability distribution. Similarly, Fattahi and Govindan (2020) modeled each facility as having two possible states, normal or disrupted. The disruption probabilities for all facilities are specified in Table 3, and this logic has been clearly described in the revised version. A total of ten facilities were identified as potential disruption sites. Following the approach of Snyder et al. (2007) and using equation (29), 1,024 disruption scenarios were generated, each associated with a corresponding probability. This methodological detail has been clarified in the revised manuscript.

Furthermore, the experimental network is constructed based on the EV battery recycling system jointly established by Jiangling Electric Vehicle Limited and Dongfeng Electric Vehicle Co., Ltd., with reference to official reports from Jiangxi Province and Dongfeng Motor (2019–2021). The experimental parameters are mainly derived from Wang et al. (2020). These parameters are presented in Table 2.

For parameters not reported in Wang's study (e.g., facility processing capacities, 3PL construction costs, 3PL transportation capacities, 3PL unit transportation costs, maximum reservation levels, and unit reservation costs), reasonable estimates were made with reference to Wang's data. These estimated values are summarized in Table 9 to enhance reproducibility.

In Problem description and Mathematical Model, lines 303-316, on Page 10:

The computation of E_θ[ƒ(y,χ,Λ,x,θ)] constitutes the main difficulty in solving the above two-stage stochastic program, and the calculation of the disruption probability under scenario θ is a key issue. To theoretically characterize possible disruptions, the following assumptions are made:

(a). Disruptions among facilities are assumed to be independent;

(b). The disruption probability of each facility is known;

(c). Each facility exposed to disruption risk has a binary state—disrupted or non-disrupted.

Assumptions (a)–(c) are commonly adopted in the existing literature. For example, Losada et al. (2012), Baghalian et al. (2013), and Fattahi et al. (2017) assumed that the facility states follow a known probability distribution. Similarly, Fattahi and Govindan (2020) modeled each facility as having two possible states, normal or disrupted. Based on these assumptions and following the method proposed by Snyder and Daskin (2007), the probability of each disruption scenario is calculated as follows:

Equation 29, on Page 10:

 

In Problem description and Mathematical Model, lines 317-321, on Page 10:

Where, P_θdenotes the disruption probability under scenario θ, S denotes the set of all collection centers that may experience disruptions, S_θ denotes the subset of collection centers disrupted in scenario θ, and p_b denotes the disruption probability of collection center ∀b in {S}. Based on p_θ, problem (P1) can be reformulated into the following deterministic form (P2).

In Numerical Experiments, lines 462-475, on Page 17:

For each facility subject to potential disruption, two possible states are considered: disrupted or not disrupted. A total of ten facilities are assumed to face potential disruption, resulting in 1024 possible disruption scenarios. The disruption probability of each facility is assumed to be known, as listed in Table 3, and the probability of each disruption scenario is calculated using Equation (29). These probabilities are determined with reference to prior studies, ensuring that the parameter settings remain within a realistic range typically encountered in recycling networks.

Under these 1024 disruption scenarios, the proposed SRDBH algorithm is compared with the commercial solver CPLEX to demonstrate that the proposed model and algorithm are more suitable than mainstream commercial solvers for disruption-prone and resource-constrained environments. Experiments are conducted on a computer equipped with a 2.60 GHz quad-core processor and 8 GB of RAM, with the runtime limited to 3600 seconds. By applying the SR technique, the original 1024 scenarios are reduced to four representative ones, which are then solved by both SRDBH and CPLEX.

Table 3, on Page 18:

In Numerical Experiments, lines 452-459, on Page 16-17:

The recycling network is based on the infrastructure jointly established by Jiangling Electric Vehicle Limited and Dongfeng Electric Vehicle Co., Ltd., drawing on reports from Jiangxi Province and Dongfeng Motor (2019–2021). The experimental parameters are primarily obtained from Wang et al.(2020), and the corresponding values are summarized in Table 2. For parameters not reported in Wang's study, including facility processing capacities, 3PL construction costs, 3PL transportation capacities, 3PL unit transportation costs, maximum reservation levels, and unit reservation costs, reasonable estimates were made with reference to Wang's data. These estimated values are presented in the Table 9 to facilitate reproducibility.

Table 2, on Page 17:

 

Table 9, on Page 27:

Comments 2. "For the ‘budget constraint on facility fortification and backup costs' in the model, the basis for setting the total budget is not clarified, nor is the logic of budget allocation among different types of facilities discussed. The study assumes a fixed value of ‘96 cells per EVB,' but in reality, the number of cells varies across vehicle types, and the boundary of the assumption's impact on model results is not explained."

Response:

We sincerely thank the editor and reviewers for the valuable comments, which are very helpful for improving the quality of our manuscript. We acknowledge that the explanation of the budget constraint on facility fortification and backup costs was not sufficiently clear in the original version. In the revised manuscript, we clarify that preventive investment is subject to an upper bound C_max, following Yin et al. (2022). This parameter serves as a key decision factor for the resilience design of the network, and we have conducted experiments to examine the effects of different values of C_max. The allocation of the budget among different types of facilities is determined endogenously through the optimization process, rather than being pre-specified, which ensures that the model adapts to varying disruption risks and cost structures.

The assumption of "96 cells per EVB" is derived from the data reported by Wang et al. (2020). We acknowledge that the actual number of cells may vary across different vehicle models. This value was adopted as a representative baseline for model validation and experimental analysis. Nevertheless, the proposed model is flexible and can be easily adapted to accommodate different numbers of cells per EVB with only minor parameter adjustments. Future research could further investigate the impact of varying battery configurations and cell compositions on the network design and optimization results. The revised content has been updated in the manuscript accordingly.

The specific revisions to the manuscript are as follows:

In Problem description and Mathematical Model, lines 225-233, on Page 6:

To mitigate facility and transportation disruptions, multiple resilience strategies are integrated into the EVBRND. These strategies include fortifying critical facilities, reserving additional capacities to enhance recovery flexibility, and introducing redundancy through multi-3PL collaboration and multi-route allocation. Preventive investment, which represents the enterprise's expenditures on fortification and backup measures, is subject to a budget C_max, as suggested by Yin et al.(2024). This upper bound functions as a key control parameter for resilience design. The specific allocation of fortification and backup resources across facilities is not predetermined; instead, it is determined by the optimization results, thereby reflecting the trade-offs among facility vulnerability, reinforcement costs, and system-wide recovery efficiency.

Comments 3. "The algorithm comparison only selects CPLEX as a benchmark, without comparing it with other mainstream heuristic algorithms or dedicated algorithms in the EVBRND field published in recent years. Performance is only evaluated based on ‘upper-lower bound gap' and ‘running time,' with no analysis of the algorithm's adaptability under different network scales."

Response:

We sincerely thank the reviewer for this valuable comment. We acknowledge that the original description may have been insufficiently clear, leading to a possible misunderstanding. The comparison with CPLEX serves to demonstrate that the proposed SRDBH algorithm is more suitable than mainstream commercial solvers for disruption-prone and resource-constrained environments. As the number of disruption scenarios increases, CPLEX fails to obtain feasible solutions within the time limit, whereas SRDBH can still generate near-optimal solutions within a short runtime.

Second, since this study focuses on a strategic engineering management problem, solution quality is of greater importance than computation time. The quality of solutions is evaluated by calculating the lower bound and assessing the upper–lower bound gap as a key indicator of algorithmic performance. A small gap indicates that SRDBH consistently yields near-optimal solutions with high reliability—an essential property for managerial decision-making under uncertainty.

The comparison results between SRDBH and CPLEX are presented in Table 4. In addition, we have supplemented the experiments with tests on both small-scale (47 nodes, denoted as SRDBH-S) and large-scale (71 nodes, denoted as SRDBH-L) networks, with the results summarized in Table 5. The findings confirm that SRDBH maintains strong computational efficiency and robustness across different problem sizes, underscoring its scalability and engineering applicability in diverse industrial contexts.

Overall, this study contributes to the engineering management field by providing a practical, scalable, and disruption-resilient network design approach for EVB recycling, effectively addressing both operational uncertainty and strategic resilience investment decisions.

The specific revisions to the manuscript are as follows:

In Numerical Experiments, lines 461-474, on Page 17:

For each facility subject to potential disruption, two possible states are considered: disrupted or non-disrupted. A total of ten facilities are assumed to face potential disruption, resulting in 1024 possible disruption scenarios. The disruption probability of each facility is assumed to be known, as listed in Table 3, and the probability of each disruption scenario is calculated using Equation (29). These probabilities are determined with reference to prior studies, ensuring that the parameter settings remain within a realistic range typically encountered in recycling networks. 
    
Under these 1024 disruption scenarios, the proposed SRDBH algorithm is compared with the commercial solver CPLEX to indicate that the proposed model and algorithm are more suitable than mainstream commercial solvers for disruption-prone and resource-constrained environments. Experiments are conducted on a computer equipped with a 2.60 GHz quad-core processor and 8 GB of RAM, with the runtime limited to 3600 seconds. By applying the SR technique, the original 1024 scenarios are reduced to four representative ones, which are then solved by both SRDBH and CPLEX. 

Table 3, on Page 18:

In Numerical Experiments, lines 469-509, on Page 17-18:

Under these 1024 disruption scenarios, the proposed SRDBH algorithm is compared with the commercial solver CPLEX to demonstrate that the proposed model and algorithm are more suitable than mainstream commercial solvers for disruption-prone and resource-constrained environments. Experiments are conducted on a computer equipped with a 2.60 GHz quad-core processor and 8 GB of RAM, with the runtime limited to 3600 seconds. By applying the SR technique, the original 1024 scenarios are reduced to four representative ones, which are then solved by both SRDBH and CPLEX.

Since this study focuses on a strategic engineering management problem, solution quality is of greater importance than computation time. Specifically, the quality of solutions is evaluated by calculating the lower bound and assessing the upper–lower bound gap as a key indicator of algorithmic performance. A small gap indicates that SRDBH consistently yields near-optimal solutions with high reliability—an essential property for managerial decision-making under uncertainty.

To further assess the scalability and practical value of SRDBH, we divide the test instances into two categories: small-scale networks (47 nodes, denoted SRDBH-S) and large-scale networks (71 nodes, denoted SRDBH-L). This classification allows us to evaluate the adaptability of the algorithm to different network sizes commonly encountered in engineering practice. The choice of 47 and 71 nodes is consistent with the assumptions proposed by Yin et al. (2022), which suggest that the number of network nodes in practical EVB recycling systems generally does not exceed 100.

The experimental results are summarized in Table4 and Table 5 (TCRN denotes the total cost, LB represents the lower bound, and N/A indicates termination due to memory overflow). The main findings are as follows:

Computational efficiency: SRDBH successfully solves all test cases within the 3600-second time limit, with runtimes significantly shorter than those of CPLEX.

Memory robustness: CPLEX frequently terminates due to insufficient memory, while SRDBH consistently produces stable outputs, demonstrating superior applicability in engineering contexts.

Solution accuracy: Even when CPLEX produces results, the gaps remain close to 100%, indicating infeasible lower bounds. By contrast, SRDBH achieves gaps below 3.5% in SRDBH-S and below 1.3% in SRDBH-L, highlighting its capability to deliver high-quality near-optimal solutions.

Scalability: SRDBH maintains low gaps and stable performance in both small- and large-scale networks, confirming its adaptability to various network sizes in engineering management practice.

In summary, the SRDBH algorithm efficiently and reliably addresses large-scale EVB recycling network design problems under multiple uncertainties and complex constraints. It effectively overcomes the computational bottlenecks of traditional commercial solvers in resource-limited environments and demonstrates strong engineering management value, particularly for enterprises that must make rapid and resilient network optimization decisions under disruption risks and budget constraints.

Table 4, on Page 19:

Table 5, on Page 19:

Comments 4. "The management implication that ‘prioritize increasing C_max rather than relying on penalty mechanisms' is overly general, with no distinction between implementation differences for different enterprise types. Barriers to practical application of the model are not discussed"

Response:

We thank the reviewer for highlighting that the managerial implication was overly general. In the revised manuscript, differentiated strategies for enterprises with sufficient versus limited budgets are discussed. Specifically, enterprises with adequate resources are advised to prioritize preventive investments, while resource-constrained enterprises can mitigate risks by enhancing redundancy in the network, thereby reducing reliance on direct budget expansion. The specific revisions are as follows.

In Managerial Implications, lines 602-645, on Page 22-23:

Through a series of numerical experiments, the effectiveness of the proposed model and solution algorithm is validated. Based on these results, the following managerial recommendations are offered for practitioners:

First, from the perspective of computational efficiency and solution feasibility, the proposed SRDBH algorithm exhibits strong stability and robustness in addressing complex scenarios. Practical optimization strategies for network design under frequent disruption risks or stringent C_max constraints are thereby enabled. For decision makers who are required to adjust network configurations within limited time horizons, such a heuristic approach can be regarded as an effective means of mitigating unexpected risks and resource fluctuations.

Second, the sensitivity analysis indicates that ϑ and C_max exert considerable influence on network performance, but their effects differ in nature. From the enterprise perspective, C_max serves as a controllable investment decision. An increase in C_max consistently reduces both TCRN and URBN; for example, increasing C_max in the sensitive range yields substantial reductions in TPFN: raising C_max from 10,000 to 20,000 reduces TPFN by about 29%, and further increasing from 20,000 to 40,000 reduces TPFN by approximately 74%. Moreover, in the example where C_max =10000, increasing ϑ leads to only a modest increase in TCRN of about 6.09%, whereas the corresponding increase in TPFN is approximately 28.0%. These results indicate that expanding C_max —when affordable—can more effectively and fundamentally lower URBN and penalty expenditures than simply raising penalty parameters.

However, for firms with limited resources, directly increasing C_max may not be feasible. In such cases, enhancing redundancy through multi-3PL collaboration and diversified routing offers an alternative. For instance, when C_max is moderate, increasing redundancy and operational flexibility can reduce URBN by an additional 7.5% compared with changes driven primarily by penalty adjustments, providing a cost-effective way to improve recovery without large upfront fortification budgets.

From the policy perspective, ϑ represents a regulatory lever controlled by governments. Higher ϑ levels encourage recycling behavior, but their marginal effects diminish when C_max is sufficiently large. For example, under low C_max settings, raising ϑ substantially increases penalty spending (TPFN rises by 28% in one tested scenario) while yielding limited improvements in completion rates; conversely, under sufficiently large C_max , penalty costs can be driven to zero and URBN approaches zero regardless of ϑ. This implies that, from a public-policy viewpoint, calibrated combinations of regulatory pressure and support for preventive investment (e.g., subsidies, cost-sharing, or co-investment schemes that effectively increase firms' available C_max) are likely to be more effective and efficient than relying only on high punitive charges.

In conclusion, the SRDBH algorithm is indicated to be a reliable decision-support instrument for enterprises operating under uncertainty and resource constraints. Managerial strategies should therefore avoid excessive dependence on ex-post penalty mechanisms and instead prioritize preventive investments when feasible. At the same time, governments should design penalty parameters with caution, ensuring that they motivate compliance without imposing unnecessary costs. A balanced coordination between enterprise-driven preventive investment and government-designed policy incentives can achieve the dual goals of cost efficiency and sustainable recovery.

Comments 5. "Refine specific pathways for future research directions (e.g., "an EVBRND model integrating a carbon trading mechanism can introduce carbon quota constraints and incorporate carbon emission costs into the objective function"). Add research suggestions for "collaborative optimization of EVB echelon utilization and recycling" (e.g., considering the impact of echelon utilization centers on facility location in recycling networks) to align with current industry needs for full-lifecycle management of EVBs and expand the application scenarios of the research."

Response:

We appreciate the reviewer's constructive suggestion regarding refining the future research directions. In line with the reviewer's advice, we have revised the section on research outlook. Specifically, we added (i) the potential integration of carbon trading mechanisms into EVBRND models to incorporate carbon emission costs and quota constraints, and (ii) the collaborative optimization of EVB echelon utilization and recycling, which considers the influence of echelon utilization centers on facility location decisions. These additions aim to better align our study with current industry needs for full-lifecycle management of EVBs and to broaden the application scenarios of the research.

The specific revisions to the manuscript are as follows:

In Conclusion, lines 680-697, on Page 24:

Despite the comprehensive exploration of model formulation and algorithmic design, several avenues remain open for future research. First, the current framework assumes that disruption probabilities are independent and known in advance, which enables the problem to be reformulated as a MILP. This assumption improves computational tractability but may not fully capture the complexities of real-world disruption patterns. Future studies may relax this assumption and extend the framework to account for correlated or uncertain disruption probabilities. Second, the model does not incorporate carbon emission constraints. The integration of mechanisms such as carbon trading or carbon taxation could enhance the policy relevance of the model by introducing carbon quota constraints and incorporating carbon emission costs into the objective function. Third, the impact of stochastic recycling demand has not yet been considered. Extending the framework to capture EVBRND problems under dual sources of uncertainty could further advance the practical applicability of resilient recycling systems. Fourth, collaborative optimization of EVB echelon utilization and recycling could be investigated. Specifically, the inclusion of echelon utilization centers in the network design may affect facility location decisions and support the full-lifecycle management of EVBs, which aligns with current industry trends and expands the potential application scenarios of this research.

 

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Review Report (1)

Journal: Sustainability (ISSN 2071-1050)

Manuscript ID: sustainability-3913311 

Type: Article

Title:  Optimizing Sustainable and Resilient Electric Vehicle Battery Recycling Network: Insights from Fourth-Party Logistics

Summary: This work deals with optimizing resilient electric vehicle battery recycling networks under disruption risks using a fourth-party logistics framework and a scenario reduction–based heuristic algorithm. I recommend major revision before publication due to the need for further clarification, methodological justification, and improved presentation.

1. Please clarify how disruption probabilities were determined—are they based on empirical data, expert opinion, or assumptions?
2. Provide more detailed dataset sources and justify the representativeness of the parameters used.
3. In the proposed SRDBH algorithm, please explain the convergence criteria and computational complexity more clearly; how generalizable is the method beyond the tested case?
4. Please expand on managerial implications and provide more quantitative comparisons between strategies.
5. Although comprehensive, it would benefit from including more recent works (2023–2025) on resilient and circular supply chains.
6. In Figures, some notations are difficult to follow. Please improve clarity and ensure consistency between text, formulas, and figures.
7. Discuss the limitations of the model and algorithm more explicitly, including assumptions (e.g., independence of disruption events).
8. Can the authors clarify how your findings can support decision-making in industry and government ?

Author Response

Comments 1. "Please clarify how disruption probabilities were determined—are they based on empirical data, expert opinion, or assumptions?"

Response:

We sincerely appreciate the reviewer's insightful comments. We acknowledge that the logic of disruption scenario generation and the data source description were not sufficiently clear in the original version. Accordingly, we have provided a more detailed explanation in the revised manuscript.

To better represent disruption situations, the following assumptions are made:

• (a). Disruptions among facilities are assumed to be independent.
• (b). The disruption probability of each facility is known.
• (c). Each facility with disruption risk has a binary state—disrupted or non-disrupted.

Assumptions (a)–(c) are commonly adopted in the existing literature. For example, Losada et al. (2012), Baghalian et al. (2013), and Fattahi et al. (2017) assumed that the facility states follow a known probability distribution. Similarly, Fattahi and Govindan (2020) modeled each facility as having two possible states, normal or disrupted. The disruption probabilities for all facilities are specified in Table 3, and this logic has been clearly described in the revised version. A total of ten facilities were identified as potential disruption sites. Following the approach of Snyder et al. (2007) and using equation (29), 1,024 disruption scenarios were generated, each associated with a corresponding probability. This methodological detail has been clarified in the revised manuscript.

Furthermore, the experimental network is constructed based on the EV battery recycling system jointly established by Jiangling Electric Vehicle Limited and Dongfeng Electric Vehicle Co., Ltd., with reference to official reports from Jiangxi Province and Dongfeng Motor (2019–2021). The experimental parameters are mainly derived from Wang et al. (2020). These parameters are presented in Table 2.

For parameters not reported in Wang's study (e.g., facility processing capacities, 3PL construction costs, 3PL transportation capacities, 3PL unit transportation costs, maximum reservation levels, and unit reservation costs), reasonable estimates were made with reference to Wang's data. These estimated values are summarized in Table 9 to enhance reproducibility.

The specific revisions to the manuscript are as follows:

In Problem description and Mathematical Model, lines 303-316, on Page 10:

The computation of  constitutes the main difficulty in solving the above two-stage stochastic program, and the calculation of the disruption probability under scenario θ is a key issue. To theoretically characterize possible disruptions, the following assumptions are made:

(a). Disruptions among facilities are assumed to be independent;

(b). The disruption probability of each facility is known;

(c). Each facility exposed to disruption risk has a binary state—disrupted or non-disrupted.

Assumptions (a)–(c) are commonly adopted in the existing literature. For example, Losada et al. (2012), Baghalian et al. (2013), and Fattahi et al. (2017) assumed that the facility states follow a known probability distribution. Similarly, Fattahi and Govindan (2020) modeled each facility as having two possible states, normal or disrupted. Based on these assumptions and following the method proposed by Snyder and Daskin (2007), the probability of each disruption scenario is calculated as follows:

Equation 29, on Page 10:

 

In Problem description and Mathematical Model, lines 317-321, on Page 10:

Where, P_θdenotes the disruption probability under scenario θ, S denotes the set of all collection centers that may experience disruptions, S_θ denotes the subset of collection centers disrupted in scenario θ, and p_b denotes the disruption probability of collection center ∀b in {S}. Based on p_θ, problem (P1) can be reformulated into the following deterministic form (P2).

In Numerical Experiments, lines 462-475, on Page 17:

For each facility subject to potential disruption, two possible states are considered: disrupted or not disrupted. A total of ten facilities are assumed to face potential disruption, resulting in 1024 possible disruption scenarios. The disruption probability of each facility is assumed to be known, as listed in Table 3, and the probability of each disruption scenario is calculated using Equation (29). These probabilities are determined with reference to prior studies, ensuring that the parameter settings remain within a realistic range typically encountered in recycling networks.

Under these 1024 disruption scenarios, the proposed SRDBH algorithm is compared with the commercial solver CPLEX to demonstrate that the proposed model and algorithm are more suitable than mainstream commercial solvers for disruption-prone and resource-constrained environments. Experiments are conducted on a computer equipped with a 2.60 GHz quad-core processor and 8 GB of RAM, with the runtime limited to 3600 seconds. By applying the SR technique, the original 1024 scenarios are reduced to four representative ones, which are then solved by both SRDBH and CPLEX.

Table 3, on Page 18:

Comments 2. "Provide more detailed dataset sources and justify the representativeness of the parameters used."

Response:

We sincerely thank the reviewer for the valuable comment. In response, the description of the experimental network and parameter settings has been clarified to enhance transparency and reproducibility. The experimental network is constructed based on the EV battery recycling system jointly established by Jiangling Electric Vehicle Limited and Dongfeng Electric Vehicle Co., Ltd., with reference to official reports from Jiangxi Province and Dongfeng Motor (2019–2021). Experimental parameters are primarily drawn from Wang et al. (2020) and are summarized in Table 2.

For parameters not reported in Wang et al. (2020)—including facility processing capacities, 3PL construction costs, 3PL transportation capacities, 3PL unit transportation costs, maximum reservation levels, and unit reservation costs—reasonable estimates were made based on Wang's data. These estimated values are presented in Table 9 to facilitate reproducibility.

The specific revisions to the manuscript are as follows:

In Numerical Experiments, lines 452-459, on Page 16-17:

The recycling network is based on the infrastructure jointly established by Jiangling Electric Vehicle Limited and Dongfeng Electric Vehicle Co., Ltd., drawing on reports from Jiangxi Province and Dongfeng Motor (2019–2021). The experimental parameters are primarily obtained from Wang et al.(2020), and the corresponding values are summarized in Table 2. For parameters not reported in Wang's study, including facility processing capacities, 3PL construction costs, 3PL transportation capacities, 3PL unit transportation costs, maximum reservation levels, and unit reservation costs, reasonable estimates were made with reference to Wang's data. These estimated values are presented in the Table 9 to facilitate reproducibility.

Table 2, on Page 17:

 

Table 9, on Page 27:

Comments 3. "In the proposed SRDBH algorithm, please explain the convergence criteria and computational complexity more clearly; how generalizable is the method beyond the tested case?"

Response:

We sincerely thank the reviewer for raising this important point. We acknowledge that the convergence process and computational complexity of the proposed SRDBH algorithm were not sufficiently explained in the original manuscript. In the revised version, we have provided a clearer description of the convergence criteria and the computational complexity analysis. Specifically, the Lagrangian dual problem is a concave unconstrained optimization problem that guarantees the existence of a global optimum. The subgradient method is adopted to solve the Lagrangian dual, and its convergence process is analogous to the steepest descent method. To improve convergence efficiency, we set , and when the optimal solution remains unchanged for three consecutive iterations, the step size is reduced to accelerate convergence. For ease of understanding, an illustrative example is added in Figure 2.

In terms of complexity, when the network structure consists of c recycling centers, r remanufacturing centers, w disposal centers, and d demand nodes, the number of decision variables and constraints can be expressed as 3(c+r+w)+k[dc+cr+cw+rw]+[k(cd+2cr+cw+rw)+d]θ and 6(c+r+w) + k(cd+cr+cw+rw) + [2d+4c+2r+w+k(2cd+3cr+2cw+2rw)]θ, respectively. This indicates that both grow substantially with the increase of scenario number θ, which significantly enlarges the problem size. The proposed decomposition algorithm addresses this issue by partitioning the problem into multiple independent scenario subproblems, thereby reducing the number of decision variables and constraints in each subproblem by a factor of θ. This greatly alleviates the computational burden.

Moreover, the algorithm proposed in this study possesses broad applicability for solving multi-scenario stochastic programming problems, extending beyond the context of recycling network design. 

 The specific revisions are as follows:

In A scenario reduction and decomposition-based heuristic, lines 413-421, on Page 15:

If the current best solution  remains unchanged for three consecutive iterations, the step size is adaptively adjusted according to  to accelerate the convergence process. Since the Lagrangian dual problem is a concave and unconstrained optimization problem, a global optimum exists, and the subgradient method is adopted to solve it. The iterative process of this method resembles that of the steepest descent algorithm but relies on subgradient directions instead of exact gradients. By adaptively reducing the step size when stagnation occurs, the proposed scheme improves convergence stability and computational efficiency. An illustrative example of this process is shown in Figure 2.

In A scenario reduction and decomposition-based heuristic, lines 424-437, on Page 16:

In the P2 problem, when the network structure includes c collection centers, r remanufacturing centers, w disposal centers, and d demand nodes, the numbers of decision variables and constraints are 3(c+r+w)+k[dc+cr+cw+rw]+[k(cd+2cr+cw+rw)+d]θ and 6(c+r+w) + k(cd+cr+cw+rw) + [2d+4c+2r+w+k(2cd+3cr+2cw+2rw)]θ, respectively. It can be observed that both quantities increase by [k(cd+2cr+cw+rw)+d]θ and [2d+4c+2r+w+k(2cd+3cr+2cw+2rw)]θ as the number of scenarios θ grows, which significantly amplifies the computational complexity of the model. To address this issue, the proposed decomposition algorithm divides the original problem into multiple independent scenario subproblems, thereby reducing the numbers of decision variables and constraints in each subproblem by a factor of θ. This decomposition strategy effectively alleviates computational burden and enhances solution efficiency.

Furthermore, the proposed algorithm demonstrates general applicability to multi-scenario stochastic programming problems, extending beyond the specific context of recycling network design.

The Figure 2, on Page 16：

Comments 4. "Please expand on managerial implications and provide more quantitative comparisons between strategies."

Response:

We appreciate the suggestion to provide more quantitative comparisons. In the revision, percentage-based changes are reported to illustrate the impacts of varying C_max and ϑ on TCRN, TPFN, and URBN. This offers practitioners a clearer understanding of relative performance differences between alternative strategies. The specific revisions are as follows:

In Managerial Implications, lines 602-645, on Page 22-23:

Through a series of numerical experiments, the effectiveness of the proposed model and solution algorithm is validated. Based on these results, the following managerial recommendations are offered for practitioners:

First, from the perspective of computational efficiency and solution feasibility, the proposed SRDBH algorithm exhibits strong stability and robustness in addressing complex scenarios. Practical optimization strategies for network design under frequent disruption risks or stringent C_max constraints are thereby enabled. For decision makers who are required to adjust network configurations within limited time horizons, such a heuristic approach can be regarded as an effective means of mitigating unexpected risks and resource fluctuations.

Second, the sensitivity analysis indicates that ϑ and C_max exert considerable influence on network performance, but their effects differ in nature. From the enterprise perspective, C_max serves as a controllable investment decision. An increase in C_max consistently reduces both TCRN and URBN; for example, increasing C_max in the sensitive range yields substantial reductions in TPFN: raising C_max from 10,000 to 20,000 reduces TPFN by about 29%, and further increasing from 20,000 to 40,000 reduces TPFN by approximately 74%. Moreover, in the example where C_max =10000, increasing ϑ leads to only a modest increase in TCRN of about 6.09%, whereas the corresponding increase in TPFN is approximately 28.0%. These results indicate that expanding C_max —when affordable—can more effectively and fundamentally lower URBN and penalty expenditures than simply raising penalty parameters.

However, for firms with limited resources, directly increasing C_max may not be feasible. In such cases, enhancing redundancy through multi-3PL collaboration and diversified routing offers an alternative. For instance, when C_max is moderate, increasing redundancy and operational flexibility can reduce URBN by an additional 7.5% compared with changes driven primarily by penalty adjustments, providing a cost-effective way to improve recovery without large upfront fortification budgets.

From the policy perspective, ϑ represents a regulatory lever controlled by governments. Higher ϑ levels encourage recycling behavior, but their marginal effects diminish when C_max is sufficiently large. For example, under low C_max settings, raising ϑ substantially increases penalty spending (TPFN rises by 28% in one tested scenario) while yielding limited improvements in completion rates; conversely, under sufficiently large C_max , penalty costs can be driven to zero and URBN approaches zero regardless of ϑ. This implies that, from a public-policy viewpoint, calibrated combinations of regulatory pressure and support for preventive investment (e.g., subsidies, cost-sharing, or co-investment schemes that effectively increase firms' available C_max) are likely to be more effective and efficient than relying only on high punitive charges.

In conclusion, the SRDBH algorithm is indicated to be a reliable decision-support instrument for enterprises operating under uncertainty and resource constraints. Managerial strategies should therefore avoid excessive dependence on ex-post penalty mechanisms and instead prioritize preventive investments when feasible. At the same time, governments should design penalty parameters with caution, ensuring that they motivate compliance without imposing unnecessary costs. A balanced coordination between enterprise-driven preventive investment and government-designed policy incentives can achieve the dual goals of cost efficiency and sustainable recovery.

Comments 5. "Although comprehensive, it would benefit from including more recent works (2023–2025) on resilient and circular supply chains."

Response:

We appreciate the reviewer's suggestion to include more recent works (2023–2025) on resilient and circular supply chains. In response, we have expanded the literature review to incorporate several recent and relevant studies that cover (i) echelon utilization and carbon policy interactions in closed-loop systems, (ii) advances in AI-assisted battery disassembly relevant to echelon utilization, (iii) resilient supply-chain frameworks with empirical risk-inference mechanisms, and (iv) integrated approaches to sustainable and resilient circular supply chains. Representative recent studies (Qi et al., 2024; Ai et al., 2024; Fu et al., 2023; Vidal et al., 2024; Mahdiraji et al., 2023) are now discussed in the manuscript to better situate our contribution within the evolving literature on resilient and circular supply chains. The revised literature review summarizes these works.

In Literature Review, lines 134-137, on Page 4:

Fu et al. (2023) investigated multi-period EVB recycling planning with demand prediction, demonstrating that data-driven models enhance long-term network adaptability. Mahdiraji et al. (2023) proposed a stochastic programming framework for resilient recycling networks, emphasizing the role of fortification and redundancy strategies in mitigating disruption risks.

In Literature Review, lines 145-149, on Page 4:

Qi et al. (2024) developed a robust optimization model for EVB recycling networks under uncertain demand, showing that the proposed approach improves system resilience and cost efficiency. Ai et al. (2024) introduced a green supply chain design integrating carbon emission constraints, highlighting the effectiveness of carbon reduction strategies in sustainable EVB recycling.

In Literature Review, lines 151-153, on Page 4:

Zhang et al. (2025) proposed a bi-objective model for disassembly–assembly line balancing that optimizes profit and worker learning, solved using a multi-objective fruit fly optimization algorithm with superior performance.

In Literature Review, lines 170-172, on Page 4:

Vidal et al. (2024) examined collaboration mechanisms among logistics providers in recycling networks, revealing that 4PL-led coordination significantly enhances operational performance.

 

Comments 6. "In Figures, some notations are difficult to follow. Please improve clarity and ensure consistency between text, formulas, and figures."

Response:

We sincerely thank the reviewer for this valuable suggestion. In response, all figures have been redrawn to enhance visual clarity, and the notations have been adjusted to ensure consistency across the text, formulas, and figures. Corresponding figure captions and in-text references have also been revised for improved readability. The updated figures are presented below:

The Figure 1, on Page 5：

The Figure 3, on Page 20：

The Figure 4, on Page 21：

Comments 7. "Discuss the limitations of the model and algorithm more explicitly, including assumptions (e.g., independence of disruption events)."

Response:

We sincerely thank the reviewer for this insightful comment. In the revised manuscript, we have more explicitly discussed the limitations of our model and algorithm in the conclusion section, and the corresponding assumptions have been clarified in the problem description. Specifically, three simplifying assumptions are made: (1) the disruption probabilities of facilities are assumed to be known in advance; (2) disruption events are assumed to be independent; and (3) only single-level disruption events are considered without accounting for cascading failures. These assumptions facilitate model tractability and allow the problem to be reformulated as a MILP. However, they may restrict the applicability of the proposed framework in more complex and dynamic real-world environments. Future research could relax these assumptions by incorporating correlated or uncertain disruption probabilities and multi-level cascading failures, thereby enhancing the robustness and generalizability of the proposed approach. The specific revisions are as follows:

In Conclusion, lines 681-697, on Page 24:

Despite the comprehensive exploration of model formulation and algorithmic design, several avenues remain open for future research. First, the current framework assumes that disruption probabilities are independent and known in advance, which enables the problem to be reformulated as a MILP. This assumption improves computational tractability but may not fully capture the complexities of real-world disruption patterns. Future studies may relax this assumption and extend the framework to account for correlated or uncertain disruption probabilities. Second, the model does not incorporate carbon emission constraints. The integration of mechanisms such as carbon trading or carbon taxation could enhance the policy relevance of the model by introducing carbon quota constraints and incorporating carbon emission costs into the objective function. Third, the impact of stochastic recycling demand has not yet been considered. Extending the framework to capture EVBRND problems under dual sources of uncertainty could further advance the practical applicability of resilient recycling systems. Fourth, collaborative optimization of EVB echelon utilization and recycling could be investigated. Specifically, the inclusion of echelon utilization centers in the network design may affect facility location decisions and support the full-lifecycle management of EVBs, which aligns with current industry trends and expands the potential application scenarios of this research.

In Problem description and Mathematical Model, lines 303-316, on Page 10:

The computation of  constitutes the main difficulty in solving the above two-stage stochastic program, and the calculation of the disruption probability under scenario θ is a key issue. To theoretically characterize possible disruptions, the following assumptions are made:

(a). Disruptions among facilities are assumed to be independent;

(b). The disruption probability of each facility is known;

(c). Each facility exposed to disruption risk has a binary state—disrupted or non-disrupted.

Assumptions (a)–(c) are commonly adopted in the existing literature. For example, Losada et al. (2012), Baghalian et al. (2013), and Fattahi et al. (2017) assumed that the facility states follow a known probability distribution. Similarly, Fattahi and Govindan (2020) modeled each facility as having two possible states, normal or disrupted.

Comments 8. "Can the authors clarify how your findings can support decision-making in industry and government ?"

Response:

We thank the reviewer for the insightful comment. In the revised manuscript, we clarify that  C_max represents a decision lever controlled by enterprises, whereas ϑ reflects policy-oriented mechanisms typically determined by government authorities. The managerial implications now explicitly discuss how enterprises can optimize their preventive investment decisions under different budgetary conditions, while governments can calibrate penalty mechanisms to incentivize recycling without imposing excessive costs. This dual perspective provides more actionable guidance for both industrial and policy decision-making. The specific revisions are as follows:

In Managerial Implications, lines 602-645, on Page 22-23:

Through a series of numerical experiments, the effectiveness of the proposed model and solution algorithm is validated. Based on these results, the following managerial recommendations are offered for practitioners:

First, from the perspective of computational efficiency and solution feasibility, the proposed SRDBH algorithm exhibits strong stability and robustness in addressing complex scenarios. Practical optimization strategies for network design under frequent disruption risks or stringent C_max constraints are thereby enabled. For decision makers who are required to adjust network configurations within limited time horizons, such a heuristic approach can be regarded as an effective means of mitigating unexpected risks and resource fluctuations.

Second, the sensitivity analysis indicates that ϑ and C_max exert considerable influence on network performance, but their effects differ in nature. From the enterprise perspective, C_max serves as a controllable investment decision. An increase in C_max consistently reduces both TCRN and URBN; for example, increasing C_max in the sensitive range yields substantial reductions in TPFN: raising C_max from 10,000 to 20,000 reduces TPFN by about 29%, and further increasing from 20,000 to 40,000 reduces TPFN by approximately 74%. Moreover, in the example where C_max =10000, increasing ϑ leads to only a modest increase in TCRN of about 6.09%, whereas the corresponding increase in TPFN is approximately 28.0%. These results indicate that expanding C_max —when affordable—can more effectively and fundamentally lower URBN and penalty expenditures than simply raising penalty parameters.

However, for firms with limited resources, directly increasing C_max may not be feasible. In such cases, enhancing redundancy through multi-3PL collaboration and diversified routing offers an alternative. For instance, when C_max is moderate, increasing redundancy and operational flexibility can reduce URBN by an additional 7.5% compared with changes driven primarily by penalty adjustments, providing a cost-effective way to improve recovery without large upfront fortification budgets.

From the policy perspective, ϑ represents a regulatory lever controlled by governments. Higher ϑ levels encourage recycling behavior, but their marginal effects diminish when C_max is sufficiently large. For example, under low C_max settings, raising ϑ substantially increases penalty spending (TPFN rises by 28% in one tested scenario) while yielding limited improvements in completion rates; conversely, under sufficiently large C_max , penalty costs can be driven to zero and URBN approaches zero regardless of ϑ. This implies that, from a public-policy viewpoint, calibrated combinations of regulatory pressure and support for preventive investment (e.g., subsidies, cost-sharing, or co-investment schemes that effectively increase firms' available C_max) are likely to be more effective and efficient than relying only on high punitive charges.

In conclusion, the SRDBH algorithm is indicated to be a reliable decision-support instrument for enterprises operating under uncertainty and resource constraints. Managerial strategies should therefore avoid excessive dependence on ex-post penalty mechanisms and instead prioritize preventive investments when feasible. At the same time, governments should design penalty parameters with caution, ensuring that they motivate compliance without imposing unnecessary costs. A balanced coordination between enterprise-driven preventive investment and government-designed policy incentives can achieve the dual goals of cost efficiency and sustainable recovery.

 

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

This paper holds an interesting study with integrating fortification and multi-3PL routine in EVBRND. However there is a space for improving the current form of the manuscript. Please find the below comments.

• The paper needs thorough editing for grammar and style. There are many typos. For example: alogorith, alogorthm (line 15, page 1); integrates incorporates strategies (line 65, page 2).
• The adaptive subgradient section uses the same equation number (49) for two different expressions (step-size relation and termination), which is confusing.
• The case data are said to come from an enterprise, with missing values filled using uniform random distributions. Please specify which parameters were missing, the ranges applied, and any other details needed for reproducibility.
• The study presents managerial implications but does not discuss research implications. These should also be included.
• The paper has a very detailed findings section but lacks a proper discussion section. A discussion section is needed where the key findings are compared with results from other similar studies in different contexts.

Author Response

Comments 1. "The paper needs thorough editing for grammar and style. There are many typos. For example: alogorith, alogorthm (line 15, page 1); integrates incorporates strategies (line 65, page 2)."

Response:

We sincerely thank the reviewer for this helpful comment. In response, we have carefully proofread the manuscript and corrected spelling and grammatical errors, including instances such as "alogorith/alogorthm" and "integrates incorporates strategies." These revisions enhance the readability and clarity of the paper.

Comments 2. "The adaptive subgradient section uses the same equation number (49) for two different expressions (step-size relation and termination), which is confusing."

Response:

We sincerely thank the reviewer for pointing out this oversight. The duplication of equation numbers in the adaptive subgradient section arose from a LaTeX editing error, which caused the step-size relation and the termination condition to share the same number (49). This issue has been carefully corrected in the revised manuscript to ensure clarity and consistency. The specific revisions are as follows:

Equation 50, on Page 15:

 

Equation 51, on Page 15:

 

Equation 52, on Page 15:

 

Equation 53, on Page 16:

 

Comments 3. "The case data are said to come from an enterprise, with missing values filled using uniform random distributions. Please specify which parameters were missing, the ranges applied, and any other details needed for reproducibility."

Response:

  We sincerely thank the reviewer for the insightful suggestion. In response, the description of the experimental network and parameter settings has been clarified to enhance transparency and reproducibility. The experimental network is constructed based on the EV battery recycling system jointly established by Jiangling Electric Vehicle Limited and Dongfeng Electric Vehicle Co., Ltd., with reference to official reports from Jiangxi Province and Dongfeng Motor (2019–2021). Experimental parameters are primarily drawn from Wang et al. (2020) and are summarized in Table 2.

For parameters not reported in Wang et al. (2020)—including facility processing capacities, 3PL construction costs, 3PL transportation capacities, 3PL unit transportation costs, maximum reservation levels, and unit reservation costs—reasonable estimates were made based on Wang's data. These estimated values are presented in Table 9 to facilitate reproducibility.

The specific revisions to the manuscript are as follows:

In Numerical Experiments, lines 452-459, on Page 16-17:

The recycling network is based on the infrastructure jointly established by Jiangling Electric Vehicle Limited and Dongfeng Electric Vehicle Co., Ltd., drawing on reports from Jiangxi Province and Dongfeng Motor (2019–2021). The experimental parameters are primarily obtained from Wang et al.(2020), and the corresponding values are summarized in Table 2. For parameters not reported in Wang's study, including facility processing capacities, 3PL construction costs, 3PL transportation capacities, 3PL unit transportation costs, maximum reservation levels, and unit reservation costs, reasonable estimates were made with reference to Wang's data. These estimated values are presented in the Table 9 to facilitate reproducibility.

Table 2, on Page 17:

 

Table 9, on Page 27:

 

Comments 4. "The study presents managerial implications but does not discuss research implications. These should also be included."

Response:

We sincerely thank the reviewer for the valuable comments. We acknowledge that the original introduction lacked clarity, which may have limited the emphasis on the research implications. To address this, the introduction has been revised to explicitly highlight both the research and managerial implications of the study. In addition, a new Discussion section has been added to further elaborate on the differences between this study and existing research, thereby clarifying the study's contributions. The specific revisions to the manuscript are as follows:

In Introduction, lines 97-103, on Page 3:

This study offers several key research contributions. The research expands the body of knowledge on resilient supply chain network design by integrating disruption risks and corresponding mitigation strategies into EVB recycling models. In addition, the incorporation of a 4PL framework into EVBRND clarifies the function of logistics coordination under uncertainty. The proposed SRDBH algorithm further advances methodological development for large-scale stochastic optimization in supply chain management. Collectively, these contributions provide a solid foundation for future studies that aim to integrate resilience, sustainability, and logistics management.

In Discussion, lines 647-662, on Page 23:

This study differs from existing research on EVBRND in several significant dimensions. At the problem level, in contrast to prior studies that primarily emphasize facility location and cost minimization, this study explicitly incorporates facility disruption risks and introduces multiple resilience-oriented strategies, including facility fortification, capacity backups, multi-source allocation, and multiple transportation routes. Experimental results reveal that these strategies substantially enhance both network resilience and cost efficiency. Preventive strategies, in particular, effectively reduce URBN and TPFN, whereas reactive measures such as higher penalty parameters yield limited improvement once preventive measures are implemented. These findings indicate that integrating strategic resilience decisions with operational optimization provides significant benefits for the design of more efficient EVB recycling networks. Furthermore, at the methodological level, the study adopts a 4PL framework to coordinate multiple 3PL providers, thereby improving network flexibility and responsiveness—an aspect that has been relatively underexplored in prior literature. Finally, the proposed two-stage stochastic programming model is solved using the SRDBH algorithm, which is validated through a real-world case study to demonstrate its practical applicability.

 

Comments 5. "The paper has a very detailed findings section but lacks a proper discussion section. A discussion section is needed where the key findings are compared with results from other similar studies in different contexts."

Response:

We sincerely appreciate the reviewer's valuable suggestion. In response, we have added a new "Discussion" section at the end of the manuscript to provide a clearer comparison between the key findings of this study and previous research. This revision emphasizes both theoretical distinctions—such as problem formulation and modeling assumptions—and practical differences revealed through managerial analyses, thereby strengthening the overall contribution of the study. The specific revisions to the manuscript are presented below:

In Discussion, lines 647-662, on Page 23:

This study differs from existing research on EVBRND in several significant dimensions. At the problem level, in contrast to prior studies that primarily emphasize facility location and cost minimization, this study explicitly incorporates facility disruption risks and introduces multiple resilience-oriented strategies, including facility fortification, capacity backups, multi-source allocation, and multiple transportation routes. Experimental results reveal that these strategies substantially enhance both network resilience and cost efficiency. Preventive strategies, in particular, effectively reduce URBN and TPFN, whereas reactive measures such as higher penalty parameters yield limited improvement once preventive measures are implemented. These findings indicate that integrating strategic resilience decisions with operational optimization provides significant benefits for the design of more efficient EVB recycling networks. Furthermore, at the methodological level, the study adopts a 4PL framework to coordinate multiple 3PL providers, thereby improving network flexibility and responsiveness—an aspect that has been relatively underexplored in prior literature. Finally, the proposed two-stage stochastic programming model is solved using the SRDBH algorithm, which is validated through a real-world case study to demonstrate its practical applicability.

 

 

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The revised manuscript has resolved all my concerns. Congratulations, this version can now be accepted.

Author Response

Comments 1: "The revised manuscript has resolved all my concerns. Congratulations, this version can now be accepted."

Response:

We would like to express our genuine gratitude for your thorough review and thoughtful feedback. Your expert guidance has greatly strengthened the rigor and presentation of our paper.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript can be accepted in its current revised form. No Revision is needed.

Author Response

Comments 1. "The manuscript can be accepted in its current revised form. No Revision is needed."

Response:

We sincerely thank you for your constructive and insightful comments on our manuscript. Your valuable suggestions have been instrumental in helping us to significantly improve the quality and clarity of this work.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you very much for addressing all the comments. The responses are comprehensive and have adequately covered the points raised. However, there is a small improvement needed in the added discussion section. In this part, I could not see any specific references to previous studies, even though the authors mention “previous studies” when discussing the findings. Therefore, the discussion section should be strengthened by explicitly showing how the findings of the current study align with or contradict those of past similar studies.

Author Response

Comments 1. "Thank you very much for addressing all the comments. The responses are comprehensive and have adequately covered the points raised. However, there is a small improvement needed in the added discussion section. In this part, I could not see any specific references to previous studies, even though the authors mention “previous studies” when discussing the findings. Therefore, the discussion section should be strengthened by explicitly showing how the findings of the current study align with or contradict those of past similar studies."

Response:

We sincerely thank the reviewer for this insightful comment. In the revised manuscript, the Discussion section has been substantially improved to explicitly compare our findings with prior studies. Specifically, references to key related works have been added to clarify how this study’s results align with or differ from existing literature.

For instance, the revised version now explicitly contrasts our findings with those of Jafari et al. (2020), Wang et al. (2020), and Fan et al. (2023), which mainly focus on deterministic facility location and cost minimization, highlighting that our research incorporates disruption risks and multiple resilience-oriented strategies. Furthermore, comparison with Mahdiraji et al. (2023) and Qi et al. (2024) shows that, although these studies also explored resilience under uncertainty, our model extends their approaches by integrating preventive and operational strategies and quantifying their joint effects under budget constraints.

In addition, from the methodological perspective, references to Du et al. (2024), He et al. (2024b), Yin et al. (2025), and Vidal et al. (2024) have been incorporated to illustrate how our adoption of a 4PL-based coordination mechanism advances prior models by enhancing flexibility and recovery efficiency.

These revisions make the discussion clearer and more comprehensive in demonstrating both the theoretical alignment and advancement of our study relative to previous research. The updated Discussion section now reads as follows:

In Discussion, lines 646-672, on Page 23-24:

In contrast to existing studies on EVBRND that primarily focus on deterministic facility configuration and cost minimization Jafari et al. (2020), Wang et al. (2020), Fan et al. (2023), this study explicitly incorporates disruption risks and develops an integrated resilience-oriented framework combining facility fortification, capacity backups, multi-source allocation, and multi-route transportation. While Mahdiraji et al. (2023) and Qi et al. (2024) also emphasized the importance of resilience under uncertainty, their analyses were limited to single mitigation mechanisms or simplified network structures. The results of this study indicate that preventive strategies—specifically, facility fortification and capacity backup decisions—significantly reduce both the number of URBN and TPFN. In contrast, reactive adjustments like increasing the parameter ϑ show only marginal effects once preventive measures are in place. These findings extend prior research by showing that a combination of preventive fortification and operational flexibility is more cost-effective in enhancing network robustness than approaches dominated by reactive measures. While consistent with Mahdiraji et al. (2023) in affirming the value of redundancy and fortification, our study further quantifies their interactive effects under realistic budget constraints.

From a methodological perspective, in contrast to traditional EVBRND models that rely on fixed 3PL structures Du et al. (2024), He et al. (2024), this study adopts a 4PL-based coordination framework to enhance network adaptability. Consistent with Yin et al. (2025) and Vidal et al. (2024), who demonstrated that 4PL-led collaboration improves operational efficiency, our findings further confirm that multi-3PL coordination effectively strengthens recovery performance, especially under limited fortification capacity. The proposed two-stage stochastic programming model, solved via the SRDBH algorithm, also demonstrates computational efficiency in large-scale uncertain environments, supporting practical network reconfiguration under disruption. Overall, this study complements existing research by integrating 4PL coordination with resilience strategies, empirically showing that preventive investment, rather than penalty escalation, leads to more sustainable and economically viable outcomes for EVB recycling systems.

Author Response File: Author Response.pdf