Reverse Logistics Network Planning for Electric Vehicle Power Batteries

1. Introduction and Research Context

The global transportation sector is undergoing a fundamental transformation driven by the urgent need to address climate change, resource scarcity, and environmental pollution. Electric vehicles (EVs) have emerged as a pivotal solution in this transition, offering the potential to significantly reduce greenhouse gas emissions compared with conventional internal combustion engine vehicles. Research indicates that throughout their full life cycle, EVs can achieve a 30% to 50% reduction in carbon emissions relative to traditional automobiles, making them a cornerstone of sustainable mobility strategies worldwide. In China, a combination of fiscal incentives, regulatory frameworks, and infrastructure development has accelerated the adoption of EVs, positioning the country as a global leader in this domain. By December 2024, the national fleet of new energy vehicles had reached approximately 31.4 million units, accounting for 8.9% of the total vehicle population. This remarkable expansion has also brought with it a critical challenge: the management of retired power batteries. Typically, EV power batteries have a lifespan of 5 to 8 years. Once their capacity degrades below 80%, they are no longer considered suitable for providing adequate driving range. This situation is precipitating a massive wave of battery retirements, with projections suggesting that the volume will reach approximately 820,000 tonnes by 2025, starting in the current years. These batteries contain hazardous materials, including heavy metals such as nickel, lead, and cobalt, as well as corrosive electrolytes. If not processed through proper channels, they pose severe threats to soil, water sources, and human health, as evidenced by incidents of illegal dumping in rural areas causing substantial ecological and agricultural damage. At the same time, these retired batteries constitute an “urban mine” — a valuable repository of metals that offers substantial economic opportunities. The challenge ahead lies in creating reverse logistics networks that are both economically viable and ecologically responsible. This study addresses such an imperative by proposing, in the context of actual operational uncertainties, two mathematical models designed to optimize the reverse logistics network for electric car power battery recovery. The core purpose is to balance minimizing cost with minimizing carbon emissions.

2. Literature Review

My review of the literature explores the research status of power battery recycling, reverse logistics networks for batteries, and their echelon utilization. The consensus is that recycling modes and industrial development are largely driven by policy, economic feasibility, and technological advancements. However, established streams of research often overlook the multimodal optimization challenges that arise from operational uncertainty in real-world networks.

For the recycling model selection, the choice of the entity responsible for take-back is critical. Studies have compared EV manufacturers, battery producers, and third-party recyclers. The research shows that collaborative “joint recycling” alliances, where manufacturers team up with retailers or specialized recycling entities, generally outperform single-participant models in terms of cost reduction and efficiency due to synergies and shared resources.

Within the domain of reverse logistics network design, the predominant research focus is improving cost-effectiveness and facility location. While earlier research relied heavily on historical data repositories, newer studies incorporate environmental indexes, such as carbon emissions, into their objective functions, reflecting a broader set of sustainability goals. Some rigorous analyses have used fuzzy programming and stochastic models to explicitly treat the quantities of returned batteries as uncertain variables in order to increase the robustness of facility location decisions.

Regarding battery echelon utilization, studies have shown that retired EV batteries possessing above 60-70% residual capacity are well-suited for secondary applications in energy storage, low-speed vehicles, and telecom backup power. However, there are gaps when it comes to standardizing the grading of performance and matching used batteries to optimal applications. My analysis seeks to address these gaps by embedding echelon utilization rates within mathematical optimization objective functions.

The literature review overall indicates a strong focus on production-side recycling strategy. My intent is to position this study’s contribution at the practical interface of joint recycling, low-carbon policy, and multi-echelon network design, so as to contribute to the further development of reverse logistics network construction for electric car power batteries in both deterministic and uncertain environments.

3. Theoretical Framework

3.1 Reverse Logistics Network Architecture

According to the research, a reverse logistics network is generally made up of nodes and links. The core value of this network is realized through the several crucial steps of collection, transportation, inspection, sorting, and reprocessing. In a recycling network context, there are different types of network structures based on the degree of reuse. The network type that is applied for high-value and high-tech products, such as EV power batteries, requires a multi-tiered hierarchy.

For the case of power batteries, I define the nodes as collection centers, inspection centers, dismantling centers, echelon utilization markets, and materials recycling units. Figure 1 presents the fundamental layout of a reverse logistics network used for power battery recycling across its multiple levels.

3.2 Uncertainty Programming Approaches

Uncertainty can be classified as stochastic or fuzzy. The uncertainty in EV battery recycling tends to present as fuzziness due to an absence of exact historical data and the ambiguity regarding the conditions of use of retired batteries. Fuzzy variables are typically modeled with mathematical programming optimization frameworks, with triangular fuzzy numbers being a very common approach. They describe the optimistic, most likely, and pessimistic values of an uncertain parameter.

In fuzzy chance-constrained programming, if a fuzzy parameter is described by a triangular fuzzy number, e.g., \(\tilde{Q} = (Q_1, Q_2, Q_3)\) where \(Q_1 \le Q_2 \le Q_3\), and with a confidence level \(\alpha\) (where \(0 \le \alpha \le 1\)), it is translated to a crisp equivalent form. A constraint, for example, where a variable x needs to be less than a fuzzy parameter with a minimum required possibility, converts as follows:

$$pos\left\{\tilde{\mu} \ge x\right\} \ge \alpha \quad \Rightarrow \quad x \le (1-\alpha)\mu_1 + \alpha\mu_2$$
$$pos\left\{\tilde{\mu} \le x\right\} \ge \beta \quad \Rightarrow \quad x \ge \beta\mu_2 + (1-\beta)\mu_3$$

This type of transformation is crucial for rendering the formal model into a tractable format that is solvable with standard mathematical programming tools. This process supports the uncertainty in recycling quantity and quality that is so characteristic of power battery reverse logistics.

3.3 Battery Recovery Modes

Based on the identity of the leading actor, I distinguish four distinct collection models. The first is the EV manufacturer-led model, which capitalizes on the current sales network for recovery. The second is the battery manufacturer-led model, which generally lacks the broad consumer-facing collection points. Third, the third-party recycler model leverages specialized processing capability but often lacks the scale to establish wide-ranging collection channels. The fourth model, which is the joint recycling model, is the most comprehensive. It draws upon the strengths of different stakeholders. In this arrangement, EV manufacturers provide the take-back channels through dealerships, battery producers offer better echelon use cases, and specialized third-party recyclers bring efficient, compliant dismantling or material treatment capabilities. This model effectively shares the risk and reduces costs while augmenting channel coverage and leveraging each party’s respective strengths. Based on this comparative analysis, the joint recovery model presents a more sustainable, cooperative paradigm. Hence, I adopt it as the foundation for designing an efficient network that manages the flow of waste batteries across electric car supply and return loops.

3.4 Sustainability Policies and Carbon Taxation

Carbon pricing has gained prominence in global policy debates as a highly effective way to internalize the negative environmental externalities of greenhouse gas emissions. The carbon tax methodology establishes a price per unit of CO2 emitted. Within supply chain management, this is an operating cost. By including a price on carbon in the mathematical model’s objective function, it becomes possible to create a single, unified objective that weighs economic and environmental trade-offs without violating their fundamentally distinct measurement dimensions. This enables the formulation of concrete, low-carbon reverse logistics planning for electric car batteries.

4. Deterministic Model Development

4.1 Problem Statement and Network Structure

Based on the joint recovery model, the multi-echelon reverse logistics network is analyzed. First, the used power batteries are collected from the public at the collection centers. Then, they are transported to inspection centers, where a battery’s condition and residual value are assessed. In this sorting step, batteries are divided into two categories: those with residual capacity greater than 60% are routed to echelon utilization markets for second-life applications; those with less than 60% capacity are sent to dismantling centers. At the dismantling stations, valuable metals are extracted and delivered to regeneration facilities to re-enter supply chains. Any residue generated in this process is transported to waste treatment facilities.

4.2 Assumptions and Notations

Before formulating the model, I establish a clear set of baseline assumptions. The quantity of used batteries collected is assumed to be known and constant for the duration of the planning horizon. Inspection and dismantling sites have known handling capabilities. All other points in the network have no capacity constraints. Transport costs, as well as facility investment costs, are fixed and linear relative to the shipment volumes. Transportation only flows between adjacent layers of the network. Finally, the emissions arising from both transport and processing operations are included in the model as linear functions of battery mass.

Table 1. Notation for the mathematical optimization

4.3 Objective Functions and Constraints in Model 1

In the deterministic model, minimizing total economic cost and minimizing the total greenhouse gas emissions are considered as the two primary objectives. Equation (1) shows the total cost objective \(Z_1\).

$$\min Z_{1} = \sum_{k} F_k Y_k + \sum_{j} F_j Y_j + \sum_{l,k} X_{lk} D_{lk} \sigma + \sum_{k,j} X_{kj} D_{kj} \sigma + \sum_{j,g} X_{jg} D_{jg} \sigma + \sum_{l,k} X_{lk} C_k + \sum_{k,j} X_{kj} C_j + P_4 \sum_{j,g} X_{jg} + P_1 \sum_{l,k} X_{lk} – P_2 \sum_{k,h} X_{kh} – P_3 \sum_{j,w} X_{jw}$$

Here, the model accounts for the cost of transporting, inspecting, dismantling, and treating hazardous waste, the investment required for new facilities, the costs associated with taking back used batteries, and the revenue earned by selling electricity and recyclable materials in appropriate markets.

For the second goal, Eq. (2), I minimize aggregate greenhouse gas emissions \(Z_2\). Emissions stem directly from the processing or treatment of goods at each stage of the chain, plus any emissions arising from fuel combustion in vehicles during the transportation of those goods.

$$\min Z_{2} = \sum_{l,k} X_{lk} E_k + \sum_{k,j} X_{kj} E_j + N\Big( \sum_{l,k} X_{lk} D_{lk} + \sum_{k,j} X_{kj} D_{kj} + \sum_{j,g} X_{jg} D_{jg} \Big)$$

To satisfy the major real-world constraints of a closed-loop system, the physical flows must obey a series of supply and demand constraints. These force all batteries from each collection location to be transported to a site where they can be processed and constrained by the capacity limits of the processing locations. The flow balances that connect inspection and dismantling centers, and the ratio equations that allocate material to different end-of-life pathways, are as follows:

$$\sum_{k} X_{lk} = Q_l, \quad \forall l$$
$$\sum_{l} X_{lk} Y_k = \sum_{j} X_{kj} Y_j + \sum_{h} X_{kh}, \quad \forall k$$
$$\sum_{k} X_{kj} Y_j = \sum_{w} X_{jw} + \sum_{g} X_{jg}, \quad \forall j$$
$$\sum_{l} X_{lk} = \sum_{h} X_{kh} \cdot \frac{1}{\theta_1}, \quad \sum_{l} X_{lk} \cdot \theta_2 = \sum_{j} X_{kj} Y_j, \quad \forall k$$
$$\sum_{k} X_{kj} \cdot \theta_3 = \sum_{w} X_{jw}, \quad \sum_{k} X_{kj} \cdot \theta_4 = \sum_{g} X_{jg}, \quad \forall j$$
$$X_{lk}, X_{kj}, X_{jg}, X_{kh}, X_{jw} \ge 0; \quad Y_k, Y_j \in \{0,1\}; \quad \sum_j Y_j \ge 1; \quad \sum_k Y_k \ge 1$$

4.4 A Single Objective Approach to Bi-objective Optimization

Given the conflicting nature of these objectives, which have different units of measurement, the problem cannot be solved by constructing a simple weighted linear combination. To resolve this issue, I introduce a price for emitting carbon dioxide, e.g., a tax rate \(\rho\). This converts the amount of carbon released into a quantifiable monetary value, therefore it becomes an internalized cost of doing business. A single objective function is constructed as the sum of the economic cost objective and the carbon tax multiplied by the total mass of emissions:

$$\min Z = \min Z_1 + \rho (\min Z_2)$$

This framing enables the model to evaluate simultaneously the costs and the environmental impacts in a single unit of account, thereby providing a direct, quantifiable measure for sustainable, cost-effective decision making during the planning of the network.

5. Deterministic Network Case Analysis

5.1 Data and Scenario Description

To assess the practical performance of this approach, a case study was conducted in Jiangsu Province, a region with high EV market penetration. In the physical network, each of its 13 prefecture cities served as a collection center. I identified seven candidate sites for inspection centers and five potential candidate sites for dismantling centers.

Estimates for the quantity of waste batteries were generated based on a standard battery lifespan model, the electric car ownership statistics for each city, and an assumption of an 80% collection rate. This yielded predicted volumes for 2027 across the respective local networks. Table 1 below shows the projected annual waste for each collection point.

Table 2. Predicted 2027 Battery Recycling Volumes in Jiangsu Province

Table 3. Facility candidates and key parameters

I set a transportation cost of 80 CNY per tonne-km and a carbon tax rate of 40 CNY per tonne of CO2. Under the estimated recycling flowchart, it was assumed that \(\theta_1\) = 31% of batteries will be suitable for echelon use and the rest will be dismantled. Of the material to be dismantled, 75% was considered recyclable (\(\theta_3\)), while 25% was residue (\(\theta_4\)).

5.2 Solution and Sensitivity Analysis in the Deterministic Case

I solve the model using LINGO 11 software. The chosen objective function resulted in a total economic cost of CNY 185,888,000. The cost was not the only figure of merit; the carbon emissions of the network were calculated at 516,140 tons, which became an additional cost of approximately CNY 20,645,600 when converted via the carbon tax. The sum, therefore, is a total network cost of around CNY 206,533,600. The optimization determined that the cities to host inspection centers are Nanjing (K2), Wuxi (K3), Xuzhou (K5), and Yancheng (K7). For the dismantling stage, the chosen cities were Nanjing (J2), Wuxi (J3), Changzhou (J4), and Taizhou (J5). Table 4 shows the flow distribution between collection zones and the selected inspection facilities.

Table 4. Waste battery flows from selected inspection to dismantling centers

Subsequent sensitivity analysis was then performed to test key variable impacts. For unit transport costs, I altered costs by ±10% and ±20%. The results are summarized in Figure 2.

The analysis reveals a very clear relationship between increases in transport cost and the overall cost, since transportation is a major cost component. Interestingly, the total carbon emissions do not always show a strict monotonic relationship and are less sensitive to cost variations than economic factors, maintaining a somewhat consistent value across ranges. Conversely, when transport costs decrease by 20%, costs can approach zero. Further decreases could lead to profits, underlining that logistics spend is substantial and a primary target for efficiency improvements.

As a second test, I adjusted the maximum processing capacity of both the inspection and dismantling centers. When capacities are increased, the total network cost and carbon emissions decrease but only up to a certain point. The overall cost eventually stabilizes even after additional capacity increases, since the optimal facility configuration remains fixed; no further network changes occur. Conversely, a capacity reduction of 10% forces the model to open new facilities, leading to higher location costs. If capacity drops further it results in path rerouting but has a smaller effect relative to the earlier change. This suggests there is a “capacity threshold”, beyond which network changes are driven by economies of scale, whereas an undersized network incurs excessive routing and construction costs. The cost is also observed to plateau more quickly when capacities are increased, indicating a saturation point where further scale-up efforts no longer produce meaningful economic or environmental gains.

6. Fuzzy Environment Reverse Logistics Model

6.1 Rationale for Model Enhancement

In reality, the deterministic model is too restrictive in its core assumptions. The amount and quality of collected batteries are hard to predict in practice. Properly treating both of these volumes as fuzzy variables makes the network plan more representative of actual reality. Transport, cost, and facility data are considered fixed, but both supply volumes and the classification split ratios are fuzzy because they are subject to variations in consumer behavior and goods quality. Additionally, I treat the re-use share and scrap recycling yield as fuzzy values, as they are heavily dependent on the inconstant quality of the goods.

6.2 Mathematical Model

Modeling the fuzzy components requires new notation. The fuzzy quantity of waste batteries at collection center l is given by \(\tilde{Q}_l = (Q_{l1}, Q_{l2}, Q_{l3})\). Likewise, the echelon use ratio is given by \(\tilde{\theta}_1 = (\theta_{11}, \theta_{12}, \theta_{13})\), and the dismantling flow ratios by \(\tilde{\theta}_2 = (\theta_{21}, \theta_{22}, \theta_{23})\). Uncertain parameters also determine the amount to be regenerated, with the regeneration rate being \(\tilde{\theta}_3 = (\theta_{31}, \theta_{32}, \theta_{33})\) and residue rate \(\tilde{\theta}_4 = (\theta_{41}, \theta_{42}, \theta_{43})\). It is worth noting that these deterministic sets of ratios can be written in a similar way to the triangular fuzzy numbers introduced in Section 3.2. The constraints are then defined more strictly to impose the necessary flow balance and routing requirements under prescribed confidence levels (\(\xi_1, \xi_2,… \xi_5\)).

One critical issue is enforcing that the mass conservation holds in the presence of probabilistic or fuzzy flows. This is expressed in the form:

$$pos\left\{ \sum_k X_{lk} Y_k \ge \tilde{Q}_l \right\} \ge \xi_1, \quad \forall l \\
pos\left\{ \sum_l X_{lk} \tilde{\theta}_1 \ge \sum_h X_{kh} \right\} \ge \xi_2, \quad \forall k \\
pos\left\{ \sum_l X_{lk} \tilde{\theta}_2 \ge \sum_j X_{kj} Y_j \right\} \ge \xi_3, \quad \forall k \\
pos\left\{ \sum_k X_{kj} \tilde{\theta}_3 \ge \sum_w X_{jw} \right\} \ge \xi_4, \quad \forall j \\
pos\left\{ \sum_k X_{kj} \tilde{\theta}_4 \ge \sum_g X_{jg} \right\} \ge \xi_5, \quad \forall j$$

To ensure correct handling of such precedence constraints across a set of possible values, I have adopted confidence levels, which are modeled through fuzzy chance-constrained programming. When a flow or a ratio has a triangular fuzzy number, the general arithmetic properties of fuzzy sets can be put to work, especially in clear-cut equivalence transformation. In particular, the inequality constraints are rewritten into their strict deterministic forms as follows, guaranteeing that they are satisfied with a degree of certainty represented by the model’s \(\alpha\)-cut level.

$$\sum_k X_{lk}Y_k \ge (1-\xi_1)Q_{l1} + \xi_1 Q_{l2}, \quad \sum_k X_{lk}Y_k \le \xi_1 Q_{l2} + (1-\xi_1)Q_{l3}$$
$$\sum_l X_{lk} \ge (1-\xi_2)\,\Big[(1-\xi_2)\theta_{11} + \xi_2 \theta_{12}\Big] + \dots$$

Here I show the general form of crisp equivalence. This transformation is how I apply uncertainty to the parameters and convert the fuzzy statements into standard crisp inequalities, allowing me to solve the problem with commercial solvers. The resultant fully linear formulation was then implemented in LINGO.

6.3 Fuzzy Case Results

For this scenario, I used the same cost and emission parameter values as in the deterministic model, while assuming the collected volume at each city center may vary by about 10% from the mean. For example, for the specific network area L1, the fuzzy quantity was represented by the triple (19,349.6, 21,499.6, 23,649.6) tonnes. Similar 10% tolerances characterized the flow or quality ratios. Echelon usage was 0.31; the regeneration and residue rates were assigned ±10% deviations. I assumed a 0.9 confidence level for each relevant chance constraint.

Under those circumstances, the model suggested the best locations for inspection centers are Suzhou (K1), Nanjing (K2), Wuxi (K3), and Zhenjiang (K6). The optimal sites for the dismantling centers are Suzhou (J1), Nanjing (J2), and Wuxi (J3). Table 5 shows the final flow distribution matrix for the model from its collection centers to its testing or inspection centers.

Table 5. Flow from collection centers to inspection centers under uncertainty

The total economic cost increased to CNY 213,849,600 in this scenario. The carbon emissions were calculated to be 515,462.5 tons. Incorporating the carbon tax into the single objective cost, the total network cost under the given uncertainty level is CNY 234,468,100. This increased monetary cost makes sense because the model must be robust enough to handle a potentially greater influx of waste batteries. The results show that within the fuzzy model, selecting the right locations helps mitigate the impact of potential operational changes, and despite these uncertainties, the network can still be planned to control emissions, achieving a very similar total emission footprint to that of the deterministic model.

6.4 Comparative Sensitivity Analysis in Fuzzy Model

I applied the same sensitivity analyses to the fuzzy model as I used for the deterministic one. The outcomes confirm and extend the earlier conclusions. Unit transport cost changes were again directly aligned with network cost changes. However, at high fuel prices, other factors come into play. It becomes increasingly apparent that managing total travelled distance is important for controlling costs. Yet, in both scenario families, transport-related emissions had a limited impact on overall cost relative to processing emissions, given the strong weight of the fixed cost factor in the solution.

Furthermore, I evaluated a broader set of analyses on maximum handling capability. In the fuzzy case, the network exhibits high sensitivity to capacity changes. A 10% decrease in processing ability forces the number and configuration of established facilities to change; this leads to an obvious cost increase. If there is a persistent, significant reduction in capacity of more than 20%, there will be so much waste that the network becomes incapable of processing it, eventually culminating in failure. In contrast, a 10% enlargement yields immediate benefits because this allows for a more economical selection of sites. Increasing the size further produces only marginal re-optimizations and does not yield substantive savings, suggesting that the model has hit an optimal efficiency threshold.

One distinguishing aspect of the uncertain environment model is how the confidence level changes operations. Adjusting confidence levels over a range, while keeping the rest constant (e.g., 0.75, 0.80, 0.85, and 0.95), gave valuable insights into the risk-cost trade-off. The analysis is presented in Figure 5. A higher confidence level requires the network to be designed for larger incoming volumes of batteries. This in turn raises overall logistics costs and carbon emissions because of the increased amount of processing, transportation, and handling activity required. Thus, for an electric car, selecting a low confidence level can minimize network costs but will make it impossible to process all the batteries if adverse scenarios occur; selecting a high confidence level protects against uncertainty but with higher costs. This points to a potential trade-off at the design stage, where operators need to weigh the expenses of overcapacity against the risks of being unable to process end-of-life batteries when they arise.

7. Conclusions and Future Directions

This study develops a comprehensive optimization framework for the design of an EV power battery reverse logistics network. The framework itself leverages a joint recovery strategy and proposes mathematical models that are specifically tailored to deterministic environments and to environments characterized by uncertainty. Through an actual case study in Jiangsu Province and detailed sensitivity analyses, I have reached several conclusions.

1. Model Feasibility: The dual-objective model is effective in the context of the EV battery take-back market. The direct inclusion of a carbon tax rate offers an efficient way to consolidate economic and environmental goals. This provides a quantitative decision support tool for managers. The deterministic model’s result is an optimal set of echelon and dismantling center locations, leading to a minimized cost and carbon footprint. The fuzzy model extends this to handle the unavoidable uncertainty in supply and battery quality, resulting in robust performance.
2. Drivers of Network Costs: Across the different models, I find that transportation costs constitute a very significant portion of total life cycle cost. There is a direct, roughly linear, relationship between unit transport cost and network total costs. At the same time, emissions remain relatively stable. This suggests route optimization or the selection of more optimal sites for facilities to shorten travel distances is a more useful carbon mitigation strategy than reducing the service frequency of transport, at least given the existing vehicle stock for the electric car end-of-life market.
3. Facility Capacities: The treatment capacity limits of inspection and dismantling sites produce a substantial impact on network outcomes. If the existing facilities have processing capacities at or near their upper bounds, the network might become congested. If maximum capacities decrease further, the network can become unviable. Conversely, adding capacity beyond a certain point provides no immediate benefit. A policy recommendation is to manage processing capacity upgrades carefully to match the path of anticipated market scaling. It is important to avoid under-sizing and over-sizing investments.
4. Uncertainty and Confidence Level: The use of fuzzy triangular sets in my model is aligned with the actual unpredictable realities of take-back. The crisp equivalents yielded scenarios under the uncertainty case that projected network costs greater than the cost from the deterministic analysis. This is expected because higher use of robustness increases throughput. The results indicate that confidence level should be tuned carefully since higher levels directly push up both costs and emissions. This demonstrates the inherent trade-off that circular economy models must solve.

Theoretical contributions are made by directly modeling fuzzy recovery rates in addition to fuzzy quantities, an area that the current literature largely overlooks. Operationally, it translates sustainability legislation into practice by explicitly using a carbon tax parameter to quantify social cost within facility location decisions. Results from the sensitivity analysis provide planners with insight into which elements of the system have the most leverage for cost savings and carbon mitigation.

The study also opens several future research pathways:

1. Model Expansion: The current scope can be widened to include multimodality, emergency tie-ups with freight partners, or collection time-windows, further complicating and improving the framework.
2. Multi-product Streams: Modeling different battery chemistries and sizes would represent commercial reality more truly. Echelon use is not yet standardized, and multiple battery types require differentiated recovery routes that are more complex to model.
3. Policy Integration: There is room to fold in other sustainability instruments—for instance, subsidies for collection in rural regions and the recently enacted Battery Regulations of the European Union—into this modeling. The extension of deposit-return systems for batteries could also be examined for its effect on recovery rates and infrastructure use. In addition, grid planning for reverse logistics can borrow the “city distribution center + county transfer station” mode that is standard in express delivery to lower costs in remote locations.
4. Solution Algorithm: While LINGO is adequate for this scale, using this MILP formulation as a basis for designing heuristics would be valuable for solving large-scale logistics networks with numerous variables and constraints. Metaheuristics like genetic and ant colony algorithms offer a worthwhile direction for improving computational efficiency and solution ability.