In CLSCs, accurately forecasting product return rates is fundamental to designing and operating an efficient reverse flow, because return volumes, timing, and condition directly shape collection capacity, remanufacturing plans, inventory policies, and transportation decisions. Early work in this area primarily relied on statistical forecasting to characterize return behavior and reduce uncertainty. In this stream, Carrasco-Gallego et al. [6], working in the Liquefied Petroleum Gas (LPG) context, introduced dynamic regression models to forecast the return of reusable cylinders in Spain by explicitly linking sales patterns to subsequent return flows, thereby translating market demand signals into reverse logistics expectations. Building on the need to represent uncertainty and heterogeneity in return processes better, Krapp et al. [7] adopted Bayesian estimation for forecasting product returns in CLSCs, showing that probabilistic inference can offer higher flexibility than conventional approaches and improve decisions—particularly in inventory management— where planners benefit from uncertainty-aware predictions; their evidence also suggested practical value for recycling and return-intensive industries in reducing operational variability.

As researchers began to recognize that return forecasting often requires going beyond a single dimension, attention shifted toward integrated predictions that jointly capture multiple return attributes. From this perspective, Liang et al. [8] proposed a method that simultaneously forecasts the quantity, quality, and timing of returns, focusing on electric vehicle battery returns and using information on sales, usage patterns, customer behavior, and product lifetime to improve predictive performance; importantly, they validated their approach via Monte Carlo simulation, reinforcing its applicability under realistic conditions. In parallel, other studies examined the planning implications of returns, particularly in remanufacturing systems where production decisions depend heavily on the availability of returned cores. Matsumoto and Komatsu [9] addressed this challenge by forecasting demand for returned products in remanufacturing, deliberately moving away from strong assumptions about new-product sales timing and fixed lifetimes; instead, they employed time-series techniques—Holt–Winters and Autoregressive Integrated Moving Average (ARIMA)—to learn trends and seasonality directly from historical signals, demonstrating improved forecasts using a long-horizon dataset of 12 years of sales across 160 types of remanufactured alternators and starters.

To better capture the process structure underlying returns and recovery, another line of research modeled remanufacturing operations as systems whose stochastic behavior can be characterized analytically. In this direction, Zhou et al. [10] developed a model that jointly predicts return amount, timing, and probability, while also estimating recoverable parts/materials and waste generation; they converted the operational remanufacturing process into a stochastic network and used the Graphical Evaluation and Review Technique (GERT) together with Mason’s rule to derive an equivalent transfer function, aiming to increase forecast fidelity by embedding process logic into the prediction mechanism. Closely related, yet focused on the dependence between sales/demand signals and delayed returns, Geda and Kwong [11] tackled forecasting used-product returns to meet remanufacturing demand by employing Distributed Lag Models (DLMs) with a normal–negative binomial delay function, and they estimated delay parameters using Bayesian Monte Carlo simulation; their evaluation using Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) indicated strong predictive capability and apparent usefulness for closed-loop planning.

While many studies addressed returns at the product level, others emphasized sector-specific return streams and the macro drivers behind them. For instance, Pereira et al. [12] examined the closed-loop tire supply chain by modeling the relationship between tires introduced into the market and tires returned for recycling, using a transfer function approach and studying its application in Brazil, where aftermarket tire volumes and new vehicle counts served as key inputs, and collected tires were treated as the output. Alongside forecasting models, inventory-focused research explored how return predictions should be operationalized into policies. Chou et al. [13] investigated periodic-review inventory models over a finite horizon with two remanufacturable part types—buyback returns and ordinary parts—treating buyback returns as a function of past demand and sales; they derived an optimal inventory policy when returns are forecast from past demand and then introduced a practical, structured policy for the case where returns are forecast from past sales, evaluating performance to ensure operational feasibility.

As methodological sophistication increased, researchers also revisited how return-forecasting parameters should be estimated—particularly in delay-based models where complexity can challenge standard estimators. Geda and Kwong [14] extended their earlier work by improving forecasts of the quantity and timing of used-product returns within the DLM framework, proposing a Bayesian inference approach coupled with Monte Carlo simulation to estimate delay-function parameters more efficiently; crucially, they showed that this method can be more robust than Maximum Likelihood Estimation (MLE) when the delay structure is complex, and their real case study reported improvements in MAPE and error variance. More recently, return forecasting has been investigated in domains where intermittency, legal constraints, and high uncertainty complicate planning. Turki et al. [15], focusing on healthcare CLSCs, addressed forecasting the supply capacity of recovered spare parts extracted from returned systems and proposed a dynamic, monthly updated forecasting procedure that combines statistical models—TSB-Croston, a 12-month moving average, ARIMA, and Seasonal ARIMA (SARIMA)—with a business-knowledge-based model; using over 1,400 intermittent time series, they compared performance against standalone methods using MAPE, MAE, Mean Squared Error (MSE), and Root Mean Squared Error (RMSE), highlighting the importance of hybrid, continuously updated forecasting in practice.

Alongside these statistical and process-based approaches, ML has increasingly been adopted to capture nonlinearities and complex interactions in return behavior, especially when rich feature data are available. Within this line, ADIGÜZEL TÜYLÜ and Eroğlu [16] studied the prediction of product return rates in reverse logistics for the textile industry, demonstrating that ML models can accurately infer return likelihood from product attributes and customer preferences, with practical implications for reducing unnecessary production and transportation costs while improving planning. In the automotive accessories context, Cui et al. [5] forecasted product return volumes using real industrial data and compared multiple ML approaches— Least Absolute Shrinkage and Selection Operator (LASSO), Elastic Net, Smoothly Clipped Absolute Deviation (SCAD), Random Forest (RF), and Gradient Boosting—finding that LASSO performed best due to its ability to select essential interactions and its implementation simplicity. At the same time, overall results supported the operational and financial value of accurate return forecasts. For settings where return behavior is driven by multiple interacting factors and fast-changing customer preferences, Tüylü and Eruglo [17] employed ensemble learning in the apparel industry’s reverse supply chain, using Stacking and Vote (Voting) to improve prediction accuracy beyond traditional time-series methods; tested on data from an international apparel company, their approach supported better control of production, distribution, warehousing, and cost in reverse logistics. Finally, with the rise of deep learning, Gao [18] explored optimization strategies for CLSC management by developing a forecasting model based on a Multi-head Attention Gated Recurrent Unit (GRU) architecture for time-series supply chain data, and then using Genetic Algorithms (GA) and Simulated Annealing (SA) to optimize decisions; the proposed hybrid pipeline illustrates the direction toward combining deep predictive models with metaheuristic optimization to improve sustainability and efficiency in industrial contexts.

Taken together, this body of work shows a steady progression from classical statistical forecasting toward richer machine-learning and hybrid paradigms—ranging from Bayesian estimation and time-series methods such as Holt–Winters and ARIMA, to stochastic-network modeling via GERT and Mason’s rule, and DLM-based delay modeling supported by Bayesian Monte Carlo inference. However, despite these advances, much of the literature still focuses on limited-return aspects (often quantity or timing) or treats forecasting as a standalone task. At the same time, the explicit, operationally linked integration of forecasting outputs into closed-loop network design and optimization decisions—such as inventory control and remanufacturing capacity planning—remains comparatively underdeveloped.

Alongside forecasting studies, a significant limitation in the CLSC literature has been that predictive results were often not translated into prescriptive network and policy decisions, even though the real value of forecasting emerges only when it informs choices such as inventory control, disposition planning, and reverse-flow configuration. Early decision-oriented work began to operationalize return forecasts within policy design: Chou et al. [13] investigated periodic-review inventory models for remanufacturable parts and embedded return forecasts—modeled as functions of past demand and sales—into the structure of optimal and implementable inventory policies. More recently, research has increasingly emphasized the need to integrate data-driven insights into broader sustainability and planning decisions. Ashtab and Tosarkani [19] linked predictive/behavioral drivers to CLSC decision-making by analyzing how brand-related information affects consumer recycling awareness and return behavior and then incorporating these insights into a closed-loop optimization setting, thereby illustrating how predictive signals can be converted into design-relevant inputs.

A key challenge in return-intensive retail systems is that product returns are often sales-dependent and delayed across multiple periods, so inventory decisions based only on “net demand” may ignore when and from which past sales returns will arrive. Addressing this gap, Gökbayrak et al. [20] developed a finite-horizon inventory model in which stochastic returns arrive from multiple previous sales periods with time-varying return probabilities, and the policy explicitly tracks a return-potential state alongside inventory. They formulated the ordering problem as a dynamic program with standard operational costs and constraints. They proposed an approximate dynamic programming solution to handle the large state space induced by the multi-period return window.

At the process-integration level, Cortes et al. [21] addressed the fragmentation of AI applications in reverse logistics by framing the reverse logistics process around three macro-stages—planning, execution, and control—and mapping AI tools to the key decision points across these stages, which clarified how predictive and decision-support methods should be positioned within activities such as collection and transport, inspection and sorting, disposition, and performance monitoring. Complementing this process lens with an explicit predictive–prescriptive pipeline, Ibrahim and Abdul-kader [22] developed an integrated framework for sustainable cellphone return management in which return-rate prediction was connected to downstream disposition planning through condition-uncertainty modeling and decision-oriented categorization of returned items. Overall, the progression of this stream shows a clear shift from using forecasts in isolated settings toward structuring and integrating return-related predictions into coherent CLSC decision models, particularly in the most recent work.

Existing research on CLSCs has generally advanced along two streams that have remained only loosely connected in terms of data, modeling assumptions, and decision interfaces. In the first stream, return-forecasting studies have focused on improving predictive accuracy for return quantity, timing, and, sometimes, quality/condition by leveraging statistical regression, time-series approaches, Bayesian inference, and, more recently, machine-learning and deep-learning methods. However, these studies have often been formulated as self-contained forecasting exercises: they typically report error metrics and predictive improvements, but stop short of specifying how the forecasted return rates should be embedded into the subsequent decision layers of a closed-loop system. In practice, this means that forecasts are frequently produced at an aggregate level (e.g., product category, period, or market region) or treated as descriptive outputs, without an explicit mapping from predicted returns to the concrete decision variables that govern reverse logistics, such as facility utilization, collection and inspection capacity, disposition volumes, and reverse-flow routing.

In the second stream, network design and prescriptive optimization models have been widely used to determine facility locations, allocation rules, and forward/reverse flows in pursuit of economic and sustainability objectives. Yet these models have often represented product returns through simplified constructs—such as fixed return ratios, scenario assumptions, stationary distributions, or deterministic averages—chosen mainly for tractability rather than fidelity to customer behavior. Even when uncertainty is considered, it is commonly introduced through generic uncertainty sets or high-level scenarios that do not originate from observed, customer-level return mechanisms. As a result, the return process is frequently exogenous to the model: the reverse flows are “assumed” rather than generated from behavioral or transactional evidence, and they do not respond endogenously to the same signals that drive forward sales. This disconnect is non-trivial because returns in many industries are delayed, sales-dependent, and heterogeneous across customers, products, and sales channels; ignoring these properties can distort strategic decisions by misestimating how much material will arrive, when, and in what condition.

To address this structural disconnect, the present work introduces an integrated forecasting–optimization framework in which a learning-based return model is positioned as a decision-relevant input rather than a descriptive add-on. Specifically, a supervised machine-learning module is developed to estimate customer/order-level return rates from historical transactional data (by benchmarking models such as Ridge Regression (RR), Support Vector Regression (SVR), and RF). The resulting predicted return rate is then embedded as a parameter within a multi-period, multi-echelon mathematical programming model for an automotive spare-parts CLSC. In this formulation, the predicted returns directly govern reverse-flow generation and, consequently, influence facility activation decisions and forward/reverse shipment plans across suppliers, plants, distribution centers, customer zones, and recovery facilities (collection/inspection, repair, recycling, and disposal). The optimization layer is structured as a sustainability-oriented multi-objective model—cost, environmental impact, and social employment—and is operationalized via Weighted Goal Programming (WGP) to obtain a single implementable plan consistent with decision-maker priorities, thereby ensuring that the learning output is used in the precise place where strategic network decisions are made.

This section introduces the ML models used to predict product return rates. Three models are examined, namely SVR, RF, and RR. These models are selected due to their strong capabilities in analyzing complex data patterns and providing accurate predictions, making them well-suited for modeling product return behavior. In the following subsections, the structure, key characteristics, and underlying mathematical foundations of each model are briefly described.

The symbols used for mathematical modeling of the problem are given in Table 1.

Cγt γ Capacity of facility γϵ{s, p, d, i, m, l, k} in period t.

FJγ Number of fixed jobs created by establishing facility γϵ{s, p, d, i, m, l, k}.

VJγ Number of variable jobs created by establishing facility γϵ{s, p, d, i, m, l, k}.

FCγ Fixed cost of establishing facility γϵ{s, p, d, i, m, l, k}.

TCsp Transportation cost per unit from suppliers to the plant p.

TCpd Transportation cost per unit from plant p to distribution center d.

TCdc Transportation cost per unit from distribution center d to customer c.

TCci Transportation cost per unit from customer c to the collection and inspection center i.

TCil Transportation cost per unit from the collection and inspection center i to the recycling center l.

TCim Transportation cost per unit from the collection and inspection center i to the disposal center m.

TCik Transportation cost per unit from the collection and inspection center i to the repair center k.

TCls Transportation cost per unit from the recycling center l to the supplier s.

TCkd Transportation cost per unit from repair center k to distribution center d.

EISsp Environmental impact per unit transported from suppliers to the plant p.

EISpd Environmental impact per unit transported from plant p to distribution center d.

EISdc Environmental impact per unit transported from the distribution center d to customer c.

EISci Environmental impact per unit transported from customer c to the collection and inspection center i.

EISil Environmental impact per unit transported from the collection and inspection center i to the recycling center l.

EISim Environmental impact per unit transported from the collection and inspection center i to the disposal center m.

EISik Environmental impact per unit transported from the collection and inspection center i to the repair center k.

EISls Environmental impact per unit transported from the recycling center l to suppliers.

EISkd Environmental impact per unit transported from repair center k to distribution center d.

EIPp Environmental impact of product manufacturing at plant p.

EIDm Environmental impact of product disposal at the disposal center m.

MCp t Production cost at plant p in period t.

DCm t Disposal cost at the disposal center, m, in period t.

RClt Recycling cost at the recycling center l in period t.

BCk t Repair cost at repair center k in period t.

DEc t Customer demand c in period t.

ρc Product return rate of customer c, predicted by the ML model.

Variables Oγt γ Binary variable equal to 1 if facility γϵ{s, p, d, i, m, l, k} is used in period t, and zero otherwise.

QSsp t Quantity shipped from suppliers to plant p in period t.

QSpd t Quantity shipped from plant p to distribution center d in period t.

QSdc t Quantity shipped from distribution center d to customer c in period t.

QSci t Quantity shipped from customer c to collection and inspection center i in period t.

QSil t Quantity shipped from collection and inspection center i to recycling center l in period t.

QSim t Quantity shipped from collection and inspection center i to disposal center m in period t. QSik t Quantity shipped from collection and inspection center i to repair center k in period t.

QSls t Quantity shipped from recycling center l to supplier s in period t.

QSkd t Quantity shipped from repair center k to distribution center d in period t.

The following is a mathematical programming model for the supply chain network.

Min OC = ∑p ∑t FCpOPp t + ∑d ∑t FCdODt d + ∑i ∑t FCiOIit + ∑m ∑t FCmOMm t + ∑l ∑t FClOLtl + ∑k ∑t FCkOKt k + ∑p ∑d ∑t MCp t QSpd t + ∑i ∑l ∑t RCltQSil t + ∑k ∑i ∑t BCk t QSik t + ∑m ∑i ∑t DCm t QSim t + ∑d ∑p ∑t TCpdQSpd t

+ ∑d ∑c ∑t TCdcQSdc t + ∑c ∑i ∑t TCciQSci t + ∑i ∑m ∑t TCimQSim t (18)

+ ∑i ∑l ∑t TCilQSil t + ∑i ∑k ∑t TCikQSik t + ∑s ∑d ∑t TCkdQSkd t

+ ∑ ∑ ∑ TCspQSsp t ,

s p t

Min EI = ∑p ∑d ∑t EIPpQSpd t + ∑i ∑m ∑t EIDmQSim t + ∑s ∑p ∑t EISspQSsp t (19)

+ ∑p ∑d ∑t EISpdQSpd t + + ∑d ∑c ∑t EISdcQSdc t + ∑c ∑i ∑t EISciQSci t + ∑i ∑m ∑t EISimQSim t + ∑i ∑l ∑t EISilQSil t + ∑i ∑k ∑t EISikQSik t + ∑ ∑ ∑ EISlsQSls t + ∑ ∑ ∑ EISkdQSkd t ,

l s t k d t

MAX SI = ∑p ∑t FJpOPp t + ∑d ∑t FJdODt d + ∑i ∑t FJiOIit + ∑m ∑t FJmOMm t (20)

+ ∑l ∑t FJlOLtl + ∑k ∑t FJkOKt k + ∑p ∑d ∑t VJpQSpd t /CPp t + ∑d ∑c ∑t VJdQSdc t /CDt d + ∑c ∑i ∑t VJiQSci t /Cit i + ∑i ∑m ∑t VJmQSim t /CMm t + ∑i ∑l ∑t VJlQSil t /CLtl VJkQSik t + ∑ ∑ ∑ t .

CKk

i k t

s.t.

∑ QSsp t ≤ OSs tCSs t, for all s, t, (21)

∑ QSt ≤ OPtCPt, for all p, t, (22)

pd p p ∑ QSt + QSt ≤ ODt CDt , for all d, t, (23)

pd kd d d

∑ QSt ≤ OItCIt, for all i, t, (24)

ci i i

∑ QSt ≤ OMt CMt , for all m, t, (25)

im m m

∑ QSt ≤ OLtCLt, for all l, t, (26)

ls l l

∑ QSt = ∑ QSt , for all p, t, (27)

sp pd

∑ QSt + ∑ QSt = ∑ QSt , for all d, t, (28)

kd pd dc k p c

∑ QSt = ∑ QSt + ∑ QSt + ∑ QSt , for all i, t, (29)

ci im il ik c m l k

∑ QSt = ∑ QSt RY , for all i, t, (30)

il ci t

∑ QSt = ∑ QSt , for all l, t, (31)

il ls

∑ QSt = ∑ QSt RV , for all i, t, (32)

ik ci t

∑ QSt = ∑ QSt , for all k, t, (33)

ik kd

∑ QSt = ∑ QSt RD , for all i, t, (34)

im ci t

∑ QSt = DEt, for all c, t, (35)

dc c

∑ QSt = DEt ∗ ρ , for all c, t, (36)

ci c c

∑ OSt ≤ S, for all t, (37)

∑ OPt ≤ P, for all t, (38)

∑ OIt ≤ I, for all t, (39)

∑ ODt ≤ D, for all t, (40)

∑ OLt ≤ L, for all t, (41)

∑ OMt ≤ M, for all t, (42)

∑ OKt ≤ K, for all t, (43)

QSsp t , QSpd t , QSdc t , QSci t , QSim t , QSil t , QSik t , QSls t , QSkd t ≥ 0, for all i, s, k, l, m, p, t, c, d, (44) OSs t, OPp t, ODt d, OIit, OMm t , OLtl, OKt k ∈ {0,1}, for all i, s, k, l, m, p, t, c, d. (45) The first objective function computes the total cost of the CLSC network. It includes three major components: 1) fixed establishment/activation costs for the different facility types considered in the network, 2) operating costs associated with production, recycling, repair, and disposal processes, and 3) transportation costs incurred across all forward and reverse links between the network echelons. The second objective function captures the environmental impacts generated by closed-loop operations. In this function, the first two terms reflect the environmental burdens of manufacturing at plants and disposing of returned items at disposal centers, respectively. In contrast, the remaining terms quantify the transportation-related environmental impacts arising from flows between facilities. The third objective function represents the social dimension of sustainability. Social impact is measured through employment creation by considering 1) fixed jobs generated by establishing facilities and 2) variable jobs induced by operational throughput. In particular, the seventh to twelfth terms correspond to variable employment created by operational activities at the facilities; therefore, this objective seeks to maximize social benefits.

The mathematical program is given in Eqs. (18)-(45). Eq. (18) minimizes total cost, Eq. (19) minimizes total environmental impact, and Eq. (20) maximizes social impact (employment). Eqs. (21)-(26) enforce capacity limits for the corresponding facilities in each period, including output capacities for suppliers, plants, and recycling centers, and input capacities for distribution, collection/inspection, and disposal centers. Eqs. (27)- (34) impose flow-balance relationships, ensuring conservation of flow at each node: manufacturing plants, distribution centers, and collection/inspection centers (27)-(29); recycling centers Eqs. (30)-(31); repair centers Eqs. (32)-(33); and disposal centers Eq. (34). Eq. (35) guarantees full demand satisfaction for each customer and period. Eq. (36) defines the collected return quantity as a function of demand and the predicted return rate. Eqs. (37)-(43) limit the allowable number of facilities that can be opened/operated for each facility type. Finally, Eqs. (44)-(45) specify the domains of decision variables: shipment quantities are non-negative continuous variables, and facility activation variables are binary, ensuring that the model remains consistent with practical operating conditions.

Since the proposed CLSC network design model is multi-objective, an explicit preference-articulation mechanism is required to obtain implementable solutions and to manage the inherent trade-offs among economic, environmental, and social performance. In reverse logistics and CLSC settings, these trade-offs are particularly pronounced because decisions such as facility activation, capacity allocation, and forward and reverse flow routing simultaneously influence total cost, emissions generated by processing and transportation, and employment creation across network echelons. Accordingly, a solution approach is needed that can incorporate decision-maker priorities transparently and operationally while producing a single plan suitable for implementation. To address this requirement, we adopt the WGP approach. WGP enables decision makers to specify aspiration (target) levels for each objective function in advance and then derive a balanced solution by minimizing weighted deviations from these targets. For minimization-type objectives (e.g., total cost and environmental impact), the goal constraints are formulated so that the deviation variables capture exceedances above the aspiration level. In contrast, for maximization-type objectives (for example, social impact measured through employment), the deviation variables represent shortfalls from the aspiration level (and, if necessary, exceedances). This formulation preserves the original direction of each objective while providing a coherent mechanism to reconcile conflicting sustainability goals within a single, implementable CLSC network design.

Step 1 (solving individual objective functions). Initially, the model is solved separately for each objective function as formulated in Eq. (46):

minfi(x), s. t. , i = 1,2,3, … , n. (46)

This step provides the optimal values of each objective function when considered in isolation. These individually optimized solutions constitute the components of the ideal objective vector and are commonly used as reference points for defining aspiration levels (target values) in goal programming models [23, 24]. Accordingly, the obtained optimal values were adopted as the target values. in the present study, allowing decision-makers to evaluate trade-offs among conflicting objectives based on these reference benchmarks. Step 2 (defining the WGP model). The aspiration levels are set based on the reference values obtained in Step 1 and can be adjusted to reflect decision-maker preferences and policy priorities. Once target values for each objective function are established, the goal programming model is formulated as follows:

n p p

min[∑ (wi−d− i + wi+d+ i ) ] . (47)

ki

Subject to:

Ax ≤ b, (48) fi(x) + d− i − d+ i = gi , for all i ∈ {1,2,3, . . , n}, (49) d− i , d+ i , x ≥ 0, (50)

where fi(x) represents the i-th objective function. does the decision-maker set the target value for the i-th objective? di − and d+ i are negative and positive deviations, representing underachievement and overachievement of the goal, respectively. wi− and wi+ are assigned to the negative and positive deviations, reflecting the relative importance of minimizing these deviations. ki = fi∗ − fi− is the normalization constant, with fi∗ and fi− being the positive and negative ideal points. p determines the aggregation type. In line with prior goal programming formulations that adopt the P = 1 achievement function, we set p = 1 to obtain a linear weighted deviation measure [25, 26].

In this study, six numerical features extracted from customer historical records and order information are used to predict the product return rate at the time of order placement. These features include: the number of the customer’s previous orders, historical return rate, average value of past orders, current order value, percentage discount applied to the order, and the duration of the customer relationship (measured in months). The dataset comprises 845 order records, of which 80% are used for model training and the remaining 20% for model evaluation.

To identify the most effective ML approach, three models—SVR, RF, and RR—are examined, and their predictive performances are compared using four evaluation metrics: MSE, MAE, RMSE, and the coefficient of determination (R²). The comparative results are presented in Fig. 3. Model training and evaluation are conducted in Python using the scikit-learn library.

According to the figure, the RF model outperforms both SVR and RR, with lower MAE and RMSE and a higher R². These performance indicators demonstrate that RF not only provides greater predictive accuracy but also explains a larger proportion of the data's variance. Therefore, it can be concluded that RF is a more suitable modeling approach for the problem under investigation.

In this study, a CLSC redesign model is implemented and solved for a company operating in Iran's automotive spare parts industry, with a particular focus on brake pads. The company previously operated a logistics network comprising suppliers, manufacturing plants, distribution centers, customers, and recycling, repair, and disposal facilities; however, due to inefficiencies in the existing structure, a network redesign was deemed necessary. The proposed model is solved over six monthly planning periods.

The solution to the mathematical model is obtained by incorporating predicted product return rates from the RF algorithm. The multi-objective mathematical programming model simultaneously addresses three primary objectives: minimizing total operational costs, minimizing environmental impacts, and maximizing social benefits through job creation. To solve the multi-objective formulation, a WGP approach is employed. The model is implemented in the Pyomo optimization framework using Python and solved with the CPLEX solver.

All computational experiments are conducted on a computer system equipped with a 12th-generation Intel Core i7 processor, 32 GB of RAM, and Windows 11. Given the moderate network size and the reasonable number of facilities, the model reaches the optimal solution within an acceptable computational time. The results of solving the model indicate that the product return rate directly affects the location of collection centers, with regions with higher return rates requiring more facilities. Fig. 4 illustrates the geographical distribution of the selected facilities in Iran for the first planning period, clearly highlighting the critical role of customer return data in the optimal design of the CLSC network.

In this analysis, to validate the proposed approach for CLSC design, product return rates are predicted using three ML methods—SVR, RF, and RR—and subsequently incorporated as input into the mathematical model. A comparison of the results across the four objective functions indicates that the RF model achieves the best overall performance, yielding an operational cost of 1,456,785, an environmental impact value of 450,123, a social index of 1,452, and a weighted goal objective function value of 842,351.

In contrast, the SVR model exhibits inferior performance, with an operational cost of 1,758,635 and an environmental impact of 678,963. These quantitative differences demonstrate that selecting an appropriate forecasting model can lead to substantial improvements in network-level decision-making. Therefore, this evaluation not only confirms the superior accuracy and effectiveness of the RF model in predicting product return rates but also implicitly validates the robustness, coherence, and generalizability of the proposed integrated framework. The comparative results of the forecasting methods and their impact on solving the mathematical model are presented in Fig. 5.

To examine the model's responsiveness to variations in key parameters, a sensitivity analysis is conducted with respect to the product return rate and the transportation cost from customers to collection centers. The left-hand diagram in Fig. 6 shows that as the product return rate increases, both the economic and environmental objective functions exhibit an increasing trend due to the higher volume of reverse flows. In contrast, the social objective function increases significantly due to greater employment generated by collection, repair, and recycling centers. Nevertheless, the weighted goal objective function indicates that when the weight assigned to the social objective is lower than that of the economic and environmental objectives, the substantial growth in social benefits is insufficient to offset the associated economic and environmental losses. Consequently, the overall value of the weighted goal function increases.

In the right-hand diagram of Fig. 6, an increase in the transportation cost from customers to collection centers leads to a rise in the economic objective value. However, its impact on the environmental objective is negative, as the network tends to reduce the number of transportation routes, resulting in a relative decrease in environmental impacts. Additionally, reduced utilization of certain facilities leads to a decline in the social