3.1.1 Notation.

Sets:

• S = set of candidate locations for suppliers;
• R = set of candidate locations for HDCCs;
• I = set of customer zones.

Parameters:

• a_r = fixed (annual) cost of building and operating a HDCC at location r, for each r ∈ R;
• a_s = fixed (annual) cost of selecting a supplier at location s, for each s ∈ S;
• b_sr = fixed administrative and handling cost of placing an order at HDCC r to the supplier s, for each s ∈ S, r ∈ R;
• c_sr = fixed shipment cost of a shipment between the supplier s and HDCC r, for each s ∈ S, r ∈ R;
• d_ri = shipment cost per unit between HDCC r and customer zone i, for each r ∈ R, i ∈ I;
• e_sr = unit variable shipment cost between the supplier s and HDCC r, for each s ∈ S, r ∈ R;
• f_r = processing cost per unit of customer returns at HDCC r, for each r ∈ R;
• h_r = (annual) holding cost per unit at HDCC r, for each r ∈ R;
• q_i = return rate at customer zone i, for each i ∈ I;
• µ_i = mean (daily) demand at customer zone i, for each i ∈ I;
• = variance of (daily) demand at customer zone i, for each i ∈ I;
• α = desired percentage of fulfilled market demand (fill rate);
• z_α = standard normal deviate such that P (z ≤ z_α) =α;
• L = order lead time (in days) at HDCCs;
• λ = working days per year;
• θ = percentage of false failure returns;
• β = percentage of true failure returns, where β=1-θ.

Decision variables:

• W_s = 1 if a supplier at location s is selected, and 0 otherwise, for each s ∈ S;
• X_r = 1 if opening one HDCC at location r, and 0 otherwise, for each r ∈ R;
• Y_sr = 1 if supplier s is assigned to HDCC r, and 0 otherwise, for each s ∈ S, r ∈ R;
• Z_ri = 1 if HDCC r is assigned to customer zone i, and 0 otherwise, for each r ∈ R, i ∈ I.

3.2.1. Location and delivery cost.

The main influences for making facility location decisions are the fixed location cost and the delivery cost between HDCCs and customer zones which usually be measured by distance [25,29]. Therefore, the location cost (C_L) can be expressed as follows:

This formulation highlights the trade-off between the upfront investment in establishing facilities and the ongoing transportation expenses, which are critical considerations in designing an efficient and cost-effective supply chain network

3.2.2. Inventory cost.

1. 1. Working inventory cost: In this study, we assume that HDCCs use a (Q, r) inventory model with type I service [39] to represent the inventory control problem. This choice is common as it allows for the approximation of the (Q, r) model with the order quantity determined by an economic order quantity (EOQ) model [40]. Therefore, we employ an EOQ model to optimize the inventory decisions in this study. The total working inventory costs of HDCCs include (a) order cost; (b) shipping cost between the suppliers and the HDCCs; and (c) holding cost of the working inventory. Let D_sr be the annual demand from supplier s to HDCC r per year, then will be the number of orders from supplier s to HDCC r per year. This formulation ensures that inventory decisions are optimized to balance ordering and holding costs, while also accounting for the transportation expenses associated with supplier-HDCC interactions.
   1. (1)  Order cost. Since the HDCC r processes the same number of orders, the fixed ordering cost can be shared among items within the same order. Therefore, the annual fixed cost of placing orders from supplier s to HDCC r is .
   2. (2)  Shipping costs between the suppliers and HDCCs. Given that false failure returns in new or good conditions are reused by HDCCs to fulfill customer orders, the shipping quantity from the suppliers to HDCCs is the difference between customer demands and false failure returns. Meanwhile, true failure returns are shipped from HDCCs to the suppliers for repair or recovery, the transportation cost of true failure returns from HDCC r to the supplier s should be added to the shipping cost. Hence, the annual shipping cost from supplier s to HDCC r is .

This approach ensures that both forward and reverse logistics costs are accounted for, providing a more accurate representation of the total shipping expenses in the CLSC network.

1. (3) Holding cost of the working inventory. The annual holding cost at HDCC r includes the holding costs of the products in both forward and reverse flows. Therefore, the holding cost in the closed-loop supply chain from the supplier s to HDCC r is .

Therefore, the total annual working inventory cost from the supplier s to HDCC r in a closed-loop supply chain is:

It is straightforward to show that the optimal value of Q_sr that minimizes this expression is equal to . The corresponding annual working inventory cost from the supplier s to HDCC r can be expressed as:

The total annual working inventory cost in the closed-loop supply chain can be expressed as follows:

1. 2. Safety stock cost: Using Eppen’s risk pooling effects [40], the safety stock required to ensure that stockouts occur with a probability of α or less is . Therefore, the holding cost for the safety stock cost at HDCCs is .

This formulation ensures that inventory decisions are optimized to minimize costs while accounting for both forward and reverse logistics activities, providing a comprehensive framework for managing inventory in a closed-loop supply chain.

3.2.3. Processing cost.

The customer returns collected at HDCCs undergo processing activities such as inspecting, repackaging, sorting, and cleaning. The processing cost at HDCCs is .

Consequently, the MINLP model is employed to solve the following:

(1)

Subject to:

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

The objective function in Equation (1), aims to minimize the total annual cost in the CLSC under study. Equations (2) and (3) dictate that at least one supplier and HDCC must be built, respectively. Equation (4) means that each customer zone is precisely assigned to one HDCC. Equation (5) ensures that each HDCC must be assigned to an existing supplier. Equation (6) means that no customer zone can be allocated to a HDCC unless it is opened. Equations (7) and (8) signify that the supplier and HDCC will be operational once built. Equation (9) ensures that each customer zone will be served by only one HDCC and supplier. Equations (10) – (13) mean that decision variables are binary. This MINLP model provides a comprehensive framework for optimizing the CLSC network, balancing cost minimization with operational constraints to achieve an efficient and sustainable supply chain design.

4.1.1. Population initialization.

In the initial phase, a population of SN solutions (food source positions) is randomly generated within the feasible solution space, where SN denotes the size of the population. The initial location of the food sources is generated as follows.

(14)

Where , D represents the dimension of the search space, and rand is a random value generated uniformly within the interval (0,1). and denote the upper and lower bound of each component, respectively. This initialization phase ensures that the algorithm starts with a diverse set of solutions, enabling a broad exploration of the search space. The subsequent phases of the algorithm, employed bees, onlooker bees, and scout bees, work collaboratively to refine these solutions, balancing exploration and exploitation to achieve near-optimal results.

4.1.2. Employed bee phase.

In the employed bee phase, each bee searches around its assigned food source and generates a new food source as below:

(15)

Where and ; is a random number within [−1, 1]. If v_i outperforms the previous food source x_i, x_i is replaced by v_i and the counter is reset to 0. Otherwise, x_i remains unchanged, and its counter is incremented by one. This process ensures that the algorithm continuously explores the search space while retaining high-quality solutions.

4.1.3. Onlooker bee phase.

After the employed bee phase ends, the onlooker bees collect information shared by the employed bees. Each onlooker bee chooses a food source for further exploration, with the selection probability p_i determined as follows:

(16)

Where p_i represents the probability of selecting the employed bee and is the fitness value of ith food source. Each onlooker bee moves to a food source x_i, chosen using the roulette wheel selection strategy, and then uses Equation (15), to generate a new candidate food source v_i. If v_i is better than x_i, then x_i is replaced by v_i, and its counter is reset to 0. Otherwise, x_s is retained, and its counter is incremented by one. This phase emphasizes exploitation by focusing on high-quality solutions while maintaining diversity through probabilistic selection.

4.1.4. Scout bee phase.

In the scout bee phase, if the counter exceeds the predefined limit, the food source is abandoned, and the corresponding employed bee evolves into a scout bee, generating a new food source randomly according to Equation (14). After generating the new food source, its counter is set to 0, and the scout bee is converted into an employed bee. This phase ensures that the algorithm avoids stagnation by exploring new regions of the search space, thereby maintaining a balance between exploration and exploitation

4.2.1. Population initialization.

Designing an efficient encoding and decoding mechanism is crucial for enhancing algorithm performance, as it directly impacts the effectiveness and efficiency of the optimization process [44]. The encoding structure of each population individual plays a pivotal role in the algorithm’s operation, as it determines how solutions are represented and manipulated. By analyzing the model’s characteristics and uncovering its intrinsic properties, we design an encoding scheme tailored to the CLLIP. Each individual consists of vectors with I + R elements. The first I elements denote the candidate HDCC location strategy and the assignment information for the customer zones, while the last R elements indicate the candidate supplier location strategy and the allocation details for the HDCCs. The structure of the individual is given by Equation (17).

(17)

Where denotes the p-th solution at iteration g. represents the identifier of HDCCs assigned to each customer zone, and indicates the identifier of suppliers assigned to each HDCC. If , then customer zone j is allocated to HDCC r, and if , then candidate HDCC j is assigned to supplier s. Table 2 illustrates decoded individuals for a scenario involving ten customer zones, five candidate HDCCs, and three suppliers, providing a clear example of how the encoding and decoding mechanisms operate. This structured representation ensures that the algorithm can efficiently explore and evaluate solutions while maintaining feasibility and relevance to the CLLIP.

In Table 3, the decoded individual is structured to display the assignment information. The first part of the decoded individual shows the following assignments: customer zones 1, 4, and 8 are allocated to HDCC 1; customer zones 3, 5, and 9 to HDCC 3; customer zones 2, 6, 7, and 10 to HDCC 2; The second part reveals that candidate HDCCs 1, 2 and 4 are assigned to supplier 2, while candidate HDCC 3 and 5 are assigned to supplier 3. Thus, the decision variables W_s, X_r, Y_sr, Z_ri can be determined based on the assignment information.

Download:

• PNG
  larger image
• TIFF
  original image

Table 3. Example of the decoded individual (S=3, R = 5, I = 10).

https://doi.org/10.1371/journal.pone.0324343.t003

The purpose of encoding is to transform the initial population into a viable solution for the proposed model. By analyzing the encoding mechanisms of the population individuals and considering the specifics of the CLLIP, a specific decoding mechanism is derived, as shown in Equation (18).

(18)

Where round ( ) denotes the rounding function, represents a uniformly distributed random number. x^L and x^U denote the lower and upper bounds, respectively, with x^L = 1 and x^U indicating the total number of candidates HDCCs. Similarly, y^L and y^U denote the lower and upper bounds for the candidate suppliers, where y^L = 1 and y^U indicates the total number of candidate suppliers. This structured representation ensures that the algorithm can efficiently map the encoded solutions to the decision variables, enabling accurate evaluation and optimization of the CLLIP model.

4.2.2. Employed bee phase.

To improve ABC’s performance, researchers have refined its search equations, resulting in the development of numerous variants. In IHABC, the DE/best/1 strategy is introduced to enhance exploitation and utilize information from the best solutions to guide candidate searches. A new candidate solution v_i is generated by using the best solution x_best. A search equation, formulated based on the DE/best/1 strategy and the properties of ABC, is presented below:

(19)

Where the function round () denotes the rounding operation. x_best is the best individual in the current population. r1 and r2 are integers randomly selected from {1, 2,..., SN}, and is a random number in the range [−1, 1]. rand is a uniformly distributed random number between [0, 1], while τ₁ represents the modification rate, which takes a value between 0 and 1. If exceeds the pre-specified upper or lower bounds, it will be randomly regenerated within the respective range. This approach ensures that the search process is guided by high-quality solutions while maintaining diversity in the population.

4.2.3. Onlooker bee phase.

The onlooker bee assesses the nectar information from all employed bees and selects a food source x_i based on its probability value p_i. The probability of selecting a food source is defined by Equation (16) and utilizes the roulette wheel selection strategy, where solutions are chosen for the update process based on fitness proportionate selection. In IHABC, the update process in the onlooker bee phase differs from that in the employed bee phase. To improve the exploration capability of ABC and enhance the diversity of perturbed parameter vectors, a new search equation Equation (20), inspired by the DE/rand/1 strategy is presented to replace Equation (19). The selective probability τ₂ is introduced to balance the exploration and exploitation of ABC. The new search mechanism is outlined below:

(20)

Where round() denotes the rounding operation, r1 and r2 are distinct random integers selected from {1, 2,..., SN}; x_best represents the best individual in the population; is a random number within the range of [−1, 1], indicating the change rate of the food source, which can affect the algorithm’s convergence speed.τ₂ denotes the selective probability, ranging from 0 to 1. rand is a uniformly distributed random number within the interval [0, 1]. If exceeds the specified bounds, it will be randomly regenerated within the appropriate range. This hybrid search mechanism ensures a balance between exploration and exploitation, enabling the algorithm to escape local optima and converge to high-quality solutions.

4.2.4. Scout bee phase.

In the scout bee phase, if a food source x_i cannot be improved after the predefined limit, it is abandoned, and the corresponding employed bee transitions to a scout. The scout then randomly generates a new food source as described in Equation (18).

Based on the previously described steps of population initialization, employed bee phase, onlooker bee phase, and scout bee phase, the pseudo-code for IHABC is presented below:

Download:

• PNG
  larger image
• TIFF
  original image

https://doi.org/10.1371/journal.pone.0324343.t013

5.2.1. Efficiency of the search strategy in the employed bee phase.

To validate the effectiveness of the proposed search strategy in the employed bee phase, the search equation from ABC is employed for comparison. To ensure a fair comparison, the two algorithms are identical except for the search strategy in the employed bee phase. The results of each instance are presented in Table 6.

Download:

• PNG
  larger image
• TIFF
  original image

Table 6. Comparison of improvement strategies results in the employed bee phase.

https://doi.org/10.1371/journal.pone.0324343.t006

A summary of these results is provided below: (1) Compared with the search strategy of ABC, the proposed search strategy in the employed bee phase yields superior results, demonstrating enhanced optimization capabilities; (2) The CPU time values further indicate that the proposed search strategy achieves higher optimization efficiency, reducing computational resource requirements. (3) The lower standard deviation values associated with the proposed strategy indicate improved algorithmic stability and robustness, ensuring more consistent performance across iterations. (4) As the problem size increases, the advantages of the proposed strategy become increasingly pronounced, outperforming the original ABC strategy in larger and more complex instances.

Therefore, applying the proposed search strategy can significantly enhance the algorithm’s performance, as evidenced by its effectiveness in the employed bee phase.

5.2.2. Efficiency of the search strategy in the onlooker bee phase.

To validate the performance of the proposed search strategy for the onlooker bee phase, the search equation derived from the ABC algorithm is employed as a benchmark for comparison. To ensure a fair assessment, the two algorithms are designed to be identical in all aspects except for the search strategy implemented during the onlooker bee phase. The results for each instance are presented in Table 7.

Download:

• PNG
  larger image
• TIFF
  original image

Table 7. Comparison of improvement strategies results in the onlooker bee phase.

https://doi.org/10.1371/journal.pone.0324343.t007

The results presented in Table 7 reveal that the proposed search strategy demonstrates significant advantages over the original ABC strategy across multiple dimensions. First, in terms of solution accuracy, the proposed search strategy significantly outperforms those of the original ABC approach, indicating its superior optimization performance and ability to identify more precise solutions. Second, while the improvement in solution efficiency is modest, the proposed search strategy still shows a slight improvement over the original, indicating that maintains competitive optimization speeds without compromising on quality. Third, the standard deviation values indicate that the proposed search strategy significantly enhances the algorithm’s stability, reducing variability in outcomes and ensuring more consistent and reliable performance. Finally, as the problem size increases, the advantages of the proposed search strategy become more pronounced, demonstrating its scalability and effectiveness in handling larger and more complex optimization tasks. These findings collectively underscore the effectiveness of the proposed search strategy for the onlooker bee phase, particularly in scenarios requiring high precision, stability, and scalability.

Managerially, the findings highlight the importance of integrating innovative methodologies into organizational decision-making frameworks. The proposed strategy’s ability to deliver consistent and reliable outcomes, particularly as problem complexity grows, makes it a valuable tool for industries such as logistics, manufacturing, and technology. By leveraging this approach, managers can improve operational efficiency, enhance strategic planning, and achieve more robust solutions to complex challenges. Moreover, the emphasis on stability and scalability underscores the need for organizations to invest in adaptive and forward-thinking strategies that can navigate the growing complexities of modern economic environments, ensuring long-term resilience and competitiveness.

5.3.1. Performance comparison.

In this subsection, to further verify the problem-solving capabilities of IHABC, GABC, CABC, qABC, ABC, and Lingo are implemented. To ensure a fair and unbiased comparison, the basic parameters for the ABC-based algorithms are standardized as follows: SN = 6I, limit = 5I, and G = 1000 for all instances. For five instances of different scales, each algorithm is executed 30 times under identical conditions to ensure robustness and reliability in the results. Key performance metrics, including the minimum (min), maximum (max), mean, standard deviation (S.D.), and CPU time are recorded for comparison. As problem sizes increase, Lingo encounters significant computational challenges, failing to solve the proposed CLLIP model for medium and large-scale instances within a reasonable time limit of 3600 Seconds. Consequently, IHABC is compared with the other algorithms for medium and large-scale instances, with detailed results presented in Tables 8–10.

Download:

• PNG
  larger image
• TIFF
  original image

Table 8. Experimental results of different algorithms in small-scale instances.

https://doi.org/10.1371/journal.pone.0324343.t008

Download:

• PNG
  larger image
• TIFF
  original image

Table 9. Experimental results of different algorithms in medium-scale instances.

https://doi.org/10.1371/journal.pone.0324343.t009

Download:

• PNG
  larger image
• TIFF
  original image

Table 10. Experimental results of different algorithms in large-scale instances.

https://doi.org/10.1371/journal.pone.0324343.t010

The results for the performance comparison are presented in Tables 8–10, which reveal the following key conclusions:

1. (1) For small-scale instances, IHABC and Lingo produce nearly identical optimal solutions, highlighting IHABC’s robust search capability and its ability to match the performance of established optimization tools. Moreover, IHABC consistently outperforms Lingo in terms of computational efficiency across all instances, highlighting its superior ability to deliver results in less time.
2. (2) IHABC consistently exhibits superior solution quality compared to other algorithms, as indicated by its lowest minimum and mean values across all instances. This highlights IHABC’s remarkable capability, effectiveness, and robustness in addressing the proposed CLLIP, making it a reliable choice for complex optimization problems.
3. (3) IHABC demonstrates notable consistency, with the lowest standard deviations in solution values among all algorithms. This reliability ensures steady performance, making IHABC particularly suitable for applications that require stable and dependable results, such as real-time decision-making or mission-critical operations.
4. (4) IHABC demonstrates outstanding computational efficiency, requiring less CPU time than other algorithms. This efficiency makes it particularly advantageous in practical scenarios where both computational resources and time are limited, enabling faster and more cost-effective solutions.

A t-test was applied to assess whether the performance difference of IHABC is statistically significant. Due to the minor impact on small-scale instances, the test was conducted on medium and large-scale instances. A t-test with a 95% confidence interval was used to determine if there is a significant difference in total cost and to provide statistical evidence of the IHABC’s performance. The test results for medium-scale and large-scale instances are presented in Tables 11 and 12.

Download:

• PNG
  larger image
• TIFF
  original image

Table 11. The results of t-test for medium-size problems.

https://doi.org/10.1371/journal.pone.0324343.t011

Download:

• PNG
  larger image
• TIFF
  original image

Table 12. The results of t-test for large-size problems.

https://doi.org/10.1371/journal.pone.0324343.t012

Tables 11 and 12 show that the p-value for most problems is less than 0.05. This indicates that, in most cases, the IHABC algorithm significantly outperforms the other algorithms, with a notably lower total cost. Therefore, IHABC is a more efficient method, providing better feasible solutions.

5.3.2. Sensitivity analysis.

In this section, we analyze the impact of three critical parameters - return rate q_i, false failure return rate θ, and true failure return rate β - on the costs in the proposed model, including location and delivery cost (C_L), inventory cost (C_I), and processing cost (C_P). The results are shown in Figs 2 and 3, which provide valuable insights into the relationships between these parameters and the associated costs.

Download:

• PNG
  larger image
• TIFF
  original image

Fig 2. Sensitivity analysis on (θ, β).

https://doi.org/10.1371/journal.pone.0324343.g002

Download:

• PNG
  larger image
• TIFF
  original image

Fig 3. Sensitivity analysis on q_i.

https://doi.org/10.1371/journal.pone.0324343.g003

In Fig 2, q_i is held constant while β and θ are varied. Since the parameters affecting distribution and recycling costs are predetermined, and both C_L and C_P are independent of β and θ, the analysis focuses on how changes in β and θ influence C_I and total cost (C_TOT). As θ increases and β decreases, both C_I and C_TOT decline. This trend can be attributed to the higher rate of false failure returns allowing more products to be reintegrated into the market via HDCCs, thereby reducing ordering and inventory costs. As a result, the system achieves better resource utilization and significant cost savings, highlighting the economic benefits of optimizing return management processes.

In Fig 3, with (θ, β) fixed at (0.7, 0.3), q_i varies within the range [0, 1]. The results indicate that as q_i increases, C_L, C_P, and C_TOT rise, while C_I decreases. This trend is likely driven by the fixed demand: as the number of returned items increases, both return handling costs and distribution costs between the HDCC and the demand point escalate. Conversely, the ordering and inventory costs between the supplier and the HDCC decrease, leading to a reduction in C_I as q_i increases. This inverse relationship underscores the trade-offs inherent in managing return rates and their impact on overall system costs. Additionally, the findings highlight the need for flexible supply chain strategies that can adapt to varying return rates, ensuring that organizations remain competitive in dynamic market environments.

In the preceding section, the impact of return rates, as well as the rates of true and false failure returns, on associated costs were analyzed, yielding several management insights. First, given that inventory costs decline as return rates increase, companies should adopt more flexible inventory management strategies, such as dynamic inventory adjustments, to alleviate inventory backlogs and their associated costs. This approach not only enhances operational efficiency but also aligns inventory levels more closely with actual demand, reducing waste and improving resource utilization. Second, companies can achieve significant cost savings by improving product quality and reducing the frequency of true failure returns. Achieving this may require strategic investments in research and development (R&D) and enhancements in production processes, which can lead to long-term competitive advantages and higher customer satisfaction. Third, the time and costs associated with processing returns can be minimized by optimizing the returns process. For instance, automating the returns processing system can streamline operations, improve efficiency, and reduce labor costs, ultimately enhancing the overall profitability of the return management system. Fourth, the rate of false failure returns can be reduced by improving customer education and technical support. This can be achieved through measures such as providing comprehensive product usage manuals, offering troubleshooting assistance, and ensuring easily accessible customer service hotlines, all of which contribute to a better customer experience and fewer unnecessary returns. Finally, managers can leverage historical return data to analyze and forecast future return trends. This data-driven approach enables proactive adjustments in inventory and production plans, thereby helping to reduce excess inventory and associated costs while ensuring that supply chain operations remain agile and responsive to market demands.

Furthermore, from an economic perspective, these insights highlight the importance of optimizing return management processes to achieve cost efficiency and operational excellence. By reducing true failure returns and minimizing false failure returns, companies can lower their overall costs while improving customer satisfaction and brand reputation. Furthermore, investments in R&D and process automation not only enhance product quality and operational efficiency but also contribute to long-term sustainability and competitiveness in the market. Ultimately, these strategies enable companies to transform return management from a cost center into a value-adding component of their operations, driving both financial and operational success.

5.3.3. Discussion.

This research introduces the improved Hybrid Artificial Bee Colony (IHABC) algorithm to tackle the complex multi-supplier closed-loop location-inventory problem (CLLIP) with customer returns. The algorithm aims to minimize the total supply chain costs, considering key factors such as location and delivery costs, inventory costs, and processing costs. The numerical experiments and sensitivity analyses conducted in this study offer valuable insights into the operational implications of various parameters and their impact on overall supply chain performance. The key findings are as follows:

1. (a) Complex supply chain management and cost reduction: The supply chain environment, especially in industries with high return rates, presents significant challenges related to facility location and inventory control. The complexity is further compounded by the need to handle a considerable volume of returned products, which directly affects operational efficiency. The IHABC algorithm proves to be an effective tool for addressing these challenges, providing viable solutions that optimize facility locations and inventory management strategies. By reducing both location and inventory costs, the algorithm allows businesses to manage returns more effectively and achieve cost savings without sacrificing service levels. The results suggest that IHABC offers a practical and robust solution to managing closed-loop supply chains, particularly in industries where returns are a significant concern.
2. (b) The role of recycling in enhancing profitability: Customer returns are an inherent part of many supply chains, especially in sectors like e-commerce. These returns, however, can be both costly and complex, involving multiple products and supply chain nodes. The study emphasizes the importance of enhancing the recycling process to mitigate the impact of returns. By improving recycling practices, companies can reintegrate returned products into the supply chain, thereby boosting sales and profitability. Recycling not only contributes to reducing waste but also ensures that companies can maintain competitive advantages in a dynamic and highly competitive market. The findings highlight that managers must focus on optimizing recycling strategies to manage returns effectively, improve product life cycles, and maximize the profitability of returned items.
3. (c) Sensitivity of costs to return rate (q_i): The sensitivity analysis reveals that the return rate (q_i) has a significant effect on supply chain costs. As the return rate increases, distribution and handling costs escalate, thereby increasing location and processing costs (C_L and C_P). However, at the same time, inventory costs (C_I) tend to decrease due to lower demand, as returns replace the need for new orders. This inverse relationship underscores the complex nature of managing returns within a supply chain and suggests that companies must carefully balance the return rate to avoid unnecessary cost increases. Therefore, firms should implement flexible supply chain strategies that can dynamically adjust to varying return rates. These strategies could include adaptive inventory management systems, dynamic demand forecasting models, and cost-sensitive return handling protocols that optimize return-related expenditures.
4. (d) Optimization of return management: The study’s sensitivity analysis further provides crucial insights into optimizing returns management processes. By minimizing both true and false failure returns, companies can significantly reduce processing costs and improve their overall cost structure. The analysis indicates that a well-designed return management strategy can lead to substantial cost savings, as it minimizes the need for redundant processes and enhances operational efficiency. For example, automating the returns process can speed up the handling of returned items, reducing labor costs and improving the accuracy of return processing. Additionally, a streamlined return process enables companies to reintegrate returned products back into the inventory more quickly, reducing inventory holding costs and improving product availability.
5. (e) IHABC’s superior performance: The numerical comparisons between IHABC and other solution methods demonstrate the algorithm’s superior performance in solving the multi-supplier CLLIP. IHABC not only provides better feasible solutions in terms of total cost (C_TOT) but also does so with fewer computational resources. This makes the algorithm particularly valuable in scenarios where computational efficiency is crucial, such as real-time decision-making processes in dynamic supply chain environments. The results clearly show that IHABC can help recycling companies and other businesses dealing with complex location-inventory problems achieve cost reductions while maintaining high service levels. Furthermore, the flexibility of the IHABC allows it to be applied to other combinatorial optimization problems, particularly those involving supply chain optimization, where both location and inventory management play crucial roles.
6. (f) Strategic implications for supply chain management: From a broader perspective, the findings of this research suggest several strategic implications for managers in industries affected by high return rates. First, companies should focus on improving product quality to reduce true failure returns, which can be costly in terms of both processing and inventory costs. Investments in R&D and process improvements can contribute to product durability and reduce the frequency of returns, thereby lowering overall costs. Second, given the substantial impact of return rates on cost structures, companies need to adopt more agile and responsive inventory management systems that can quickly adjust to changes in demand and return patterns. This includes the use of predictive analytics to forecast future return trends, allowing firms to plan better for potential surpluses or shortages of returned products.

Finally, the economic benefits of optimizing return management go beyond mere cost reduction. By improving the returns process, companies can increase customer satisfaction by offering quicker and more seamless return experiences. This, in turn, can enhance brand loyalty and increase the likelihood of repeat business. Furthermore, by transforming return management from a cost center into a value-adding operation, companies can improve both their profitability and operational sustainability.