Location Model and Optimization Algorithm of Recycling Chain Store in Multi-Objective Dual-Element Closed-Loop Supply Chain

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Location Model and Optimization Algorithm of Recycling Chain Store in Multi-Objective Dual-Element Closed-Loop Supply Chain

Introduction

In the context of green and low-carbon circular economic development, the efficient recycling and effective utilization of renewable resources have become crucial. Recycling points serve as bridges between consumers and manufacturers, acting as intermediaries in recycling systems to meet the needs of multiple stakeholders. The scientific planning and rational layout of enterprise recycling networks not only impact corporate value—such as cost savings and profit growth—but also influence social value by enhancing satisfaction and promoting recycling.

This paper applies game theory to construct a dual closed-loop supply chain system with mixed competition and recycling channels. From the perspective of reverse supply chains, the study investigates the location of recycling chain stores, considering not only store locations and distances but also store scale and the range of services provided. A multi-objective dual closed-loop supply chain recycling chain store location model is established, aiming to minimize construction and service costs, maximize customer satisfaction, and maximize recycling profits. To solve this optimization problem, an improved mushroom reproduction algorithm (MRO) incorporating Pareto non-dominated solution sets is designed. Numerical examples are used to verify the model’s feasibility and the algorithm’s effectiveness. Finally, comparative analyses of competitors’ price sensitivity and cross-price sensitivity are conducted to explain location strategies under different scenarios, providing decision-making references for recycling chain store location optimization in reverse supply chains.

Background and Problem Description

The study addresses the profit optimization problem in a competitive environment, constructing a dual closed-loop supply chain system that includes manufacturers, recyclers, competitors, and consumers. The system is based on game theory from the perspective of reverse supply chains. The model considers dynamic changes in recycling demand under competitive conditions, where consumers choose recycling channels based on price and service quality.

Key assumptions include:

  1. Consumers generate a total amount of recyclable waste, distributed between two competing recycling channels based on price sensitivity.
  2. The recycling volume of each channel is influenced by its own price and the competitor’s price, with cross-price sensitivity reflecting competition intensity.
  3. Prices must satisfy logical relationships to ensure economic benefits for all parties in the supply chain.
  4. Manufacturers refurbish recycled products at a lower cost than producing new ones, and market demand depends on retail prices.
  5. Manufacturers act as leaders in a Stackelberg game, while recyclers and competitors follow, each pursuing profit maximization.

The recycling chain store location problem involves selecting candidate sites from a predefined set, each with different service scales and coverage radii. Larger stores offer broader service ranges and higher customer satisfaction but incur higher construction costs. Consumers can choose from multiple recycling methods: mail-in, in-store, or doorstep pickup, depending on their proximity to the stores.

Model Construction

The multi-objective dual closed-loop supply chain recycling chain store location model is formulated with three objectives:

  1. Minimizing Construction and Service Costs (Z₁): This includes fixed construction costs for stores and variable costs for mail-in and doorstep pickup services, which depend on distance.
  2. Maximizing Customer Satisfaction (Z₂): Satisfaction is measured based on in-store recycling services, which are influenced by store scale and proximity to demand points.
  3. Maximizing Recycling Profit (Z₃): Total profit is derived from optimal profits at each demand point, considering price sensitivity and initial recycling volumes.

Decision Variables and Constraints

• Decision Variables: Binary variables indicate whether a candidate site is selected and its scale. Continuous variables represent the allocation of recycling services (mail-in, in-store, doorstep) to demand points.

• Constraints:

• Each candidate site can host only one store scale.

• Demand points must be fully serviced, with in-store recycling limited to a maximum proportion.

• Only established stores can provide services.

• Price sensitivity at each demand point depends on coverage and distance to the nearest store.

Solution Methodology

Improved Mushroom Reproduction Algorithm (MRO)

The MRO algorithm mimics the growth and reproduction mechanisms of mushrooms, where spores explore and colonize fertile regions. The algorithm is enhanced with genetic operations (crossover and mutation) and an elite retention strategy to improve search efficiency. For multi-objective optimization, a Pareto non-dominated solution set method is incorporated.

Key Steps:

  1. Solution Representation: Each solution is encoded as a vector indicating store scales at candidate sites. A colony consists of multiple solutions, and its fitness is the average fitness of its members.

  2. Colony Generation: Initial solutions are randomly generated and perturbed to form colonies, ensuring diversity and local search capability.

  3. Fitness Function: A weighted sum approach normalizes the three objectives, eliminating scale differences.

  4. Pareto Non-Dominated Sorting: Solutions are ranked based on dominance relationships, with non-dominated solutions forming the Pareto front.

  5. Search Operations:
    • Local Search: If a colony’s average fitness is high, it undergoes mutation (single-column exchange or real-value mutation).

    • Global Search: If fitness is low, crossover with elite solutions is performed.

  6. Iterative Process: The algorithm iterates until convergence, updating the Pareto front at each generation.

Experimental Results and Analysis

Case Study

A case study involves 13 candidate sites and 48 demand points, with parameters derived from industry data. Three store scales are considered, each with distinct service radii and construction costs. The algorithm parameters are set as follows: initial colonies = 40, solutions per colony = 5, maximum iterations = 50.

Performance Evaluation

The algorithm’s performance is compared with an improved MRO and a basic genetic algorithm. Results show that the proposed algorithm outperforms others in solution quality and convergence speed.

Representative Solutions:

  1. Optimal Construction Cost (Opt_1): Focuses on minimizing costs but yields lower satisfaction and profit.
  2. Optimal Customer Satisfaction (Opt_2) and Profit (Opt_3): These solutions coincide, indicating a trade-off between satisfaction and profit.
  3. Best Compromise Solution (Best): Balances all three objectives effectively.
  4. Worst Solution (Worst): Equivalent to Opt_1, highlighting the drawbacks of prioritizing cost alone.

Sensitivity Analysis

  1. Competitor Price Sensitivity (β₂):
    • Lower β₂ (higher competitor price sensitivity) improves customer satisfaction and profit but increases costs.

    • Decision-makers should prioritize regions with low competitor price sensitivity for better overall performance.

  2. Cross-Price Sensitivity (γ):
    • Higher γ (stronger competition) reduces satisfaction and profit but may lower costs.

    • Locations with low cross-price sensitivity are preferable for balanced objectives.

Optimal Location Strategies

Table 6 summarizes the best location schemes under different scenarios. Key observations:
• Candidate sites 2 and 13 consistently adopt the same scale across scenarios.

• Sites 6 and 7 show similar scales, while others vary significantly.

Conclusion

This study addresses the critical challenge of recycling chain store location in competitive environments by integrating game theory and multi-objective optimization. The proposed model and algorithm provide practical decision-making tools for enterprises, balancing economic and social objectives. Key findings include:

  1. Prioritizing customer satisfaction and profit leads to significant gains with marginal cost increases.
  2. Competitor price sensitivity and cross-price sensitivity are critical factors in location decisions.
  3. The improved MRO algorithm effectively solves the complex multi-objective problem, outperforming traditional methods.

Future research could incorporate additional factors such as storage capacity, product flow efficiency, and inventory cycles to further refine the model.

doi.org/10.19734/j.issn.1001-3695.2024.07.0302

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