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

Customer returns are an unavoidable and increasingly costly challenge in business operations, especially in online marketplaces. This study addresses this issue by introducing a practical multi-supplier closed-loop location-inventory problem (CLLIP) that incorporates customer returns. The objective of the CLLIP is to minimize overall supply chain costs by optimizing facility location and inventory management strategies. To solve this complex problem, an improved hybrid artificial bee colony algorithm (IHABC) is proposed, which integrates two novel search equations to generate candidate solutions during the employed bee and onlooker bee phases, effectively balancing exploration and exploitation. The performance of IHABC is evaluated against various artificial bee colony variants as well as the commercial solver Lingo. The results of numerical experiments demonstrate that IHABC consistently outperforms competing methods, achieving superior solutions with the lowest mean values and optimal total cost results, while also requiring less computation time. The results of numerical experiments demonstrate that IHABC consistently outperforms competing methods, achieving up to 29.97% improvement in solution quality over the standard ABC algorithm. These findings confirm that IHABC is a highly effective and efficient tool for solving the proposed CLLIP. Furthermore, a sensitivity analysis is conducted to provide actionable insights, enabling managers to make informed and strategic decisions in real-world supply chain operations.

客户退货是商业运营中不可避免且成本日益攀升的难题，在在线市场中尤为突出。本研究针对该问题，提出了一款融入客户退货场景的多供应商闭环选址-库存问题（Closed-loop Location-inventory Problem, CLLIP）。该问题的优化目标为通过优化设施选址与库存管理策略，实现供应链整体成本最小化。为求解该复杂问题，本文提出一种改进混合人工蜂群算法（Improved Hybrid Artificial Bee Colony Algorithm, IHABC），其在引领蜂与跟随蜂阶段融入两种全新的搜索方程以生成候选解，有效平衡了全局探索与局部开发能力。本文将IHABC与多种人工蜂群算法变体以及商业求解器Lingo进行性能对比评估。数值实验结果表明，IHABC始终优于各类对比方法，不仅可获得最低平均解与最优总成本解，同时计算耗时更短。数值实验结果进一步显示，相较于标准人工蜂群算法，IHABC的解质量最高可提升29.97%。上述研究结果证实，IHABC是求解所提出的CLLIP问题的高效实用工具。此外，本文还开展了敏感性分析，以提供可落地的决策参考，助力管理者在实际供应链运营中制定科学合理的战略决策。