An improved hybrid artificial bee colony algorithm for a multi-supplier closed-loop location inventory problem with customer returns.

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.