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A Lagrangian relaxation based approach for the capacitated lot sizing problem in closed-loop supply chain

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  • Zhang, Zhi-Hai
  • Jiang, Hai
  • Pan, Xunzhang

Abstract

This paper investigates the capacitated lot sizing problem in closed-loop supply chain considering setup costs, product returns, and remanufacturing. We formulate the problem as a mixed integer program and propose a Lagrangian relaxation-based solution approach. The resulting Lagrangian subproblems are then solved by polynomial time algorithms. Compared to existing solution methods in the literature, our Lagrangian relaxation based approach is advantageous in that it naturally provides a lower bound on the optimal objective function value, which allows us to assess the quality of solutions found. Numerical experiments using synthesized data demonstrate that our approach can find quality solutions efficiently.

Suggested Citation

  • Zhang, Zhi-Hai & Jiang, Hai & Pan, Xunzhang, 2012. "A Lagrangian relaxation based approach for the capacitated lot sizing problem in closed-loop supply chain," International Journal of Production Economics, Elsevier, vol. 140(1), pages 249-255.
    • Handle: RePEc:eee:proeco:v:140:y:2012:i:1:p:249-255
    DOI: 10.1016/j.ijpe.2012.01.018
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    2. Andreas Goerler & Stefan Voß, 2016. "Dynamic lot-sizing with rework of defective items and minimum lot-size constraints," International Journal of Production Research, Taylor & Francis Journals, vol. 54(8), pages 2284-2297, April.
    3. Özceylan, Eren & Paksoy, Turan & Bektaş, Tolga, 2014. "Modeling and optimizing the integrated problem of closed-loop supply chain network design and disassembly line balancing," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 61(C), pages 142-164.
    4. Dhahri, Akrem & Gharbi, Ali & Ouhimmou, Mustapha, 2022. "Integrated production-delivery control policy for an unreliable manufacturing system and multiple retailers," International Journal of Production Economics, Elsevier, vol. 245(C).
    5. Suzanne, Elodie & Absi, Nabil & Borodin, Valeria, 2020. "Towards circular economy in production planning: Challenges and opportunities," European Journal of Operational Research, Elsevier, vol. 287(1), pages 168-190.
    6. Huang, Min & Song, Min & Lee, Loo Hay & Ching, Wai Ki, 2013. "Analysis for strategy of closed-loop supply chain with dual recycling channel," International Journal of Production Economics, Elsevier, vol. 144(2), pages 510-520.
    7. Yongjian Li & Xiaoqiang Cai & Lei Xu & Wenxia Yang, 2016. "Heuristic approach on dynamic lot-sizing model for durable products with end-of-use constraints," Annals of Operations Research, Springer, vol. 242(2), pages 265-283, July.
    8. Wu, Xin & Nie, Lei & Xu, Meng & Zhao, Lili, 2019. "Distribution planning problem for a high-speed rail catering service considering time-varying demands and pedestrian congestion: A lot-sizing-based model and decomposition algorithm," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 123(C), pages 61-89.
    9. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    10. G. Rius-Sorolla & J. Maheut & Jairo R. Coronado-Hernandez & J. P. Garcia-Sabater, 2020. "Lagrangian relaxation of the generic materials and operations planning model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 105-123, March.
    11. Felix T.S. Chan & Nan Li & S.H. Chung & Mozafar Saadat, 2017. "Management of sustainable manufacturing systems-a review on mathematical problems," International Journal of Production Research, Taylor & Francis Journals, vol. 55(4), pages 1210-1225, February.
    12. Liu, Kanglin & Zhang, Zhi-Hai, 2018. "Capacitated disassembly scheduling under stochastic yield and demand," European Journal of Operational Research, Elsevier, vol. 269(1), pages 244-257.
    13. Chen, Jen-Ming & Chang, Chia-I, 2013. "Dynamic pricing for new and remanufactured products in a closed-loop supply chain," International Journal of Production Economics, Elsevier, vol. 146(1), pages 153-160.
    14. S. Saha & S.P. Sarmah & Ilkyeong Moon, 2016. "Dual channel closed-loop supply chain coordination with a reward-driven remanufacturing policy," International Journal of Production Research, Taylor & Francis Journals, vol. 54(5), pages 1503-1517, March.

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