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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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    References listed on IDEAS

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    3. Cárdenas-Barrón, Leopoldo Eduardo, 2010. "Adaptive genetic algorithm for lot-sizing problem with self-adjustment operation rate: A discussion," International Journal of Production Economics, Elsevier, vol. 123(1), pages 243-245, January.
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    Cited by:

    1. repec:eee:proeco:v:198:y:2018:i:c:p:25-37 is not listed on IDEAS
    2. 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.
    3. 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.
    4. repec:spr:annopr:v:242:y:2016:i:2:d:10.1007_s10479-013-1526-x is not listed on IDEAS
    5. repec:eee:ejores:v:263:y:2017:i:3:p:838-863 is not listed on IDEAS
    6. repec:eee:ejores:v:269:y:2018:i:1:p:244-257 is not listed on IDEAS
    7. 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.

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