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A hybrid optimization approach for multi-level capacitated lot-sizing problems

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  • Almeder, Christian

Abstract

Solving multi-level capacitated lot-sizing problems is still a challenging task, in spite of increasing computational power and faster algorithms. In this paper a new approach combining an ant-based algorithm with an exact solver for (mixed-integer) linear programs is presented. A MAX-MIN ant system is developed to determine the principal production decisions, a LP/MIP solver is used to calculate the corresponding production quantities and inventory levels. Two different local search methods and an improvement strategy based on reduced mixed-integer problems are developed and integrated into the ant algorithm. This hybrid approach provides superior results for small and medium-sized problems in comparison to the existing approaches in the literature. For large-scale problems the performance of this method is among the best.

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  • Almeder, Christian, 2010. "A hybrid optimization approach for multi-level capacitated lot-sizing problems," European Journal of Operational Research, Elsevier, vol. 200(2), pages 599-606, January.
    • Handle: RePEc:eee:ejores:v:200:y:2010:i:2:p:599-606
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    Cited by:

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    2. Sereshti, Narges & Adulyasak, Yossiri & Jans, Raf, 2024. "Managing flexibility in stochastic multi-level lot sizing problem with service level constraints," Omega, Elsevier, vol. 122(C).
    3. Schmid, Verena & Doerner, Karl F. & Laporte, Gilbert, 2013. "Rich routing problems arising in supply chain management," European Journal of Operational Research, Elsevier, vol. 224(3), pages 435-448.
    4. Chen, Haoxun, 2015. "Fix-and-optimize and variable neighborhood search approaches for multi-level capacitated lot sizing problems," Omega, Elsevier, vol. 56(C), pages 25-36.
    5. Almeder, Christian & Klabjan, Diego & Traxler, Renate & Almada-Lobo, Bernardo, 2015. "Lead time considerations for the multi-level capacitated lot-sizing problem," European Journal of Operational Research, Elsevier, vol. 241(3), pages 727-738.
    6. Melega, Gislaine Mara & de Araujo, Silvio Alexandre & Jans, Raf, 2018. "Classification and literature review of integrated lot-sizing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 271(1), pages 1-19.
    7. Wei, Mingyuan & Qi, Mingyao & Wu, Tao & Zhang, Canrong, 2019. "Distance and matching-induced search algorithm for the multi-level lot-sizing problem with substitutable bill of materials," European Journal of Operational Research, Elsevier, vol. 277(2), pages 521-541.
    8. Yilmaz, Dogacan & Büyüktahtakın, İ. Esra, 2024. "An expandable machine learning-optimization framework to sequential decision-making," European Journal of Operational Research, Elsevier, vol. 314(1), pages 280-296.
    9. Tao Wu, 2022. "Predictive Search for Capacitated Multi-Item Lot Sizing Problems," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 385-406, January.
    10. Hao, Jun & Li, Jianping & Wu, Dengsheng & Sun, Xiaolei, 2020. "Portfolio optimisation of material purchase considering supply risk – A multi-objective programming model," International Journal of Production Economics, Elsevier, vol. 230(C).
    11. Cunha, Artur Lovato & Santos, Maristela Oliveira & Morabito, Reinaldo & Barbosa-Póvoa, Ana, 2018. "An integrated approach for production lot sizing and raw material purchasing," European Journal of Operational Research, Elsevier, vol. 269(3), pages 923-938.
    12. Marcos Mansano Furlan & Maristela Oliveira Santos, 2017. "BFO: a hybrid bees algorithm for the multi-level capacitated lot-sizing problem," Journal of Intelligent Manufacturing, Springer, vol. 28(4), pages 929-944, April.
    13. 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.

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