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Formulations and heuristics for the multi-item uncapacitated lot-sizing problem with inventory bounds

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  • Rafael A. Melo
  • Celso C. Ribeiro

Abstract

We consider the multi-item uncapacitated lot-sizing problem with inventory bounds, in which a production plan for multiple items has to be determined considering that they share a storage capacity. We present (a) a shortest path formulation and (b) a formulation based on the a priori addition of valid inequalities, which are compared with a facility location formulation available in the literature. Two easy-to-implement mixed integer programming heuristic frameworks are also presented, (a) a rounding scheme and (b) a relax-and-fix approach performed in a time partitioning fashion. Computational experiments are performed to evaluate the different approaches. The numerical results show that the proposed relax-and-fix heuristic outperforms all other approaches. Its solutions are within 4.0% of optimality in less than 10 minutes of running time for all tested instances, with mean gaps in the order of 2.1 and 1.8% for instances with more relaxed and tighter capacities, respectively. The obtained solutions were always better than those obtained by a commercial MIP solver running for one hour using any of the available formulations.

Suggested Citation

  • Rafael A. Melo & Celso C. Ribeiro, 2017. "Formulations and heuristics for the multi-item uncapacitated lot-sizing problem with inventory bounds," International Journal of Production Research, Taylor & Francis Journals, vol. 55(2), pages 576-592, January.
    • Handle: RePEc:taf:tprsxx:v:55:y:2017:i:2:p:576-592
    DOI: 10.1080/00207543.2016.1215567
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    Cited by:

    1. Jing, Fuying & Chao, Xiangrui, 2021. "A dynamic lot size model with perishable inventory and stockout," Omega, Elsevier, vol. 103(C).
    2. Zhou, Shenghan & Zhou, Yuliang & Zuo, Xiaorong & Xiao, Yiyong & Cheng, Yang, 2018. "Modeling and solving the constrained multi-items lot-sizing problem with time-varying setup cost," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 202-207.

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