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Models and Lagrangian heuristics for a two-level lot-sizing problem with bounded inventory

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Abstract

We consider a two-level dynamic lot-sizing problem where the first level consists of N finished products competing for a single type of purchased raw material in the second level. While the procurement and production capacities are unlimited, the storage capacity of the raw material is limited and must be carefully managed. The goal is to simultaneously determine a replenishment plan for the raw material and optimal production plans for the finished products on a horizon of T periods while minimizing production, purchasing, setup and inventory holding costs. The problem is modeled using mixed-integer linear programs and solved using both a Lagrangian relaxation-based heuristic and a commercial mixed-integer linear programming solver. Learning capabilities are integrated in the Lagrangian relaxation to update step size in the subgradient algorithm. The computational results show that the Lagrangian heuristic outperforms the solver on different formulations, in particular for large problems with long time horizons.

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Acknowledgments

The authors would like to thank anonymous referees for their careful reading, thorough reviews and valuable comments that helped us improving the quality of the paper. The first author would like to express his gratitude to the University of Sharjah (U.A.E.) for its financial support while the author was a faculty member at the department of Industrial Engineering and Management.

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Authors and Affiliations

  1. Département d’Automatique, Productique et Informatique, Ecole des Mines de Nantes, IRCCyN (CNRS UMR 6597), 4, rue Alfred Kastler, BP 20722, 44307, Nantes Cedex 3, France

    Nadjib Brahimi

  2. Department of Manufacturing Sciences and Logistics, Ecole des Mines de Saint-Etienne (CNRS UMR 6158 LIMOS), CMP Campus G. Charpak Provence - 880, Route de Mimet, F-13541, Gardanne, France

    Nabil Absi & Stéphane Dauzère-Pérès

  3. LIP6 - UPMC, Sorbonne University, Univ. Paris 06 (CNRS UMR 7606), 75005, Paris, France

    Safia Kedad-Sidhoum

Authors
  1. Nadjib Brahimi
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  2. Nabil Absi
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  3. Stéphane Dauzère-Pérès
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  4. Safia Kedad-Sidhoum
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Corresponding author

Correspondence to Nadjib Brahimi.

Additional information

N. Brahimi: Most of this work was done while N. Brahimi was at the department of Industrial Engineering and Management of the University of Sharjah and during his summer stays at the CMP of Gardanne supported by the University of Sharjah, U.A.E.

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Brahimi, N., Absi, N., Dauzère-Pérès, S. et al. Models and Lagrangian heuristics for a two-level lot-sizing problem with bounded inventory. OR Spectrum 37, 983–1006 (2015). https://doi.org/10.1007/s00291-015-0404-0

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