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The single item uncapacitated lot-sizing problem with time-dependent batch sizes: NP-hard and polynomial cases

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  • Akbalik, Ayse
  • Rapine, Christophe

Abstract

This paper considers the uncapacitated lot sizing problem with batch delivery, focusing on the general case of time-dependent batch sizes. We study the complexity of the problem, depending on the other cost parameters, namely the setup cost, the fixed cost per batch, the unit procurement cost and the unit holding cost. We establish that if any one of the cost parameters is allowed to be time-dependent, the problem is NP-hard. On the contrary, if all the cost parameters are stationary, and assuming no unit holding cost, we show that the problem is polynomially solvable in time O(T3), where T denotes the number of periods of the horizon. We also show that, in the case of divisible batch sizes, the problem with time varying setup costs, a stationary fixed cost per batch and no unit procurement nor holding cost can be solved in time O(T3 logT).

Suggested Citation

  • Akbalik, Ayse & Rapine, Christophe, 2013. "The single item uncapacitated lot-sizing problem with time-dependent batch sizes: NP-hard and polynomial cases," European Journal of Operational Research, Elsevier, vol. 229(2), pages 353-363.
    • Handle: RePEc:eee:ejores:v:229:y:2013:i:2:p:353-363
    DOI: 10.1016/j.ejor.2013.02.052
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Chung-Lun Li & Qingying Li, 2016. "Polynomial-Time Solvability of Dynamic Lot Size Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-20, June.
    3. Hnaien, Faicel & Afsar, Hasan Murat, 2017. "Robust single-item lot-sizing problems with discrete-scenario lead time," International Journal of Production Economics, Elsevier, vol. 185(C), pages 223-229.
    4. Farhat, Mlouka & Akbalik, Ayse & Hadj-Alouane, Atidel B. & Sauer, Nathalie, 2019. "Lot sizing problem with batch ordering under periodic buyback contract and lost sales," International Journal of Production Economics, Elsevier, vol. 208(C), pages 500-511.
    5. Akbalik, Ayse & Hadj-Alouane, Atidel B. & Sauer, Nathalie & Ghribi, Houcem, 2017. "NP-hard and polynomial cases for the single-item lot sizing problem with batch ordering under capacity reservation contract," European Journal of Operational Research, Elsevier, vol. 257(2), pages 483-493.
    6. Akbalik, Ayse & Rapine, Christophe, 2018. "Lot sizing problem with multi-mode replenishment and batch delivery," Omega, Elsevier, vol. 81(C), pages 123-133.
    7. Ou, Jinwen & Feng, Jiejian, 2019. "Production lot-sizing with dynamic capacity adjustment," European Journal of Operational Research, Elsevier, vol. 272(1), pages 261-269.
    8. Aria Shahsavar & Nima Zoraghi & Babak Abbasi, 2018. "Integration of resource investment problem with quantity discount problem in material ordering for minimizing resource costs of projects," Operational Research, Springer, vol. 18(2), pages 315-342, July.

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