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An O(Tˆ3) algorithm for the capacitated lot sizing problem with minimum order quantities

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  • Okhrin, Irena
  • Richter, Knut

Abstract

This paper explores a single-item capacitated lot sizing problem with minimum order quantity, which plays the role of minor set-up cost. We work out the necessary and suffcient solvability conditions and apply the general dynamic programming technique to develop an O(T³) exact algorithm that is based on the concept of minimal sub-problems. An investigation of the properties of the optimal solution structure allows us to construct explicit solutions to the obtained sub-problems and prove their optimality. In this way, we reduce the complexity of the algorithm considerably and confirm its efficiency in an extensive computational study.

Suggested Citation

  • Okhrin, Irena & Richter, Knut, 2010. "An O(Tˆ3) algorithm for the capacitated lot sizing problem with minimum order quantities," Discussion Papers 284, European University Viadrina Frankfurt (Oder), Department of Business Administration and Economics.
  • Handle: RePEc:zbw:euvwdp:284
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Hellion, Bertrand & Mangione, Fabien & Penz, Bernard, 2012. "A polynomial time algorithm to solve the single-item capacitated lot sizing problem with minimum order quantities and concave costs," European Journal of Operational Research, Elsevier, vol. 222(1), pages 10-16.
    2. repec:eee:ejores:v:263:y:2017:i:3:p:838-863 is not listed on IDEAS
    3. Hong, Zhaofu & Chu, Chengbin & Yu, Yugang, 2016. "Dual-mode production planning for manufacturing with emission constraints," European Journal of Operational Research, Elsevier, vol. 251(1), pages 96-106.
    4. Zhu, Han & Liu, Xing & Chen, Youhua (Frank), 2015. "Effective inventory control policies with a minimum order quantity and batch ordering," International Journal of Production Economics, Elsevier, vol. 168(C), pages 21-30.
    5. Absi, Nabil & Dauzère-Pérès, Stéphane & Kedad-Sidhoum, Safia & Penz, Bernard & Rapine, Christophe, 2016. "The single-item green lot-sizing problem with fixed carbon emissions," European Journal of Operational Research, Elsevier, vol. 248(3), pages 849-855.
    6. Ou, Jinwen, 2017. "Improved exact algorithms to economic lot-sizing with piecewise linear production costs," European Journal of Operational Research, Elsevier, vol. 256(3), pages 777-784.
    7. Sazvar, Z. & Mirzapour Al-e-hashem, S.M.J. & Govindan, K. & Bahli, B., 2016. "A novel mathematical model for a multi-period, multi-product optimal ordering problem considering expiry dates in a FEFO system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 93(C), pages 232-261.
    8. 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.

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    Keywords

    production planning; capacitated lot sizing problem; single item; minimum order quantities; capacity constraints; dynamic programming;

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