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An efficient approach for solving the lot-sizing problem with time-varying storage capacities

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  • Gutiérrez, J.
  • Sedeí±o-Noda, A.
  • Colebrook, M.
  • Sicilia, J.

Abstract

We address the dynamic lot size problem assuming time-varying storage capacities. The planning horizon is divided into T periods and stockouts are not allowed. Moreover, for each period, we consider a setup cost, a holding unit cost and a production/ordering unit cost, which can vary through the planning horizon. Although this model can be solved using O(T3) algorithms already introduced in the specialized literature, we show that under this cost structure an optimal solution can be obtained in O(T log T) time. In addition, we show that when production/ordering unit costs are assumed to be constant (i.e., the Wagner-Whitin case), there exists an optimal plan satisfying the Zero Inventory Ordering (ZIO) property.

Suggested Citation

  • Gutiérrez, J. & Sedeí±o-Noda, A. & Colebrook, M. & Sicilia, J., 2008. "An efficient approach for solving the lot-sizing problem with time-varying storage capacities," European Journal of Operational Research, Elsevier, vol. 189(3), pages 682-693, September.
    • Handle: RePEc:eee:ejores:v:189:y:2008:i:3:p:682-693
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    References listed on IDEAS

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    1. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    2. Alan S. Manne, 1958. "Programming of Economic Lot Sizes," Management Science, INFORMS, vol. 4(2), pages 115-135, January.
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    Cited by:

    1. Fan, Jie & Wang, Guoqing, 2018. "Joint optimization of dynamic lot and warehouse sizing problems," European Journal of Operational Research, Elsevier, vol. 267(3), pages 849-854.
    2. van den Heuvel, Wilco & Gutiérrez, José Miguel & Hwang, Hark-Chin, 2011. "Note on "An efficient approach for solving the lot-sizing problem with time-varying storage capacities"," European Journal of Operational Research, Elsevier, vol. 213(2), pages 455-457, September.
    3. José M. Gutiérrez & Beatriz Abdul-Jalbar & Joaquín Sicilia & Inmaculada Rodríguez-Martín, 2021. "Effective Algorithms for the Economic Lot-Sizing Problem with Bounded Inventory and Linear Fixed-Charge Cost Structure," Mathematics, MDPI, vol. 9(6), pages 1-21, March.
    4. Hark‐Chin Hwang & Wilco van den Heuvel, 2012. "Improved algorithms for a lot‐sizing problem with inventory bounds and backlogging," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(3‐4), pages 244-253, April.
    5. Hwang, H.C., 2009. "Economic Lot-Sizing Problem with Bounded Inventory and Lost-Sales," Econometric Institute Research Papers EI 2009-01, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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