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A simple FPTAS for a single-item capacitated economic lot-sizing problem with a monotone cost structure

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  • Ng, C.T.
  • Kovalyov, Mikhail Y.
  • Cheng, T.C.E.

Abstract

The single-item capacitated economic lot-sizing (CELS) problem is a fundamental problem of production and inventory management. The first fully polynomial approximation scheme (FPTAS) for this problem with concave cost functions was developed by Van Hoesel and Wagelmans [C.P.M. Van Hoesel, A.P.M. Wagelmans, Fully polynomial approximation schemes for single-item capacitated economic lot-sizing problems, Mathematics of Operations Research 26 (2001) 339-357]. Chubanov et al. [S. Chubanov, M.Y. Kovalyov, E. Pesch, An FPTAS for a single-item capacitated economic lot-sizing problem, Mathematical Programming Series A 106 (2006) 453-466] later presented a sophisticated FPTAS for the general case of the CELS problem with a monotone cost structure. In this paper, we present a better FPTAS for this case. The ideas and presentation of our FPTAS are simple and straightforward. Its running time is about times faster than that of Chubanov et al. [5], where n is the number of production periods and [epsilon] is the anticipated relative error of the approximate solution.

Suggested Citation

  • Ng, C.T. & Kovalyov, Mikhail Y. & Cheng, T.C.E., 2010. "A simple FPTAS for a single-item capacitated economic lot-sizing problem with a monotone cost structure," European Journal of Operational Research, Elsevier, vol. 200(2), pages 621-624, January.
    • Handle: RePEc:eee:ejores:v:200:y:2010:i:2:p:621-624
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    Cited by:

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    2. 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.
    3. 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.
    4. Jing, Fuying & Chao, Xiangrui, 2022. "Forecast horizons for a two-echelon dynamic lot-sizing problem," Omega, Elsevier, vol. 110(C).
    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. Xu, Zhou, 2012. "A strongly polynomial FPTAS for the symmetric quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 218(2), pages 377-381.
    8. Nir Halman & James B. Orlin & David Simchi-Levi, 2012. "Approximating the Nonlinear Newsvendor and Single-Item Stochastic Lot-Sizing Problems When Data Is Given by an Oracle," Operations Research, INFORMS, vol. 60(2), pages 429-446, April.

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