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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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    4. Toy, Ayhan Özgür & Berk, Emre, 2013. "Dynamic lot sizing for a warm/cold process: Heuristics and insights," International Journal of Production Economics, Elsevier, vol. 145(1), pages 53-66.
    5. 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.
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    7. 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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