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Worst-Case Analysis for a General Class of Online Lot-Sizing Heuristics

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  • Wilco Van den Heuvel

    (Econometric Institute and Erasmus Research Institute of Management, Erasmus University Rotterdam, 3000 DR Rotterdam, The Netherlands)

  • Albert P. M. Wagelmans

    (Econometric Institute and Erasmus Research Institute of Management, Erasmus University Rotterdam, 3000 DR Rotterdam, The Netherlands)

Abstract

In this paper, we analyze the worst-case performance of heuristics for the classical economic lot-sizing problem with time-invariant cost parameters. We consider a general class of online heuristics that is often applied in a rolling-horizon environment. We develop a procedure to systematically construct worst-case instances for a fixed time horizon and use it to derive worst-case problem instances for an infinite time horizon. Our analysis shows that any online heuristic has a worst-case ratio of at least 2.

Suggested Citation

  • Wilco Van den Heuvel & Albert P. M. Wagelmans, 2010. "Worst-Case Analysis for a General Class of Online Lot-Sizing Heuristics," Operations Research, INFORMS, vol. 58(1), pages 59-67, February.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:1:p:59-67
    DOI: 10.1287/opre.1080.0662
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    References listed on IDEAS

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    1. Sven Axsäter, 1988. "A Sequential Lot Sizing Heuristic with Optimal Average Performance," Management Science, INFORMS, vol. 34(11), pages 1324-1332, November.
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    Cited by:

    1. Wenqiang Dai & Meng Zheng & Xu Chen & Zhuolin Yang, 0. "Online economic ordering problem for deteriorating items with limited price information," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-23.
    2. Adam N. Elmachtoub & Retsef Levi, 2016. "Supply Chain Management with Online Customer Selection," Operations Research, INFORMS, vol. 64(2), pages 458-473, April.
    3. Absi, Nabil & van den Heuvel, Wilco, 2019. "Worst case analysis of Relax and Fix heuristics for lot-sizing problems," European Journal of Operational Research, Elsevier, vol. 279(2), pages 449-458.
    4. J. Brinkhuis, 2009. "Convex Duality and Calculus: Reduction to Cones," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 439-453, December.
    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.
    6. Niv Buchbinder & Tracy Kimbrel & Retsef Levi & Konstantin Makarychev & Maxim Sviridenko, 2013. "Online Make-to-Order Joint Replenishment Model: Primal-Dual Competitive Algorithms," Operations Research, INFORMS, vol. 61(4), pages 1014-1029, August.
    7. Massonnet, G. & Gayon, J.-P. & Rapine, C., 2014. "Approximation algorithms for deterministic continuous-review inventory lot-sizing problems with time-varying demand," European Journal of Operational Research, Elsevier, vol. 234(3), pages 641-649.
    8. van den Heuvel, W.J. & Wagelmans, A.P.M., 2008. "A holding cost bound for the economic lot-sizing problem with time-invariant cost parameters," Econometric Institute Research Papers EI 2008-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    9. Guanqun Ni, 2023. "An improved online replenishment policy and its competitive ratio analysis for a purchase-to-order seller," Journal of Combinatorial Optimization, Springer, vol. 46(2), pages 1-14, September.
    10. Adam N. Elmachtoub & Retsef Levi, 2015. "From Cost Sharing Mechanisms to Online Selection Problems," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 542-557, March.
    11. Wenqiang Dai & Meng Zheng & Xu Chen & Zhuolin Yang, 2022. "Online economic ordering problem for deteriorating items with limited price information," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2246-2268, November.

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