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A holding cost bound for the economic lot-sizing problem with time-invariant cost parameters

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  • van den Heuvel, W.J.
  • Wagelmans, A.P.M.

Abstract

In this paper we derive a new structural property for an optimal solution of the economic lot-sizing problem with time-invariant cost parameters. We show that the total holding cost in an order interval of an optimal solution is bounded from above by a quantity proportional to the setup cost and the logarithm of the number of periods in the interval. Since we can also show that this bound is tight, this is in contrast to the optimality property of the economic order quantity (EOQ) model, where setup cost and holding cost are perfectly balanced. Furthermore, we show that this property can be used for the design of a new heuristic and that the result may be useful in worst case analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:ems:eureir:12548
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    References listed on IDEAS

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    1. 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.
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    5. Axsater, Sven, 1982. "Worst case performance for lot sizing heuristics," European Journal of Operational Research, Elsevier, vol. 9(4), pages 339-343, April.
    6. Hoesel, C. P. M. Van & Wagelmans, A. P. M., 2000. "Parametric analysis of setup cost in the economic lot-sizing model without speculative motives," International Journal of Production Economics, Elsevier, vol. 66(1), pages 13-22, June.
    7. Awi Federgruen & Michal Tzur, 1991. "A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0(n log n) or 0(n) Time," Management Science, INFORMS, vol. 37(8), pages 909-925, August.
    8. Alok Aggarwal & James K. Park, 1993. "Improved Algorithms for Economic Lot Size Problems," Operations Research, INFORMS, vol. 41(3), pages 549-571, June.
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    1. 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.
    2. Hark-Chin Hwang & Wilco van den Heuvel & Albert P. M. Wagelmans, 2023. "Multilevel Lot-Sizing with Inventory Bounds," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1470-1490, November.

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