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A geometric algorithm to solve the NI/G/NI/ND capacitated lot-sizing problem in O(T2) time

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

Abstract

In this paper we consider the capacitated lot-sizing problem (CLSP) with linear costs. It is known that this problem is NP-hard, but there exist special cases that can be solved in polynomial time. The purpose of this paper is twofold. First, we derive a backward algorithm based on the forward algorithm by Chen et al. (1994), which solves the general CLSP. We give a problem instances that requires exponential running time using the backward algo- rithm. Second, we provide a new O(T2) algorithm for the CLSP with non-increasing setup cost, general holding cost, non-increasing production cost and non-decreasing capacities over time. This is done by adapting the backward algorithm. Numerical tests show the better performance of our algorithm compared to the algorithm proposed by Chung and Lin (1988).

Suggested Citation

  • van den Heuvel, W.J. & Wagelmans, A.P.M., 2003. "A geometric algorithm to solve the NI/G/NI/ND capacitated lot-sizing problem in O(T2) time," Econometric Institute Research Papers EI 2003-24, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:18017
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    References listed on IDEAS

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    1. Dong X. Shaw & Albert P. M. Wagelmans, 1998. "An Algorithm for Single-Item Capacitated Economic Lot Sizing with Piecewise Linear Production Costs and General Holding Costs," Management Science, INFORMS, vol. 44(6), pages 831-838, June.
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    8. van Hoesel, Stan & Wagelmans, Albert & Moerman, Bram, 1994. "Using geometric techniques to improve dynamic programming algorithms for the economic lot-sizing problem and extensions," European Journal of Operational Research, Elsevier, vol. 75(2), pages 312-331, June.
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    Cited by:

    1. Stan van Hoesel & H. Edwin Romeijn & Dolores Romero Morales & Albert P. M. Wagelmans, 2005. "Integrated Lot Sizing in Serial Supply Chains with Production Capacities," Management Science, INFORMS, vol. 51(11), pages 1706-1719, November.

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    More about this item

    Keywords

    capacitated lot-sizing problem; inventory; production;
    All these keywords.

    JEL classification:

    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management
    • R4 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics

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