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An O(T 2 ) Algorithm for the NI/G/NI/ND Capacitated Lot Size Problem

Author

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  • Chia-Shin Chung

    (Department of Quantitative Business Analysis, Cleveland State University, Cleveland, Ohio 44115)

  • Chien-Hua Mike Lin

    (Department of Computer and Information Science, Cleveland State University, Cleveland, Ohio 44115)

Abstract

In this paper, we study a class of the capacitated dynamic lot size problem, where, over time, the setup costs are nonincreasing, the unit holding costs have arbitrary pattern, the unit production costs are nonincreasing and the capacities are nondecreasing. We investigate the properties of the optimal solution for the problem and develop the concept of candidate subplan. It is proven that only the candidate subplans need to be examined in searching for an optimal solution. A dynamic programming algorithm, incorporating the concept of candidate subplan, is then devised which has run time complexity of O(T 2 ).

Suggested Citation

  • Chia-Shin Chung & Chien-Hua Mike Lin, 1988. "An O(T 2 ) Algorithm for the NI/G/NI/ND Capacitated Lot Size Problem," Management Science, INFORMS, vol. 34(3), pages 420-426, March.
    • Handle: RePEc:inm:ormnsc:v:34:y:1988:i:3:p:420-426
    DOI: 10.1287/mnsc.34.3.420
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    Citations

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    Cited by:

    1. Chubanov, Sergei & Kovalyov, Mikhail Y. & Pesch, Erwin, 2008. "A single-item economic lot-sizing problem with a non-uniform resource: Approximation," European Journal of Operational Research, Elsevier, vol. 189(3), pages 877-889, September.
    2. Jinwen Ou, 2012. "Economic lot sizing with constant capacities and concave inventory costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(7), pages 497-501, October.
    3. 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.
    4. Okhrin, Irena & Richter, Knut, 2011. "An O(T3) algorithm for the capacitated lot sizing problem with minimum order quantities," European Journal of Operational Research, Elsevier, vol. 211(3), pages 507-514, June.
    5. Berk, Emre & Toy, Ayhan Ozgur & Hazir, Oncu, 2008. "Single item lot-sizing problem for a warm/cold process with immediate lost sales," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1251-1267, June.
    6. 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.
    7. van Hoesel, C.P.M. & Wagelmans, A., 1997. "Fully polynomial approximation schemes for single-item capacitated economic lot-sizing problems," Research Memorandum 029, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    8. van Hoesel, C.P.M. & Romeijn, H.E. & Romero Morales, M.D. & Wagelmans, A., 2002. "Polynomial time algorithms for some multi-level lot-sizing problems with production capacities," Research Memorandum 018, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    9. 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.
    10. Shaw, D.X. & Wagelmans, A.P.M., 1995. "An Algorithm for Single-item Capacitated Economic Lot Sizing with Piecewise Linear Production Costs and General Holding Costs," Econometric Institute Research Papers EI 9526-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    11. Hwang, Hark-Chin & Kang, Jangha, 2020. "The two-level lot-sizing problem with outbound shipment," Omega, Elsevier, vol. 90(C).

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    Keywords

    lot sizing; dynamic programming;

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