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Polynomial Time Algorithms For Some Multi-Level Lot-Sizing Problems With Production Capacities

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Listed:
  • van Hoesel, S.
  • Romeijn, H.E.
  • Romero Morales, D.
  • Wagelmans, A.P.M.

Abstract

We consider a model for a serial supply chain in which production, inventory, and transportation decisions are integrated, in the presence of production capacities and for different transportation cost functions. The model we study is a generalization of the traditional single-item economic lot-sizing model, adding stationary production capacities at the manufacturer, as well as multiple intermediate storage levels (including the retailer level), and transportation between these levels. Allowing for general concave production costs and linear holding costs, we provide polynomialtime algorithms for the cases where the transportation costs are either linear, or are concave with a fixed-charge structure. In the latter case, we make the additional common and reasonable assumption that the variable transportation and inventory costs are such that holding inventories at higher levels in the supply chain is more attractive from a variable cost perspective. The running times of the algorithms are remarkably insensitive to the number of levels in the supply chain.

Suggested Citation

  • van Hoesel, S. & Romeijn, H.E. & Romero Morales, D. & Wagelmans, A.P.M., 2002. "Polynomial Time Algorithms For Some Multi-Level Lot-Sizing Problems With Production Capacities," ERIM Report Series Research in Management ERS-2002-59-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
  • Handle: RePEc:ems:eureri:213
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    References listed on IDEAS

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    1. Gabriel R. Bitran & Horacio H. Yanasse, 1982. "Computational Complexity of the Capacitated Lot Size Problem," Management Science, INFORMS, vol. 28(10), pages 1174-1186, October.
    2. Michael Florian & Morton Klein, 1971. "Deterministic Production Planning with Concave Costs and Capacity Constraints," Management Science, INFORMS, vol. 18(1), pages 12-20, September.
    3. Thomas, Douglas J. & Griffin, Paul M., 1996. "Coordinated supply chain management," European Journal of Operational Research, Elsevier, vol. 94(1), pages 1-15, October.
    4. Albert Wagelmans & Stan van Hoesel & Antoon Kolen, 1992. "Economic Lot Sizing: An O(n log n) Algorithm That Runs in Linear Time in the Wagner-Whitin Case," Operations Research, INFORMS, vol. 40(1-supplem), pages 145-156, February.
    5. Kenneth R. Baker & Paul Dixon & Michael J. Magazine & Edward A. Silver, 1978. "An Algorithm for the Dynamic Lot-Size Problem with Time-Varying Production Capacity Constraints," Management Science, INFORMS, vol. 24(16), pages 1710-1720, December.
    6. Chandra, Pankaj & Fisher, Marshall L., 1994. "Coordination of production and distribution planning," European Journal of Operational Research, Elsevier, vol. 72(3), pages 503-517, February.
    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.
    9. M. Florian & J. K. Lenstra & A. H. G. Rinnooy Kan, 1980. "Deterministic Production Planning: Algorithms and Complexity," Management Science, INFORMS, vol. 26(7), pages 669-679, July.
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    Cited by:

    1. Wei Huang & H. Edwin Romeijn & Joseph Geunes, 2005. "The continuous‐time single‐sourcing problem with capacity expansion opportunities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(3), pages 193-211, April.
    2. Jans, R.F. & Degraeve, Z., 2005. "Modeling Industrial Lot Sizing Problems: A Review," ERIM Report Series Research in Management ERS-2005-049-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.

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    More about this item

    Keywords

    Lot-Sizing; dynamic programming; integration of production planning and transportation; polynomial time algorithms;
    All these keywords.

    JEL classification:

    • 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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