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Integrated Lot Sizing in Serial Supply Chains with Production Capacities

Author

Listed:
  • Stan van Hoesel

    (Faculty of Economics and Business Administration, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands)

  • H. Edwin Romeijn

    (Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, Gainesville, Florida 32611-6595)

  • Dolores Romero Morales

    (Saïd Business School, University of Oxford, Park End Street, Oxford OX1 1HP, United Kingdom)

  • Albert P. M. Wagelmans

    (Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands)

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 concave cost functions. The model we study generalizes the uncapacitated serial single-item multilevel economic lot-sizing model by adding stationary production capacities at the manufacturer level. We present algorithms with a running time that is polynomial in the planning horizon when all cost functions are concave. In addition, we consider different transportation and inventory holding cost structures that yield improved running times: inventory holding cost functions that are linear and transportation cost functions that 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. While the running times of the algorithms are exponential in the number of levels in the supply chain in the general concave cost case, the running times are remarkably insensitive to the number of levels for the other two cost structures.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:51:y:2005:i:11:p:1706-1719
    DOI: 10.1287/mnsc.1050.0378
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    References listed on IDEAS

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    1. 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.
    2. Arthur M. Geoffrion & Richard F. Powers, 1995. "Twenty Years of Strategic Distribution System Design: An Evolutionary Perspective," Interfaces, INFORMS, vol. 25(5), pages 105-127, October.
    3. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    4. 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.
    5. Willard I. Zangwill, 1969. "A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System--A Network Approach," Management Science, INFORMS, vol. 15(9), pages 506-527, May.
    6. van den Heuvel, W. & Wagelmans, A.P.M., 2003. "A Geometric Algorithm to solve the NI/G/NI/ND Capacitated Lot-Sizing Problem in O(T^2) Time," ERIM Report Series Research in Management ERS-2003-066-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.
    7. 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.
    8. Michael Florian & Morton Klein, 1971. "Deterministic Production Planning with Concave Costs and Capacity Constraints," Management Science, INFORMS, vol. 18(1), pages 12-20, September.
    9. 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.
    10. 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.
    11. Thomas, Douglas J. & Griffin, Paul M., 1996. "Coordinated supply chain management," European Journal of Operational Research, Elsevier, vol. 94(1), pages 1-15, October.
    12. 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.
    13. Alok Aggarwal & James K. Park, 1993. "Improved Algorithms for Economic Lot Size Problems," Operations Research, INFORMS, vol. 41(3), pages 549-571, June.
    14. Chung-Yee Lee & Sila Çetinkaya & Wikrom Jaruphongsa, 2003. "A Dynamic Model for Inventory Lot Sizing and Outbound Shipment Scheduling at a Third-Party Warehouse," Operations Research, INFORMS, vol. 51(5), pages 735-747, October.
    15. Bruce C. Arntzen & Gerald G. Brown & Terry P. Harrison & Linda L. Trafton, 1995. "Global Supply Chain Management at Digital Equipment Corporation," Interfaces, INFORMS, vol. 25(1), pages 69-93, February.
    16. 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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