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98%-Effective Lot-Sizing for Assembly Inventory Systems with Backlogging

Author

Listed:
  • Daning Sun

    (The University College of the Cariboo, Kamloops, B.C., Canada, and University of British Columbia)

  • Derek Atkins

    (University of British Columbia, Vancouver, B.C., Canada)

Abstract

In the previous work, we have shown that for a production/inventory system arranged in series with backlogging at its final product, the total cost of the best power-of-two frequency lot-size heuristic is within 6% of the optimal (or 2% if the base period is allowed to vary). In this paper, we extend our results to an assembly production/inventory system with constant external demand at its final product with backlogging allowed. By using a submodular property, we show that the total cost of any feasible policy is bounded below by finding the minimum of a set of series systems. In this way, we can get a best power-of-two frequency policy that is within 2% of the optimal: However, the number of series systems to be considered can be proportional to, in the worst case, the factorial of n (the number of nodes in the assembly system). As a consequence, this reduction cannot give us a polynomial algorithm and we have to use a different approach. By using a series of transformations, we reduce our problem to a special case of a polymatroidal network flow problem. The lower bound and the optimal power-of-two frequency policy for assembly systems with backlogging can then be found in O ( n 6 ) time.

Suggested Citation

  • Daning Sun & Derek Atkins, 1997. "98%-Effective Lot-Sizing for Assembly Inventory Systems with Backlogging," Operations Research, INFORMS, vol. 45(6), pages 940-951, December.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:6:p:940-951
    DOI: 10.1287/opre.45.6.940
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    Cited by:

    1. Abdul-Jalbar, Beatriz & Gutiérrez, José M. & Sicilia, Joaquín, 2009. "A two-echelon inventory/distribution system with power demand pattern and backorders," International Journal of Production Economics, Elsevier, vol. 122(2), pages 519-524, December.
    2. Daning Sun, 2004. "Existence and Properties of Optimal Production and Inventory Policies," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 923-934, November.
    3. Daning Sun & Maurice Queyranne, 2002. "Production and Inventory Model Using Net Present Value," Operations Research, INFORMS, vol. 50(3), pages 528-537, June.
    4. Li, Xiuhui & Wang, Qinan, 2007. "Coordination mechanisms of supply chain systems," European Journal of Operational Research, Elsevier, vol. 179(1), pages 1-16, May.

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