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Bounds, Heuristics, and Approximations for Distribution Systems

Author

Listed:
  • Guillermo Gallego

    (Columbia University, 500 West 120th Street, MC 4704, New York, New York 10027)

  • Özalp Özer

    (Stanford University, Terman 314, 380 Panama Way, Stanford, California 94305)

  • Paul Zipkin

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

Abstract

This paper develops simple approximate methods to analyze a two-stage distribution system consisting of one warehouse and multiple retailers with stochastic demand. We consider local and central control schemes. The main ideas are based on relaxing and or decomposing the system into more manageable newsvendor-type subsystems. We also provide bounds on the optimal policy and the optimal expected cost. We show that one of the heuristics is asymptotically optimal in the number of retailers. These results provide practically useful techniques as well as insights into stock-positioning issues and the drivers of system performance.

Suggested Citation

  • Guillermo Gallego & Özalp Özer & Paul Zipkin, 2007. "Bounds, Heuristics, and Approximations for Distribution Systems," Operations Research, INFORMS, vol. 55(3), pages 503-517, June.
    • Handle: RePEc:inm:oropre:v:55:y:2007:i:3:p:503-517
    DOI: 10.1287/opre.1060.0373
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    References listed on IDEAS

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    Cited by:

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    2. Yazdekhasti, Amin & sharifzadeh, Shila & Ma, Junfeng, 2022. "A two-echelon two-indenture warranty distribution network development and optimization under batch-ordering inventory policy," International Journal of Production Economics, Elsevier, vol. 249(C).
    3. Qinan Wang & Sven Axsäter, 2013. "Fixed‐interval joint‐replenishment policies for distribution systems with multiple retailers and stochastic demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 637-651, December.
    4. Kim, Nayeon & Montreuil, Benoit & Klibi, Walid, 2022. "Inventory availability commitment under uncertainty in a dropshipping supply chain," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1155-1174.
    5. Sumit Kunnumkal & Huseyin Topaloglu, 2008. "A duality‐based relaxation and decomposition approach for inventory distribution systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(7), pages 612-631, October.
    6. Kunnumkal, Sumit & Topaloglu, Huseyin, 2011. "Linear programming based decomposition methods for inventory distribution systems," European Journal of Operational Research, Elsevier, vol. 211(2), pages 282-297, June.
    7. De Schrijver, Steven K. & Aghezzaf, El-Houssaine & Vanmaele, Hendrik, 2014. "Double precision rational approximation algorithm for the inverse standard normal second order loss function," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 247-253.
    8. Awi Federgruen & C. Daniel Guetta & Garud Iyengar, 2018. "Two‐echelon distribution systems with random demands and storage constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 594-618, December.
    9. Wang, Qinan & Wan, Guangyu, 2023. "Fixed-interval order-up-to policies and myopic optimal warehouse stock allocation for one-warehouse multiple-retailer systems," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1112-1124.
    10. Wang, Qinan, 2013. "A periodic-review inventory control policy for a two-level supply chain with multiple retailers and stochastic demand," European Journal of Operational Research, Elsevier, vol. 230(1), pages 53-62.
    11. Felipe Caro & Jérémie Gallien, 2010. "Inventory Management of a Fast-Fashion Retail Network," Operations Research, INFORMS, vol. 58(2), pages 257-273, April.

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