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A duality‐based relaxation and decomposition approach for inventory distribution systems

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  • Sumit Kunnumkal
  • Huseyin Topaloglu

Abstract

We propose a new method for making the inventory replenishment decisions in distribution systems. In particular, we consider distribution systems consisting of multiple retailers that face random demand and a warehouse that supplies the retailers. The method that we propose is based on formulating the distribution problem as a dynamic program, and relaxing the constraints that ensure the nonnegativity of the shipments to the retailers, by associating Lagrange multipliers with them. We show that our method provides lower bounds on the value functions, and a good set of values for the Lagrange multipliers can be obtained by maximizing a concave function in a relatively straightforward manner. Computational experiments indicate that our method can provide significant improvements over the traditional approaches for making the inventory replenishment decisions, in terms of both the tightness of the lower bounds on the value functions and the performance of the policies. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:55:y:2008:i:7:p:612-631
    DOI: 10.1002/nav.20306
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    References listed on IDEAS

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    Cited by:

    1. Archis Ghate & Robert L. Smith, 2013. "A Linear Programming Approach to Nonstationary Infinite-Horizon Markov Decision Processes," Operations Research, INFORMS, vol. 61(2), pages 413-425, April.
    2. Peter L. Jackson & John A. Muckstadt & Yuexing Li, 2019. "Multiperiod Stock Allocation via Robust Optimization," Management Science, INFORMS, vol. 65(2), pages 794-818, February.
    3. Lixin Tang & Gongshu Wang & Jiyin Liu & Jingyi Liu, 2011. "A combination of Lagrangian relaxation and column generation for order batching in steelmaking and continuous‐casting production," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(4), pages 370-388, June.
    4. 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.

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