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Heuristics for a One-Warehouse Multiretailer Distribution Problem with Performance Bounds

Author

Listed:
  • Yale Herer

    (Technion-Israel Institute of Technology, Haifa, Israel)

  • Robin Roundy

    (Cornell University, Ithaca, New York)

Abstract

We investigate the one warehouse multiretailer distribution problem with traveling salesman tour vehicle routing costs. We model the system in the framework of the more general production/distribution system with arbitrary non-negative monotone joint order costs. We develop polynomial time heuristics whose policy costs are provably close to the cost of an optimal policy. In particular, we show that given a submodular function which is close to the true order cost then we can find a power-of-two policy whose cost is only moderately greater than the cost of an optimal policy. Since such submodular approximations exist for traveling salesman tour vehicle routing costs we present a detailed description of heuristics for the one warehouse multiretailer distribution problem.We formulate a nonpolynomial dynamic program that computes optimal power-of-two policies for the one warehouse multiretailer system assuming only that the order costs are non-negative monotone.Finally, we perform computational tests which compare our heuristics to optimal power of two policies for problems of up to sixteen retailers. We also perform computational tests on larger problems; these tests give us insight into what policies one should employ.

Suggested Citation

  • Yale Herer & Robin Roundy, 1997. "Heuristics for a One-Warehouse Multiretailer Distribution Problem with Performance Bounds," Operations Research, INFORMS, vol. 45(1), pages 102-115, February.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:1:p:102-115
    DOI: 10.1287/opre.45.1.102
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    Citations

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    Cited by:

    1. Yu Zhang & Vidyadhar Kulkarni, 2018. "Automated Teller Machine Replenishment Policies with Submodular Costs," Manufacturing & Service Operations Management, INFORMS, vol. 20(3), pages 517-530, July.
    2. Jaeheon Jung & Kamlesh Mathur, 2007. "An Efficient Heuristic Algorithm for a Two-Echelon Joint Inventory and Routing Problem," Transportation Science, INFORMS, vol. 41(1), pages 55-73, February.
    3. Jia Shu, 2010. "An Efficient Greedy Heuristic for Warehouse-Retailer Network Design Optimization," Transportation Science, INFORMS, vol. 44(2), pages 183-192, May.
    4. Chung-Piaw Teo & Jia Shu, 2004. "Warehouse-Retailer Network Design Problem," Operations Research, INFORMS, vol. 52(3), pages 396-408, June.
    5. N Rizk & A Martel & S D'Amours, 2008. "Synchronized production–distribution planning in a single-plant multi-destination network," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(1), pages 90-104, January.
    6. Anton J. Kleywegt & Vijay S. Nori & Martin W. P. Savelsbergh, 2004. "Dynamic Programming Approximations for a Stochastic Inventory Routing Problem," Transportation Science, INFORMS, vol. 38(1), pages 42-70, February.
    7. Luca Bertazzi, 2008. "Analysis of Direct Shipping Policies in an Inventory-Routing Problem with Discrete Shipping Times," Management Science, INFORMS, vol. 54(4), pages 748-762, April.
    8. Li, Xiuhui & Wang, Qinan, 2007. "Coordination mechanisms of supply chain systems," European Journal of Operational Research, Elsevier, vol. 179(1), pages 1-16, May.
    9. Leandro C. Coelho & Jean-François Cordeau & Gilbert Laporte, 2014. "Thirty Years of Inventory Routing," Transportation Science, INFORMS, vol. 48(1), pages 1-19, February.

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