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Approximation Procedures for the One-Warehouse Multi-Retailer System

Author

Listed:
  • Lu Lu

    (Department of Industrial and Systems Engineering, The Ohio State University, Columbus, Ohio 43210)

  • Marc E. Posner

    (Department of Industrial and Systems Engineering, The Ohio State University, Columbus, Ohio 43210)

Abstract

Two heuristic procedures for a one-warehouse multi-retailer system are developed. Based on the accuracy desired, the first heuristic evaluates a specified number of points. The relative error is within a bound that approaches 1/(\root 2 ln 2) - 1 \approx 2.014%. The complexity of the heuristic is O(n) for a fixed number of evaluations. Although our bound only approaches the one of Roundy (1985), when only a small number of points are evaluated, our method is faster. We show that the bound for our procedure and two bounds proposed by Roundy (1985) are tight. The second heuristic pertains to a class of polities called stationary interval policies. For this class of policies, we develop a fully polynomial-time approximation scheme where the relative error is within \varepsilon > 0, and the computational effort increases as a linear function of 1/\root \varepsilon . Computational experiments show that these heuristics perform well in practice.

Suggested Citation

  • Lu Lu & Marc E. Posner, 1994. "Approximation Procedures for the One-Warehouse Multi-Retailer System," Management Science, INFORMS, vol. 40(10), pages 1305-1316, October.
    • Handle: RePEc:inm:ormnsc:v:40:y:1994:i:10:p:1305-1316
    DOI: 10.1287/mnsc.40.10.1305
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    Citations

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    Cited by:

    1. Lee, Dong Joo & Jeong, In-Jae, 2010. "A distributed coordination for a single warehouse-multiple retailer problem under private information," International Journal of Production Economics, Elsevier, vol. 125(1), pages 190-199, May.
    2. Wen-Tsung Ho & Shu-Fang Lai & Yun-Kuei Huang, 2014. "An Optimal Mixed Batch Shipment Policy for Multiple Items in a Single-Supplier Multiple-Retailer Integrated System," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 636-658, February.
    3. Erenguc, S. Selcuk & Simpson, N. C. & Vakharia, Asoo J., 1999. "Integrated production/distribution planning in supply chains: An invited review," European Journal of Operational Research, Elsevier, vol. 115(2), pages 219-236, June.
    4. Karabati, Selcuk & Sayin, Serpil, 2008. "Single-supplier/multiple-buyer supply chain coordination: Incorporating buyers' expectations under vertical information sharing," European Journal of Operational Research, Elsevier, vol. 187(3), pages 746-764, June.
    5. Shiman Ding & Philip M. Kaminsky, 2020. "Centralized and Decentralized Warehouse Logistics Collaboration," Manufacturing & Service Operations Management, INFORMS, vol. 22(4), pages 812-831, July.
    6. Wee, H. M. & Yang, P. C., 2004. "The optimal and heuristic solutions of a distribution network," European Journal of Operational Research, Elsevier, vol. 158(3), pages 626-632, November.
    7. Tamar Cohen-Hillel & Liron Yedidsion, 2018. "The Periodic Joint Replenishment Problem Is Strongly 𝒩𝒫-Hard," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1269-1289, November.
    8. Yang, P. C. & Wee, H. M., 2002. "A single-vendor and multiple-buyers production-inventory policy for a deteriorating item," European Journal of Operational Research, Elsevier, vol. 143(3), pages 570-581, December.
    9. Chu, Chi-Leung & Leon, V. Jorge, 2008. "Power-of-two single-warehouse multi-buyer inventory coordination with private information," International Journal of Production Economics, Elsevier, vol. 111(2), pages 562-574, February.
    10. Chung-Piaw Teo & Dimitris Bertsimas, 2001. "Multistage Lot Sizing Problems via Randomized Rounding," Operations Research, INFORMS, vol. 49(4), pages 599-608, August.
    11. Adeinat, Hamza & Pazhani, Subramanian & Mendoza, Abraham & Ventura, Jose A., 2022. "Coordination of pricing and inventory replenishment decisions in a supply chain with multiple geographically dispersed retailers," International Journal of Production Economics, Elsevier, vol. 248(C).

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