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The one‐period, N‐location distribution problem

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  • Uday S. Karmarkar
  • Nitin R. Patel

Abstract

This paper studies the one‐period, general network distribution problem with linear costs. The approach is to decompose the problem into a transportation problem that represents a stocking decision, and into decoupled newsboy problems that represent the realization of demand with the usual associated holding and shortage costs. This approach leads to a characterization of optimal policies in terms of the dual of the transportation problem. This method is not directly suitable for the solution for large problems, but the exact solution for small problems can be obtained. For the numerical solutions of large problems, the problem has been formulated as a linear program with column generation. This latter approach is quite robust in the sense that it is easily extended to incorporate capacity constraints and the multiproduct case.

Suggested Citation

  • Uday S. Karmarkar & Nitin R. Patel, 1977. "The one‐period, N‐location distribution problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 24(4), pages 559-575, December.
    • Handle: RePEc:wly:navlog:v:24:y:1977:i:4:p:559-575
    DOI: 10.1002/nav.3800240405
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    Cited by:

    1. Bhatnagar, Rohit & Lin, Bing, 2019. "The joint transshipment and production control policies for multi-location production/inventory systems," European Journal of Operational Research, Elsevier, vol. 275(3), pages 957-970.
    2. Naderi, Siamak & Kilic, Kemal & Dasci, Abdullah, 2020. "A deterministic model for the transshipment problem of a fast fashion retailer under capacity constraints," International Journal of Production Economics, Elsevier, vol. 227(C).
    3. Zhou, Zihan & Wang, Xinhui, 2023. "Replenishment and transshipment in periodic-review systems with a fixed order cost," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1240-1247.
    4. Andrew Lim & Zhaowei Miao & Brian Rodrigues & Zhou Xu, 2005. "Transshipment through crossdocks with inventory and time windows," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(8), pages 724-733, December.

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