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Coordinated replenishments of items under time‐varying demand: Dynamic programming formulation

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  • Edward A Silver

Abstract

We consider a group (or family) of items having deterministic, but time‐varying, demand patterns. The group is defined by a setup‐cost structure that makes coordination attractive (a major setup cost for each group replenishment regardless of how many of the items are involved). The problem is to determine the timing and sizes of the replenishments of all of the items so as to satisfy the demand out to a given horizon in a cost‐minimizing fashion. A dynamic programming formulation is illustrated for the case of a two‐item family. It is demonstrated that the dynamic programming approach is computationally reasonable, in an operational sense, only for small family sizes. For large families heuristic solution methods appear necessary.

Suggested Citation

  • Edward A Silver, 1979. "Coordinated replenishments of items under time‐varying demand: Dynamic programming formulation," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(1), pages 141-151, March.
    • Handle: RePEc:wly:navlog:v:26:y:1979:i:1:p:141-151
    DOI: 10.1002/nav.3800260113
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    Cited by:

    1. Yılmaz, Seren Bilge & Yücel, Eda, 2021. "Optimizing onboard catering loading locations and plans for airlines," Omega, Elsevier, vol. 99(C).
    2. Chia‐Shin Chung & H. Murat Mercan, 1994. "Heuristic procedure for a multiproduct dynamic lot‐sizing problem with coordinated replenishments," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(2), pages 273-286, March.
    3. S. Selcuk Erenguc & H. Murat Mercan, 1990. "A multifamily dynamic lot‐sizing model with coordinated replenishments," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(4), pages 539-558, August.
    4. Ian R. Webb & Bruce R. Buzby & Gerard M. Campbell, 1997. "Cyclical schedules for the joint replenishment problem with dynamic demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(6), pages 577-589, September.

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