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Coordinated Replenishments in a Multi-Item Inventory System with Compound Poisson Demands


Author Info

  • A. Federgruen

    (Columbia University)

  • H. Groenevelt

    (Columbia University)

  • H. C. Tijms

    (Vrije Universiteit, Amsterdam, The Netherlands)


In many practical applications or multi-item inventory systems significant economies of scale can be exploited when coordinating replenishment orders for groups of items. This paper considers a continuous review multi-item inventory system with compound Poisson demand processes; excess demands are backlogged and each replenishment requires a lead time. There is a major setup cost associated with any replenishment of the family of items, and a minor (item dependent) setup cost when including a particular item in this replenishment. Moreover there are holding and penalty costs. We present an algorithm which searches for a simple coordinated control rule minimizing the long-run average cost per unit time subject to a service level constraint per item on the fraction of demand satisfied directly from on-hand inventory. This algorithm is based on a heuristic decomposition procedure and a specialized policy-iteration method to solve the single-item subproblems generated by the decomposition procedure. The model applies to multi-location inventory systems with similar cost structures for coordinated deliveries.

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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 30 (1984)
Issue (Month): 3 (March)
Pages: 344-357

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Handle: RePEc:inm:ormnsc:v:30:y:1984:i:3:p:344-357

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Keywords: multi-item inventory systems; coordinated replenishments; compound Poisson demand processes; service level constraint; policy-iteration algorithm;


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Cited by:
  1. Schultz, Helle & Johansen, Soren Glud, 1999. "Can-order policies for coordinated inventory replenishment with Erlang distributed times between ordering," European Journal of Operational Research, Elsevier, vol. 113(1), pages 30-41, February.
  2. repec:dgr:uvatin:2097026 is not listed on IDEAS
  3. Kiesmüller, G.P., 2009. "A multi-item periodic replenishment policy with full truckloads," International Journal of Production Economics, Elsevier, vol. 118(1), pages 275-281, March.
  4. Tsai, Chieh-Yuan & Tsai, Chi-Yang & Huang, Po-Wen, 2009. "An association clustering algorithm for can-order policies in the joint replenishment problem," International Journal of Production Economics, Elsevier, vol. 117(1), pages 30-41, January.
  5. J.B.G. Frenk & M.J. Kleijn & R. Dekker, 1997. "An Efficient Algorithm for a Generalized Joint Replenishment Problem," Tinbergen Institute Discussion Papers 97-026/4, Tinbergen Institute.
  6. Melchiors, Philip, 2002. "Calculating can-order policies for the joint replenishment problem by the compensation approach," European Journal of Operational Research, Elsevier, vol. 141(3), pages 587-595, September.
  7. Wijnmalen, Diederik J. D. & Hontelez, Jan A. M., 1997. "Coordinated condition-based repair strategies for components of a multi-component maintenance system with discounts," European Journal of Operational Research, Elsevier, vol. 98(1), pages 52-63, April.


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