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

Author

Listed:
  • A. Federgruen

    (Columbia University)

  • H. Groenevelt

    (Columbia University)

  • H. C. Tijms

    (Vrije Universiteit, Amsterdam, The Netherlands)

Abstract

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.

Suggested Citation

  • A. Federgruen & H. Groenevelt & H. C. Tijms, 1984. "Coordinated Replenishments in a Multi-Item Inventory System with Compound Poisson Demands," Management Science, INFORMS, vol. 30(3), pages 344-357, March.
  • Handle: RePEc:inm:ormnsc:v:30:y:1984:i:3:p:344-357
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    File URL: http://dx.doi.org/10.1287/mnsc.30.3.344
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    References listed on IDEAS

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    1. Ian I. Mitroff, 1972. "The Myth of Objectivity OR Why Science Needs a New Psychology of Science," Management Science, INFORMS, vol. 18(10), pages 613-618, June.
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    Citations

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    Cited by:

    1. Dellaert, Nico & van de Poel, Erik, 1996. "Global inventory control in an academic hospital," International Journal of Production Economics, Elsevier, vol. 46(1), pages 277-284, December.
    2. Eynan, Amit & Kropp, Dean H., 2007. "Effective and simple EOQ-like solutions for stochastic demand periodic review systems," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1135-1143, August.
    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. Liu, Liming & Yuan, Xue-Ming, 2000. "Coordinated replenishments in inventory systems with correlated demands," European Journal of Operational Research, Elsevier, vol. 123(3), pages 490-503, June.
    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. 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.
    7. McGee, Victor E. & Pyke, David F., 1996. "Periodic production scheduling at a fastener manufacturer," International Journal of Production Economics, Elsevier, vol. 46(1), pages 65-87, December.
    8. Mustafa Çagri Gürbüz & Kamran Moinzadeh & Yong-Pin Zhou, 2007. "Coordinated Replenishment Strategies in Inventory/Distribution Systems," Management Science, INFORMS, pages 293-307.
    9. Rommert Dekker & Ralph Wildeman & Frank Duyn Schouten, 1997. "A review of multi-component maintenance models with economic dependence," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(3), pages 411-435, October.
    10. repec:eee:ejores:v:263:y:2017:i:3:p:827-837 is not listed on IDEAS
    11. Berg, J. P. van den & Zijm, W. H. M., 1999. "Models for warehouse management: Classification and examples," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 519-528, March.
    12. Matthew J. Sobel, 2004. "Fill Rates of Single-Stage and Multistage Supply Systems," Manufacturing & Service Operations Management, INFORMS, pages 41-52.
    13. Sivakumar, B., 2008. "Two-commodity inventory system with retrial demand," European Journal of Operational Research, Elsevier, vol. 187(1), pages 70-83, May.
    14. repec:pal:jorsoc:v:54:y:2003:i:3:d:10.1057_palgrave.jors.2601499 is not listed on IDEAS
    15. Timmer, Judith & Chessa, Michela & Boucherie, Richard J., 2013. "Cooperation and game-theoretic cost allocation in stochastic inventory models with continuous review," European Journal of Operational Research, Elsevier, vol. 231(3), pages 567-576.
    16. Larsen, Christian & Turkensteen, Marcel, 2014. "A vendor managed inventory model using continuous approximations for route length estimates and Markov chain modeling for cost estimates," International Journal of Production Economics, Elsevier, vol. 157(C), pages 120-132.
    17. 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.
    18. 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.
    19. 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.
    20. Uday S. Rao, 2003. "Properties of the Periodic Review (R, T) Inventory Control Policy for Stationary, Stochastic Demand," Manufacturing & Service Operations Management, INFORMS, pages 37-53.
    21. Frenk, J. B. G. & Kleijn, M. J. & Dekker, R., 1999. "An efficient algorithm for a generalized joint replenishment problem," European Journal of Operational Research, Elsevier, vol. 118(2), pages 413-428, October.
    22. Khouja, Moutaz & Goyal, Suresh, 2008. "A review of the joint replenishment problem literature: 1989-2005," European Journal of Operational Research, Elsevier, vol. 186(1), pages 1-16, April.
    23. Larsen, Christian, 2009. "The Q(s,S) control policy for the joint replenishment problem extended to the case of correlation among item-demands," International Journal of Production Economics, Elsevier, vol. 118(1), pages 292-297, March.
    24. Kiesmüller, G.P., 2010. "Multi-item inventory control with full truckloads: A comparison of aggregate and individual order triggering," European Journal of Operational Research, Elsevier, vol. 200(1), pages 54-62, January.
    25. Kouki, Chaaben & Babai, M. Zied & Jemai, Zied & Minner, Stefan, 2016. "A coordinated multi-item inventory system for perishables with random lifetime," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 226-237.

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