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A Family of Inventory Models

Author

Listed:
  • G. Hadley

    (University of Chicago)

  • T. M. Whitin

    (University of California, Berkeley)

Abstract

An inventory control model in which the state of the system is reviewed only at discrete, equally spaced time intervals is studied. A procurement is made if at the review period the inventory position of the system is less than or equal to a number k. The quantity procured is an integral multiple of a number Q. The total expected cost of review, procurement, holding inventory, and stockouts is determined under the assumption that all demands are ultimately met. The cost of a stockout is taken to consist of a fixed cost per unit out of stock plus a variable cost which is proportional to the time out of stock. Specific expressions for all the cost expressions are found for the case of (1) Poisson demands and fixed lead times, and (2) Poisson demands and gamma lead times. It is shown that many of the inventory models discussed in the literature are special cases of the model here described.

Suggested Citation

  • G. Hadley & T. M. Whitin, 1961. "A Family of Inventory Models," Management Science, INFORMS, vol. 7(4), pages 351-371, July.
    • Handle: RePEc:inm:ormnsc:v:7:y:1961:i:4:p:351-371
    DOI: 10.1287/mnsc.7.4.351
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    Cited by:

    1. Li, Xiaoming, 2008. "Demand evolution in stochastic inventory systems: Riskiness increase," International Journal of Production Economics, Elsevier, vol. 116(2), pages 182-189, December.
    2. Kochel, P., 2007. "Order optimisation in multi-location models with hub-and-spoke structure," International Journal of Production Economics, Elsevier, vol. 108(1-2), pages 368-387, July.
    3. Wanke, Peter F., 2008. "The uniform distribution as a first practical approach to new product inventory management," International Journal of Production Economics, Elsevier, vol. 114(2), pages 811-819, August.
    4. Fangruo Chen, 1998. "Echelon Reorder Points, Installation Reorder Points, and the Value of Centralized Demand Information," Management Science, INFORMS, vol. 44(12-Part-2), pages 221-234, December.
    5. Fangruo Chen, 2000. "Optimal Policies for Multi-Echelon Inventory Problems with Batch Ordering," Operations Research, INFORMS, vol. 48(3), pages 376-389, June.
    6. Jing-Sheng Song, 2000. "A Note on Assemble-to-Order Systems with Batch Ordering," Management Science, INFORMS, vol. 46(5), pages 739-743, May.
    7. Ying Wei, 2020. "Optimizing constant pricing and inventory decisions for a periodic review system with batch ordering," Annals of Operations Research, Springer, vol. 291(1), pages 939-957, August.
    8. Aswin Dhamodharan & Ruben Proano, 2012. "Determining the optimal vaccine vial size in developing countries: a Monte Carlo simulation approach," Health Care Management Science, Springer, vol. 15(3), pages 188-196, September.
    9. Li, Xiaoming & Sridharan, V., 2008. "Characterizing order processes of using (R,nQ) inventory policies in supply chains," Omega, Elsevier, vol. 36(6), pages 1096-1104, December.

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