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A Min-Max Inventory Model


  • Norman Agin

    (Columbia University and MATHEMATICA)


An inventory model is considered where every N periods an order is placed for an amount which brings the sum of stock-on-hand plus on-order up to some level S. The model treats a single item for which there is random demand. Demands that arrive when there is no positive inventory on hand are back-ordered. Leadtime is treated as random and the receipts of orders are allowed to cross in time. Values N* and S* which minimize steady state expected costs per unit time cannot be found. In this paper approximations, N 0 and S 0 are found. These are determined by minimizing an expected cost per unit time which has been maximized over all distributions of stock deficit with a given mean and variance. The method is applicable even when the functional form of the distribution of demand is not known. Computer simulations are used to indicate the values of the input parameters for which the expected costs per unit time associated with N 0 and S 0 are close to the similar quantities for N* and S*.

Suggested Citation

  • Norman Agin, 1966. "A Min-Max Inventory Model," Management Science, INFORMS, vol. 12(7), pages 517-529, March.
  • Handle: RePEc:inm:ormnsc:v:12:y:1966:i:7:p:517-529

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    Cited by:

    1. Hayya, Jack C. & Bagchi, Uttarayan & Kim, Jeon G. & Sun, Daewon, 2008. "On static stochastic order crossover," International Journal of Production Economics, Elsevier, vol. 114(1), pages 404-413, July.
    2. Hayya, Jack C. & Bagchi, Uttarayan & Ramasesh, Ranga, 2011. "Cost relationships in stochastic inventory systems: A simulation study of the (S, S-1, t=1) model," International Journal of Production Economics, Elsevier, vol. 130(2), pages 196-202, April.
    3. Wang, Xun & Disney, Stephen M., 2017. "Mitigating variance amplification under stochastic lead-time: The proportional control approach," European Journal of Operational Research, Elsevier, vol. 256(1), pages 151-162.

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