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Technical Note—Cost Formulas for Continuous Review Inventory Models with Fixed Delivery Lags

Author

Listed:
  • Awi Federgruen

    (Columbia University, New York, New York)

  • Zvi Schechner

    (Columbia University, New York, New York)

Abstract

In continuous review models with a fixed delivery lag T , the state of the system is conveniently described by the net inventory position = (inventory on hand) plus (outstanding orders), in spite of most cost components depending on the actual inventory on hand . To relate these two inventory concepts one observes that the distribution of the inventory on hand at time t + T is determined by the inventory position at time t . This explains the standard convention of charging the expected costs incurred in [ S n + T , S n +1 + T ) to the decision made at time S n , where S n denotes the n th decision epoch. This paper derives simple expressions for the expected costs in [ S n + T , S n +1 + T ) as a function of the inventory position just after decision epoch S n .

Suggested Citation

  • Awi Federgruen & Zvi Schechner, 1983. "Technical Note—Cost Formulas for Continuous Review Inventory Models with Fixed Delivery Lags," Operations Research, INFORMS, vol. 31(5), pages 957-965, October.
    • Handle: RePEc:inm:oropre:v:31:y:1983:i:5:p:957-965
    DOI: 10.1287/opre.31.5.957
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    Citations

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    Cited by:

    1. Alain Bensoussan & Lama Moussawi-Haidar & Metin Çakanyıldırım, 2010. "Inventory control with an order-time constraint: optimality, uniqueness and significance," Annals of Operations Research, Springer, vol. 181(1), pages 603-640, December.
    2. 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.
    3. Yu‐Sheng Zheng & Fangruo Chen, 1992. "Inventory policies with quantized ordering," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 285-305, April.
    4. Jim Shi, 2022. "Optimal continuous production-inventory systems subject to stockout risk," Annals of Operations Research, Springer, vol. 317(2), pages 777-804, October.
    5. Fangruo Chen, 1999. "94%-Effective Policies for a Two-Stage Serial Inventory System with Stochastic Demand," Management Science, INFORMS, vol. 45(12), pages 1679-1696, December.
    6. Farvid, Mojtaba & Rosling, Kaj, 2014. "The discounted (R,Q) inventory model—The Shrewd Accountant's Heuristic," International Journal of Production Economics, Elsevier, vol. 149(C), pages 17-27.
    7. Kaj Rosling, 2002. "Inventory Cost Rate Functions with Nonlinear Shortage Costs," Operations Research, INFORMS, vol. 50(6), pages 1007-1017, December.
    8. Roni, Mohammad S. & Jin, Mingzhou & Eksioglu, Sandra D., 2015. "A hybrid inventory management system responding to regular demand and surge demand," Omega, Elsevier, vol. 52(C), pages 190-200.
    9. 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.
    10. Nielsen, Christina & Larsen, Christian, 2005. "An analytical study of the Q(s,S) policy applied to the joint replenishment problem," European Journal of Operational Research, Elsevier, vol. 163(3), pages 721-732, June.
    11. Michael N. Katehakis & Benjamin Melamed & Jim Junmin Shi, 2022. "Optimal replenishment rate for inventory systems with compound Poisson demands and lost sales: a direct treatment of time-average cost," Annals of Operations Research, Springer, vol. 317(2), pages 665-691, October.

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