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The Classical Average-Cost Inventory Models of Iglehart and Veinott–Wagner Revisited

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  • D. Beyer

    (Hewlett-Packard Laboratories)

  • S. P. Sethi

    (University of Texas at Dallas)

Abstract

This paper revisits the classical papers of Iglehart (Ref. 1) and Veinott and Wagner (Ref. 2) devoted to stochastic inventory problems with the criterion of long-run average cost minimization. We indicate some of the assumptions that are used implicitly without verification in their stationary distribution approach to the problems and provide the missing (nontrivial) verification. In addition to completing their analysis, we examine the relationship between the stationary distribution approach and the dynamic programming approach to the average-cost stochastic inventory problems.

Suggested Citation

  • D. Beyer & S. P. Sethi, 1999. "The Classical Average-Cost Inventory Models of Iglehart and Veinott–Wagner Revisited," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 523-555, June.
    • Handle: RePEc:spr:joptap:v:101:y:1999:i:3:d:10.1023_a:1021734003033
    DOI: 10.1023/A:1021734003033
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    References listed on IDEAS

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    1. Awi Federgruen & Paul Zipkin, 1984. "An Efficient Algorithm for Computing Optimal ( s , S ) Policies," Operations Research, INFORMS, vol. 32(6), pages 1268-1285, December.
    2. Shaler Stidham, 1977. "Cost Models for Stochastic Clearing Systems," Operations Research, INFORMS, vol. 25(1), pages 100-127, February.
    3. Michael C. Fu, 1994. "Sample Path Derivatives for (s, S) Inventory Systems," Operations Research, INFORMS, vol. 42(2), pages 351-364, April.
    4. Suresh P. Sethi & Feng Cheng, 1997. "Optimality of ( s , S ) Policies in Inventory Models with Markovian Demand," Operations Research, INFORMS, vol. 45(6), pages 931-939, December.
    5. Evan L. Porteus, 1985. "Numerical Comparisons of Inventory Policies for Periodic Review Systems," Operations Research, INFORMS, vol. 33(1), pages 134-152, February.
    6. D. Beyer & S. P. Sethi & M. Taksar, 1998. "Inventory Models with Markovian Demands and Cost Functions of Polynomial Growth," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 281-323, August.
    7. D. Beyer & S. P. Sethi, 1997. "Average Cost Optimality in Inventory Models with Markovian Demands," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 497-526, March.
    8. Yu-Sheng Zheng & A. Federgruen, 1991. "Finding Optimal (s, S) Policies Is About As Simple As Evaluating a Single Policy," Operations Research, INFORMS, vol. 39(4), pages 654-665, August.
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    Cited by:

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    4. Van Foreest, Nicky D. & Kilic, Onur A., 2023. "An intuitive approach to inventory control with optimal stopping," European Journal of Operational Research, Elsevier, vol. 311(3), pages 921-924.
    5. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Discrete‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 131-153, January.
    6. Woonghee Tim Huh & Ganesh Janakiraman & Mahesh Nagarajan, 2011. "Average Cost Single-Stage Inventory Models: An Analysis Using a Vanishing Discount Approach," Operations Research, INFORMS, vol. 59(1), pages 143-155, February.
    7. Eugene A. Feinberg & Yan Liang, 2022. "Structure of optimal policies to periodic-review inventory models with convex costs and backorders for all values of discount factors," Annals of Operations Research, Springer, vol. 317(1), pages 29-45, October.

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