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Average Cost Optimality in Inventory Models with Markovian Demands and Lost Sales

In: Analysis, Control and Optimization of Complex Dynamic Systems

Author

Listed:
  • Dirk Beyer
  • Suresh P. Sethi

Abstract

This paper is concerned with long-run average cost minimization of a stochastic inventory problem with Markovian demand, fixed ordering cost, convex surplus cost, and lost sales. The states of the Markov chain represent different possible states of the environment. Using a vanishing discount approach, a dynamic programming equation and the corresponding verification theorem are established. Finally, the existence of an optimal state-dependent (s, S) policy is proved.

Suggested Citation

  • Dirk Beyer & Suresh P. Sethi, 2005. "Average Cost Optimality in Inventory Models with Markovian Demands and Lost Sales," Springer Books, in: El Kébir Boukas & Roland P. Malhamé (ed.), Analysis, Control and Optimization of Complex Dynamic Systems, chapter 0, pages 3-23, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-25477-7_1
    DOI: 10.1007/0-387-25477-3_1
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    Citations

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    Cited by:

    1. Erhan Bayraktar & Michael Ludkovski, 2010. "Inventory management with partially observed nonstationary demand," Annals of Operations Research, Springer, vol. 176(1), pages 7-39, April.
    2. 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.
    3. 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.

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