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Average Cost Optimality in Inventory Models with Markovian Demands

Author

Listed:
  • D. Beyer

    (University of Toronto)

  • S. P. Sethi

    (University of Toronto)

Abstract

This paper is concerned with long-run average cost minimization of a stochastic inventory problem with Markovian demand, fixed ordering cost, and convex surplus cost. 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

  • 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.
    • Handle: RePEc:spr:joptap:v:92:y:1997:i:3:d:10.1023_a:1022651322174
    DOI: 10.1023/A:1022651322174
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    References listed on IDEAS

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    Cited by:

    1. Hong-Qiao Chen & Xiao-Song Ding & Ji-Hong Zhang & Hua-Yi Li, 2020. "Optimal Production-Inventory Policy for a Periodic-Review Energy Buy-Back System over an Infinite Planning Horizon," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(02), pages 1-32, March.
    2. Alp Muharremoglu & John N. Tsitsiklis, 2008. "A Single-Unit Decomposition Approach to Multiechelon Inventory Systems," Operations Research, INFORMS, vol. 56(5), pages 1089-1103, October.
    3. Hao Yuan & Qi Luo & Cong Shi, 2021. "Marrying Stochastic Gradient Descent with Bandits: Learning Algorithms for Inventory Systems with Fixed Costs," Management Science, INFORMS, vol. 67(10), pages 6089-6115, October.
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    7. 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.
    8. Komeyl Baghizadeh & Nafiseh Ebadi & Dominik Zimon & Luay Jum’a, 2022. "Using Four Metaheuristic Algorithms to Reduce Supplier Disruption Risk in a Mathematical Inventory Model for Supplying Spare Parts," Mathematics, MDPI, vol. 11(1), pages 1-19, December.
    9. Roman Kapuściński & Sridhar Tayur, 1998. "A Capacitated Production-Inventory Model with Periodic Demand," Operations Research, INFORMS, vol. 46(6), pages 899-911, December.
    10. 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.
    11. 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.
    12. Yossi Aviv & Awi Federgruen, 2001. "Capacitated Multi-Item Inventory Systems with Random and Seasonally Fluctuating Demands: Implications for Postponement Strategies," Management Science, INFORMS, vol. 47(4), pages 512-531, April.
    13. Hekimoğlu, Mustafa & van der Laan, Ervin & Dekker, Rommert, 2018. "Markov-modulated analysis of a spare parts system with random lead times and disruption risks," European Journal of Operational Research, Elsevier, vol. 269(3), pages 909-922.
    14. Fangruo Chen & Jing-Sheng Song, 2001. "Optimal Policies for Multiechelon Inventory Problems with Markov-Modulated Demand," Operations Research, INFORMS, vol. 49(2), pages 226-234, April.
    15. Erhan Bayraktar & Michael Ludkovski, 2010. "Inventory management with partially observed nonstationary demand," Annals of Operations Research, Springer, vol. 176(1), pages 7-39, April.
    16. Feng Cheng & Suresh P. Sethi, 1999. "A Periodic Review Inventory Model with Demand Influenced by Promotion Decisions," Management Science, INFORMS, vol. 45(11), pages 1510-1523, November.
    17. 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.
    18. Li Chen & Jing-Sheng Song & Yue Zhang, 2017. "Serial Inventory Systems with Markov-Modulated Demand: Derivative Bounds, Asymptotic Analysis, and Insights," Operations Research, INFORMS, vol. 65(5), pages 1231-1249, October.
    19. Suresh P. Sethi & Houmin Yan & Hanqin Zhang, 2003. "Inventory Models with Fixed Costs, Forecast Updates, and Two Delivery Modes," Operations Research, INFORMS, vol. 51(2), pages 321-328, April.
    20. Xiang, Mengyuan & Rossi, Roberto & Martin-Barragan, Belen & Tarim, S. Armagan, 2023. "A mathematical programming-based solution method for the nonstationary inventory problem under correlated demand," European Journal of Operational Research, Elsevier, vol. 304(2), pages 515-524.
    21. Jianqiang Hu & Cheng Zhang & Chenbo Zhu, 2016. "( s , S ) Inventory Systems with Correlated Demands," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 603-611, November.
    22. 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.
    23. Harun Avci & Kagan Gokbayrak & Emre Nadar, 2020. "Structural Results for Average‐Cost Inventory Models with Markov‐Modulated Demand and Partial Information," Production and Operations Management, Production and Operations Management Society, vol. 29(1), pages 156-173, January.
    24. Xiuli Chao & Xiting Gong & Cong Shi & Chaolin Yang & Huanan Zhang & Sean X. Zhou, 2018. "Approximation Algorithms for Capacitated Perishable Inventory Systems with Positive Lead Times," Management Science, INFORMS, vol. 64(11), pages 5038-5061, November.
    25. Xiaoming Li, 2013. "Managing Dynamic Inventory Systems with Product Returns: A Markov Decision Process," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 577-592, May.

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