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Average Cost Optimal Stationary Policies in Infinite State Markov Decision Processes with Unbounded Costs

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  • Linn I. Sennott

    (Illinois State University, Normal, Illinois)

Abstract

We deal with infinite state Markov decision processes with unbounded costs. Three simple conditions, based on the optimal discounted value function, guarantee the existence of an expected average cost optimal stationary policy. Sufficient conditions are the existence of a distinguished state of smallest discounted value and a single stationary policy inducing an irreducible, ergodic Markov chain for which the average cost of a first passage from any state to the distinguished state is finite. A result to verify this is also given. Two examples illustrate the ease of applying the criteria.

Suggested Citation

  • Linn I. Sennott, 1989. "Average Cost Optimal Stationary Policies in Infinite State Markov Decision Processes with Unbounded Costs," Operations Research, INFORMS, vol. 37(4), pages 626-633, August.
    • Handle: RePEc:inm:oropre:v:37:y:1989:i:4:p:626-633
    DOI: 10.1287/opre.37.4.626
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    Citations

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    Cited by:

    1. Fleischmann, Moritz & Kuik, Roelof, 2003. "On optimal inventory control with independent stochastic item returns," European Journal of Operational Research, Elsevier, vol. 151(1), pages 25-37, November.
    2. Arie Hordijk & Olaf Passchier & Floske Spieksma, 1997. "Optimal service control against worst case admission policies: A multichained stochastic game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(2), pages 281-301, June.
    3. Oscar Vega-Amaya & Raúl Montes-de-Oca, 1998. "Application of average dynamic programming to inventory systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(3), pages 451-471, October.
    4. David L. Kaufman & Mark E. Lewis, 2007. "Machine maintenance with workload considerations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(7), pages 750-766, October.
    5. Linn Sennott, 1997. "On computing average cost optimal policies with application to routing to parallel queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(1), pages 45-62, February.
    6. Ping Cao & Jingui Xie, 2016. "Optimal control of a multiclass queueing system when customers can change types," Queueing Systems: Theory and Applications, Springer, vol. 82(3), pages 285-313, April.
    7. Awi Federgruen & Aliza Heching, 1999. "Combined Pricing and Inventory Control Under Uncertainty," Operations Research, INFORMS, vol. 47(3), pages 454-475, June.
    8. Wallace J. Hopp & Seyed M. R. Iravani & Biying Shou, 2005. "Serial Agile Production Systems with Automation," Operations Research, INFORMS, vol. 53(5), pages 852-866, October.
    9. Fleischmann, Moritz & Kuik, Roelof & Dekker, Rommert, 2002. "Controlling inventories with stochastic item returns: A basic model," European Journal of Operational Research, Elsevier, vol. 138(1), pages 63-75, April.
    10. Linwei Xin & David A. Goldberg, 2018. "Asymptotic Optimality of Tailored Base-Surge Policies in Dual-Sourcing Inventory Systems," Management Science, INFORMS, vol. 64(1), pages 437-452, January.
    11. Olivier Bilenne, 2021. "Dispatching to parallel servers," Queueing Systems: Theory and Applications, Springer, vol. 99(3), pages 199-230, December.
    12. Kuo, Yarlin, 2004. "Order arrival control of an M/M/1 failure prone service station," International Journal of Production Economics, Elsevier, vol. 91(2), pages 179-188, September.
    13. Dmitry Efrosinin & Natalia Stepanova, 2021. "Optimal Open-Loop Routing and Threshold-Based Allocation in TWO Parallel QUEUEING Systems with Heterogeneous Servers," Mathematics, MDPI, vol. 9(21), pages 1-18, October.
    14. Rodney P. Parker & Roman Kapuscinski, 2004. "Optimal Policies for a Capacitated Two-Echelon Inventory System," Operations Research, INFORMS, vol. 52(5), pages 739-755, October.
    15. 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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