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Approximate dynamic programming for stochastic linear control problems on compact state spaces

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  • Woerner, Stefan
  • Laumanns, Marco
  • Zenklusen, Rico
  • Fertis, Apostolos

Abstract

This paper addresses Markov Decision Processes over compact state and action spaces. We investigate the special case of linear dynamics and piecewise-linear and convex immediate costs for the average cost criterion. This model is very general and covers many interesting examples, for instance in inventory management. Due to the curse of dimensionality, the problem is intractable and optimal policies usually cannot be computed, not even for instances of moderate size.

Suggested Citation

  • Woerner, Stefan & Laumanns, Marco & Zenklusen, Rico & Fertis, Apostolos, 2015. "Approximate dynamic programming for stochastic linear control problems on compact state spaces," European Journal of Operational Research, Elsevier, vol. 241(1), pages 85-98.
    • Handle: RePEc:eee:ejores:v:241:y:2015:i:1:p:85-98
    DOI: 10.1016/j.ejor.2014.08.003
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    References listed on IDEAS

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    1. Robert S. Kaplan, 1970. "A Dynamic Inventory Model with Stochastic Lead Times," Management Science, INFORMS, vol. 16(7), pages 491-507, March.
    2. Donald L. Iglehart, 1963. "Optimality of (s, S) Policies in the Infinite Horizon Dynamic Inventory Problem," Management Science, INFORMS, vol. 9(2), pages 259-267, January.
    3. Yoichiro Fukuda, 1964. "Optimal Policies for the Inventory Problem with Negotiable Leadtime," Management Science, INFORMS, vol. 10(4), pages 690-708, July.
    4. Daniela Pucci de Farias & Benjamin Van Roy, 2004. "On Constraint Sampling in the Linear Programming Approach to Approximate Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 462-478, August.
    5. Senthil Veeraraghavan & Alan Scheller-Wolf, 2008. "Now or Later: A Simple Policy for Effective Dual Sourcing in Capacitated Systems," Operations Research, INFORMS, vol. 56(4), pages 850-864, August.
    6. Shapiro, Alexander, 2011. "Analysis of stochastic dual dynamic programming method," European Journal of Operational Research, Elsevier, vol. 209(1), pages 63-72, February.
    7. Arthur F. Veinott, Jr. & Harvey M. Wagner, 1965. "Computing Optimal (s, S) Inventory Policies," Management Science, INFORMS, vol. 11(5), pages 525-552, March.
    8. Minner, Stefan, 2003. "Multiple-supplier inventory models in supply chain management: A review," International Journal of Production Economics, Elsevier, vol. 81(1), pages 265-279, January.
    9. Richard Ehrhardt, 1984. "( s , S ) Policies for a Dynamic Inventory Model with Stochastic Lead Times," Operations Research, INFORMS, vol. 32(1), pages 121-132, February.
    10. D. P. de Farias & B. Van Roy, 2003. "The Linear Programming Approach to Approximate Dynamic Programming," Operations Research, INFORMS, vol. 51(6), pages 850-865, December.
    11. Janssen, Fred & de Kok, Ton, 1999. "A two-supplier inventory model," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 395-403, March.
    12. Klosterhalfen, Steffen & Kiesmüller, Gudrun & Minner, Stefan, 2011. "A comparison of the constant-order and dual-index policy for dual sourcing," International Journal of Production Economics, Elsevier, vol. 133(1), pages 302-311, September.
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    Cited by:

    1. Svoboda, Josef & Minner, Stefan & Yao, Man, 2021. "Typology and literature review on multiple supplier inventory control models," European Journal of Operational Research, Elsevier, vol. 293(1), pages 1-23.

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