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The LP/POMDP marriage: Optimization with imperfect information

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  • Kirk A. Yost
  • Alan R. Washburn

Abstract

A new technique for solving large‐scale allocation problems with partially observable states and constrained action and observation resources is introduced. The technique uses a master linear program (LP) to determine allocations among a set of control policies, and uses partially observable Markov decision processes (POMDPs) to determine improving policies using dual prices from the master LP. An application is made to a military problem where aircraft attack targets in a sequence of stages, with information acquired in one stage being used to plan attacks in the next. © 2000 John Wiley & Sons, Inc., Naval Research Logistics 47: 607–619, 2000

Suggested Citation

  • Kirk A. Yost & Alan R. Washburn, 2000. "The LP/POMDP marriage: Optimization with imperfect information," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(8), pages 607-619, December.
    • Handle: RePEc:wly:navres:v:47:y:2000:i:8:p:607-619
    DOI: 10.1002/1520-6750(200012)47:83.0.CO;2-F
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    References listed on IDEAS

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    1. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    2. Christos H. Papadimitriou & John N. Tsitsiklis, 1987. "The Complexity of Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 441-450, August.
    3. Richard D. Smallwood & Edward J. Sondik, 1973. "The Optimal Control of Partially Observable Markov Processes over a Finite Horizon," Operations Research, INFORMS, vol. 21(5), pages 1071-1088, October.
    4. P. C. Gilmore & R. E. Gomory, 1963. "A Linear Programming Approach to the Cutting Stock Problem---Part II," Operations Research, INFORMS, vol. 11(6), pages 863-888, December.
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    Cited by:

    1. Huseyin Topaloglu & Sumit Kunnumkal, 2006. "Approximate dynamic programming methods for an inventory allocation problem under uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(8), pages 822-841, December.
    2. Daniel Adelman & Adam J. Mersereau, 2008. "Relaxations of Weakly Coupled Stochastic Dynamic Programs," Operations Research, INFORMS, vol. 56(3), pages 712-727, June.

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