DGOR pp 468-482 | Cite as

Linear Programming Methods for Solving Finite Markovian Decision Problems

  • A. Hordijk
  • L. C. M. Kallenberg
Conference paper
Part of the Operations Research Proceedings 1980 book series (ORP, volume 1980)

Summary

An overview is given of linear programming methods for solving (semi-) Markov decision problems.

Keywords

Hull Tria 

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References

  1. De Ghellinck, G.T. [ 1960 ]. Les problèmes de décisions sequentielles. Cahiers du Centre d’Etudes de Recherche Opérationelle, 2, 161–179.Google Scholar
  2. De Ghellinck, G.T. and G.D. Eppen [ 1967 ]. Linear programming solutions for separable Markovian decision problems. Management Science, 13, 371–394.CrossRefGoogle Scholar
  3. Denardo, E.V. and B.L. Fox [ 1968 ]. Multichain Markov renewal programs. Siam Journal on Applied Mathematics, 16, 468–487.CrossRefGoogle Scholar
  4. Denardo, E.V. and U.G. Rothblum [ 1979 ]. Optimal stopping, exponential utility, and linear programming. Mathematical Programming, 16, 228–244.CrossRefGoogle Scholar
  5. D’Epenoux, F. [1960]. Sur un problème de production et de stockage dans l’aléatoire. Revue Française de Recherche Opérationelle, 14, 3–16.Google Scholar
  6. Derman, C. [ 1970 ]. Finite state Markovian decision processes. Academic Press, New York.Google Scholar
  7. Derman, C. and A.F. Veinott Jr. [ 1972 ]. Constrained Markov decision chains. Management Science, 19, 389–390.CrossRefGoogle Scholar
  8. Heilmann,W.-R. [ 1977 ]. Lineare Programmierung stochastischer dynamischer Entscheidungsmodelle. Thesis, University of Hamburg.Google Scholar
  9. Heilmann,W.-R. [ 1978 ]. Solving stochastic dynamic programming problems by linear programming - An annotated bibliography. Zeitschrift für Operations Research 22, 43–53.CrossRefGoogle Scholar
  10. Hordijk, A. and L.C.M. Kallenberg [ 1979 ]. Linear programming and Markov decision chains. Management Science, 25, 352–362.CrossRefGoogle Scholar
  11. Kallenberg, L.C.M. [ 1980 ]. Linear programming and finite Markovian control problems Thesis, University of Leiden.Google Scholar
  12. Manne, A.S. [1960]. Linear programming and sequential decisions. Management Science, 6, 259–267.CrossRefGoogle Scholar
  13. Mine, H. and S. Osaki [ 1970 ]. Markovian decision processes. Elsevier, New York.Google Scholar
  14. Schweitzer, P.J. [ 1971 ]. Iterative solution of the functional equations of undiscounted Markov renewal programming. Journal of Mathematical Analysis and Applications, 34, 495–501.CrossRefGoogle Scholar
  15. Wessels, J. and J.A.E.E. van Nunen [ 1975 ]. Discounted semi-Markov decision processes: linear programming and policy iteration. Statistica Neerlandica, 29, 1–7.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • A. Hordijk
    • 1
  • L. C. M. Kallenberg
    • 1
  1. 1.Department of MathematicsUniversity of LeidenLeidenThe Netherlands

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