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Representation and Solution of Decision Problems Using Sequential Decision Diagrams

Author

Listed:
  • Zvi Covaliu

    (School of Business and Public Management, George Washington University, Washington, DC 20052)

  • Robert M. Oliver

    (Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720)

Abstract

In this paper we introduce a new graph, the sequential decision diagram, to aid in modeling formulation, and solution of sequential decision problems under uncertainty. While as compact as an influence diagram, the sequential diagram captures the asymmetric and sequential aspects of decision problems as effectively as decision trees. We show that a unified framework consisting of a sequential diagram, an influence diagram, and a common formulation table for the problem's data, suffices for compact and consistent representation, economical formulation, and efficient solution of (asymmetric) decision problems. In addition to asymmetry, the framework exploits other sources of computational efficiency, such as conditional independence and value function decomposition, making it also useful in evaluating dynamic-programming problems. The formulation table and recursive algorithm can be readily implemented in computers for solving large-scale problems. Examples are provided to illustrate the methodology in both asymmetric and symmetric cases.

Suggested Citation

  • Zvi Covaliu & Robert M. Oliver, 1995. "Representation and Solution of Decision Problems Using Sequential Decision Diagrams," Management Science, INFORMS, vol. 41(12), pages 1860-1881, December.
    • Handle: RePEc:inm:ormnsc:v:41:y:1995:i:12:p:1860-1881
    DOI: 10.1287/mnsc.41.12.1860
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    Citations

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    Cited by:

    1. Concha Bielza & Prakash P. Shenoy, 1999. "A Comparison of Graphical Techniques for Asymmetric Decision Problems," Management Science, INFORMS, vol. 45(11), pages 1552-1569, November.
    2. Thwaites, Peter A. & Smith, Jim Q., 2018. "A graphical method for simplifying Bayesian games," Reliability Engineering and System Safety, Elsevier, vol. 179(C), pages 3-11.
    3. Peter Davison & Bruce Cameron & Edward F. Crawley, 2015. "Technology Portfolio Planning by Weighted Graph Analysis of System Architectures," Systems Engineering, John Wiley & Sons, vol. 18(1), pages 45-58, January.
    4. C. L. Smith & E. Borgonovo, 2007. "Decision Making During Nuclear Power Plant Incidents—A New Approach to the Evaluation of Precursor Events," Risk Analysis, John Wiley & Sons, vol. 27(4), pages 1027-1042, August.
    5. Shenoy, Prakash P., 2000. "Valuation network representation and solution of asymmetric decision problems," European Journal of Operational Research, Elsevier, vol. 121(3), pages 579-608, March.
    6. Bielza, Concha & Gómez, Manuel & Shenoy, Prakash P., 2011. "A review of representation issues and modeling challenges with influence diagrams," Omega, Elsevier, vol. 39(3), pages 227-241, June.
    7. Borgonovo, Emanuele & Tonoli, Fabio, 2014. "Decision-network polynomials and the sensitivity of decision-support models," European Journal of Operational Research, Elsevier, vol. 239(2), pages 490-503.
    8. Prakash Shenoy, 1998. "Game Trees For Decision Analysis," Theory and Decision, Springer, vol. 44(2), pages 149-171, April.
    9. Demirer, Riza & Shenoy, Prakash P., 2006. "Sequential valuation networks for asymmetric decision problems," European Journal of Operational Research, Elsevier, vol. 169(1), pages 286-309, February.
    10. Ruth Y. Dicdican & Yacov Y. Haimes, 2005. "Relating multiobjective decision trees to the multiobjective risk impact analysis method," Systems Engineering, John Wiley & Sons, vol. 8(2), pages 95-108.
    11. Anissa Frini & Adel Guitouni & Abderrezak Benaskeur, 2017. "Solving Dynamic Multi-Criteria Resource-Target Allocation Problem Under Uncertainty: A Comparison of Decomposition and Myopic Approaches," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(06), pages 1465-1496, November.
    12. Debarun Bhattacharjya & Ross D. Shachter, 2012. "Formulating Asymmetric Decision Problems as Decision Circuits," Decision Analysis, INFORMS, vol. 9(2), pages 138-145, June.
    13. Lopez-Diaz, Miguel & Rodriguez-Muniz, Luis J., 2007. "Influence diagrams with super value nodes involving imprecise information," European Journal of Operational Research, Elsevier, vol. 179(1), pages 203-219, May.

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