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An Algebraic Approach to Formulating and Solving Large Models for Sequential Decisions Under Uncertainty

Author

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  • Craig W. Kirkwood

    (Department of Decision and Information Systems, Arizona State University, Tempe, Arizona 85287-4206)

Abstract

This article presents an algebraic approach to formulating and solving large models for sequential decisions under uncertainty. With this approach, decision analysis optimization methods can be applied to complex decision problems which are generally analyzed in management science practice using heuristics. Using the approach, a decision problem is formulated in terms of decision variables, random variables, and functions relating these variables. This leads to a compact representation, and a simple algorithm can be used to quickly solve algebraic models that would have decision trees with several hundred thousand endpoints. An application to research and development planning illustrates the usefulness of such large sequential decision models.

Suggested Citation

  • Craig W. Kirkwood, 1993. "An Algebraic Approach to Formulating and Solving Large Models for Sequential Decisions Under Uncertainty," Management Science, INFORMS, vol. 39(7), pages 900-913, July.
    • Handle: RePEc:inm:ormnsc:v:39:y:1993:i:7:p:900-913
    DOI: 10.1287/mnsc.39.7.900
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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. 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.
    3. 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.
    4. Haoying Han & Shih-Kung Lai, 2011. "Decision Network: A Planning Tool for Making Multiple, Linked Decisions," Environment and Planning B, , vol. 38(1), pages 115-128, February.
    5. Borgonovo, Emanuele & Marinacci, Massimo, 2015. "Decision analysis under ambiguity," European Journal of Operational Research, Elsevier, vol. 244(3), pages 823-836.
    6. Prakash Shenoy, 1998. "Game Trees For Decision Analysis," Theory and Decision, Springer, vol. 44(2), pages 149-171, April.
    7. 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.
    8. 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.
    9. Guo, Rui & Shenoy, Prakash P., 1996. "A note on Kirkwood's algebraic method for decision problems," European Journal of Operational Research, Elsevier, vol. 93(3), pages 628-638, September.
    10. Beroggi, Giampiero E. G., 2001. "Visual-interactive decision modeling (VIDEMO) in policy management: Bridging the gap between analytic and conceptual decision modeling," European Journal of Operational Research, Elsevier, vol. 128(2), pages 338-350, January.

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