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Generating Scenario Trees for Multistage Decision Problems


  • Kjetil Høyland

    () (Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, N-7491 Trondheim, Norway)

  • Stein W. Wallace

    () (Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, N-7491 Trondheim, Norway)


In models of decision making under uncertainty we often are faced with the problem of representing the uncertainties in a form suitable for quantitative models. If the uncertainties are expressed in terms of multivariate continuous distributions, or a discrete distribution with far too many outcomes, we normally face two possibilities: either creating a decision model with internal sampling, or trying to find a simple discrete approximation of the given distribution that serves as input to the model. This paper presents a method based on nonlinear programming that can be used to generate a limited number of discrete outcomes that satisfy specified statistical properties. Users are free to specify any statistical properties they find relevant, and the method can handle inconsistencies in the specifications. The basic idea is to minimize some measure of distance between the statistical properties of the generated outcomes and the specified properties. We illustrate the method by single- and multiple-period problems. The results are encouraging in that a limited number of generated outcomes indeed have statistical properties that are close to or equal to the specifications. We discuss how to verify that the relevant statistical properties are captured in these specifications, and argue that what are the relevant properties, will be problem dependent.

Suggested Citation

  • Kjetil Høyland & Stein W. Wallace, 2001. "Generating Scenario Trees for Multistage Decision Problems," Management Science, INFORMS, vol. 47(2), pages 295-307, February.
  • Handle: RePEc:inm:ormnsc:v:47:y:2001:i:2:p:295-307

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    References listed on IDEAS

    1. Donald L. Keefer & Samuel E. Bodily, 1983. "Three-Point Approximations for Continuous Random Variables," Management Science, INFORMS, vol. 29(5), pages 595-609, May.
    2. Allen C. Miller, III & Thomas R. Rice, 1983. "Discrete Approximations of Probability Distributions," Management Science, INFORMS, vol. 29(3), pages 352-362, March.
    3. James E. Smith, 1993. "Moment Methods for Decision Analysis," Management Science, INFORMS, vol. 39(3), pages 340-358, March.
    4. Hoyland, Kjetil & Wallace, Stein W., 2001. "Analyzing legal regulations in the Norwegian life insurance business using a multistage asset-liability management model," European Journal of Operational Research, Elsevier, vol. 134(2), pages 293-308, October.
    5. Donald L. Keefer, 1994. "Certainty Equivalents for Three-Point Discrete-Distribution Approximations," Management Science, INFORMS, vol. 40(6), pages 760-773, June.
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