Representing and Solving Asymmetric Decision Problems Using Valuation Networks

  • Prakash P. Shenoy
Part of the Lecture Notes in Statistics book series (LNS, volume 112)

Abstract

This paper deals with asymmetric decision problems. We describe a generalization of the valuation network representation and solution technique to enable efficient representation and solution of asymmetric decision problems. The generalization includes the concepts of indicator valuations and effective frames. We illustrate our technique by solving Raiffa’s oil wildcatter’s problem in complete detail.

Keywords

Drilling 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Call, H. J. and W. A. Miller (1990), “A comparison of approaches and implementations for automating decision analysis,” Reliability Engineering and System Safety,30, 115–162.CrossRefGoogle Scholar
  2. Covaliu, Z. and R. M. Oliver (1996), “Formulation and solution of decision problems using sequential decision diagrams,” Management Science, to appear.Google Scholar
  3. Fung, R. M. and R. D. Shachter (1990), “Contingent influence diagrams,” Working Paper, Advanced Decision Systems, Mountain View, CA.Google Scholar
  4. Howard, R. A. and J. E. Matheson (1981), “Influence diagrams,” in R. A. Howard and J. E. Matheson (eds.) (1984), The Principles and Applications of Decision Analysis, 2, 719–762, Strategic Decisions Group, Menlo Park, CA.Google Scholar
  5. Raiffa, H. (1968), Decision Analysis, Addison-Wesley, Reading, MA.MATHGoogle Scholar
  6. Shenoy, P. P. (1992), “Valuation-based systems for Bayesian decision analysis,” Operations Research, 40 (3), 463–484.MathSciNetMATHCrossRefGoogle Scholar
  7. Shenoy, P. P. (1993a), “A new method for representing and solving Bayesian decision problems,” in D. J. Hand (ed.), Artificial Intelligence Frontiers in Statistics: AI and Statistics III, 119–138, Chapman & Hall, London.Google Scholar
  8. Shenoy, P. P. (1993b), “Valuation network representation and solution of asymmetric decision problems,” Working Paper No. 246, School of Business, University of Kansas, Lawrence, KS.Google Scholar
  9. Shenoy, P. P. (1994), “Consistency in valuation-based systems,” ORSA Journal on Computing, 6 (3), 281–291.MathSciNetMATHGoogle Scholar
  10. Shenoy, P. P. and G. Shafer (1990), “Axioms for probability and belief-function propagation,” in R. D. Shachter, T. S. Levitt, J. F. Lemmer and L. N. Kanal (eds.), Uncertainty in Artificial Intelligence, 4, 169–198, North-Holland, Amsterdam.Google Scholar
  11. Smith, J. E., S. Holtzman and J. E. Matheson (1993), “Structuring conditional relationships in influence diagrams,” Operations Research, 41 (2), 280–297.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Prakash P. Shenoy
    • 1
  1. 1.School of BusinessUniversity of KansasLawrenceUSA

Personalised recommendations