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Sharp Bounds on the Value of Perfect Information

Author

Listed:
  • C. C. Huang

    (Memorial University of Newfoundland, St. Johns, Newfoundland)

  • I. Vertinsky

    (International Institute of Management, Berlin)

  • W. T. Ziemba

    (University of British Columbia, Vancouver, British Columbia)

Abstract

We present sharp bounds on the value of perfect information for static and dynamic simple recourse stochastic programming problems. The bounds are sharper than the available bounds based on Jensen's inequality. The new bounds use some recent extensions of Jensen's upper bound and the Edmundson-Madansky lower bound on the expectation of a concave function of several random variables. Bounds are obtained for nonlinear return functions and linear and strictly increasing concave utility functions for static and dynamic problems. When the random variables are jointly dependent, the Edmundson-Madansky type bound must be replaced by a less sharp “feasible point” bound. Bounds that use constructs from mean-variance analysis are also presented. With independent random variables the calculation of the bounds generally involves several simple univariate numerical integrations and the solution of several similar nonlinear programs. These bounds may be made as sharp as desired with increasing computational effort. The bounds are illustrated on a well-known problem in the literature and on a portfolio selection problem.

Suggested Citation

  • C. C. Huang & I. Vertinsky & W. T. Ziemba, 1977. "Sharp Bounds on the Value of Perfect Information," Operations Research, INFORMS, vol. 25(1), pages 128-139, February.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:1:p:128-139
    DOI: 10.1287/opre.25.1.128
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    Cited by:

    1. Rostami, Salim & Creemers, Stefan & Leus, Roel, 2024. "Maximizing the net present value of a project under uncertainty: Activity delays and dynamic policies," European Journal of Operational Research, Elsevier, vol. 317(1), pages 16-24.
    2. Francesca Maggioni & Elisabetta Allevi & Marida Bertocchi, 2016. "Monotonic bounds in multistage mixed-integer stochastic programming," Computational Management Science, Springer, vol. 13(3), pages 423-457, July.
    3. Bomze, Immanuel M. & Gabl, Markus & Maggioni, Francesca & Pflug, Georg Ch., 2022. "Two-stage stochastic standard quadratic optimization," European Journal of Operational Research, Elsevier, vol. 299(1), pages 21-34.
    4. Francesca Maggioni & Elisabetta Allevi & Asgeir Tomasgard, 2020. "Bounds in multi-horizon stochastic programs," Annals of Operations Research, Springer, vol. 292(2), pages 605-625, September.
    5. Marcio Costa Santos & Michael Poss & Dritan Nace, 2018. "A perfect information lower bound for robust lot-sizing problems," Annals of Operations Research, Springer, vol. 271(2), pages 887-913, December.
    6. Ali E. Abbas & N. Onur Bakır & Georgia-Ann Klutke & Zhengwei Sun, 2013. "Effects of Risk Aversion on the Value of Information in Two-Action Decision Problems," Decision Analysis, INFORMS, vol. 10(3), pages 257-275, September.
    7. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    8. Zhengwei Sun & Ali E. Abbas, 2014. "On the sensitivity of the value of information to risk aversion in two-action decision problems," Environment Systems and Decisions, Springer, vol. 34(1), pages 24-37, March.

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