IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v204y2013i1p223-24810.1007-s10479-012-1263-6.html
   My bibliography  Save this article

Probabilistic decision graphs for optimization under uncertainty

Author

Listed:
  • Finn Jensen
  • Thomas Nielsen

Abstract

This paper provides a survey on probabilistic decision graphs for modeling and solving decision problems under uncertainty. We give an introduction to influence diagrams, which is a popular framework for representing and solving sequential decision problems with a single decision maker. As the methods for solving influence diagrams can scale rather badly in the length of the decision sequence, we present a couple of approaches for calculating approximate solutions. The modeling scope of the influence diagram is limited to so-called symmetric decision problems. This limitation has motivated the development of alternative representation languages, which enlarge the class of decision problems that can be modeled efficiently. We present some of these alternative frameworks and demonstrate their expressibility using several examples. Finally, we provide a list of software systems that implement the frameworks described in the paper. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Finn Jensen & Thomas Nielsen, 2013. "Probabilistic decision graphs for optimization under uncertainty," Annals of Operations Research, Springer, vol. 204(1), pages 223-248, April.
    • Handle: RePEc:spr:annopr:v:204:y:2013:i:1:p:223-248:10.1007/s10479-012-1263-6
    DOI: 10.1007/s10479-012-1263-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-012-1263-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-012-1263-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Koller, Daphne & Milch, Brian, 2003. "Multi-agent influence diagrams for representing and solving games," Games and Economic Behavior, Elsevier, vol. 45(1), pages 181-221, October.
    2. Cobb, Barry R. & Shenoy, Prakash P., 2008. "Decision making with hybrid influence diagrams using mixtures of truncated exponentials," European Journal of Operational Research, Elsevier, vol. 186(1), pages 261-275, April.
    3. 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.
    4. John M. Charnes & Prakash P. Shenoy, 2004. "Multistage Monte Carlo Method for Solving Influence Diagrams Using Local Computation," Management Science, INFORMS, vol. 50(3), pages 405-418, March.
    5. Steffen L. Lauritzen & Dennis Nilsson, 2001. "Representing and Solving Decision Problems with Limited Information," Management Science, INFORMS, vol. 47(9), pages 1235-1251, September.
    6. Prakash P. Shenoy, 1992. "Valuation-Based Systems for Bayesian Decision Analysis," Operations Research, INFORMS, vol. 40(3), pages 463-484, June.
    7. Ross D. Shachter & C. Robert Kenley, 1989. "Gaussian Influence Diagrams," Management Science, INFORMS, vol. 35(5), pages 527-550, May.
    8. Ross D. Shachter, 1986. "Evaluating Influence Diagrams," Operations Research, INFORMS, vol. 34(6), pages 871-882, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Manuele Leonelli & James Smith, 2015. "Bayesian decision support for complex systems with many distributed experts," Annals of Operations Research, Springer, vol. 235(1), pages 517-542, December.
    2. Xiaoge Zhang & Andrew Adamatzky & Felix T. S. Chan & Sankaran Mahadevan & Yong Deng, 2017. "Physarum solver: a bio-inspired method for sustainable supply chain network design problem," Annals of Operations Research, Springer, vol. 254(1), pages 533-552, July.
    3. Andrew J. Keith & Darryl K. Ahner, 2021. "A survey of decision making and optimization under uncertainty," Annals of Operations Research, Springer, vol. 300(2), pages 319-353, May.
    4. Manuele Leonelli & Eva Riccomagno & Jim Q. Smith, 2020. "Coherent combination of probabilistic outputs for group decision making: an algebraic approach," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(2), pages 499-528, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Yijing Li & Prakash P. Shenoy, 2012. "A Framework for Solving Hybrid Influence Diagrams Containing Deterministic Conditional Distributions," Decision Analysis, INFORMS, vol. 9(1), pages 55-75, March.
    4. Cobb, Barry R. & Shenoy, Prakash P., 2008. "Decision making with hybrid influence diagrams using mixtures of truncated exponentials," European Journal of Operational Research, Elsevier, vol. 186(1), pages 261-275, April.
    5. Barry R. Cobb, 2007. "Influence Diagrams with Continuous Decision Variables and Non-Gaussian Uncertainties," Decision Analysis, INFORMS, vol. 4(3), pages 136-155, September.
    6. Apiruk Detwarasiti & Ross D. Shachter, 2005. "Influence Diagrams for Team Decision Analysis," Decision Analysis, INFORMS, vol. 2(4), pages 207-228, December.
    7. Koller, Daphne & Milch, Brian, 2003. "Multi-agent influence diagrams for representing and solving games," Games and Economic Behavior, Elsevier, vol. 45(1), pages 181-221, October.
    8. Erik Jørgensen & Anders Kristensen & Dennis Nilsson, 2014. "Markov Limid processes for representing and solving renewal problems," Annals of Operations Research, Springer, vol. 219(1), pages 63-84, August.
    9. John M. Charnes & Prakash P. Shenoy, 2004. "Multistage Monte Carlo Method for Solving Influence Diagrams Using Local Computation," Management Science, INFORMS, vol. 50(3), pages 405-418, March.
    10. Salo, Ahti & Andelmin, Juho & Oliveira, Fabricio, 2022. "Decision programming for mixed-integer multi-stage optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 299(2), pages 550-565.
    11. Tan, Kim Hua & Zhan, YuanZhu & Ji, Guojun & Ye, Fei & Chang, Chingter, 2015. "Harvesting big data to enhance supply chain innovation capabilities: An analytic infrastructure based on deduction graph," International Journal of Production Economics, Elsevier, vol. 165(C), pages 223-233.
    12. Prakash Shenoy, 1998. "Game Trees For Decision Analysis," Theory and Decision, Springer, vol. 44(2), pages 149-171, April.
    13. 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.
    14. 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.
    15. 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.
    16. Debarun Bhattacharjya & Ross D. Shachter, 2012. "Formulating Asymmetric Decision Problems as Decision Circuits," Decision Analysis, INFORMS, vol. 9(2), pages 138-145, June.
    17. Misuri, Alessio & Khakzad, Nima & Reniers, Genserik & Cozzani, Valerio, 2019. "A Bayesian network methodology for optimal security management of critical infrastructures," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    18. Concha Bielza & Peter Müller & David Ríos Insua, 1999. "Decision Analysis by Augmented Probability Simulation," Management Science, INFORMS, vol. 45(7), pages 995-1007, July.
    19. Francisco Javier Díez & Manuel Arias & Jorge Pérez-Martín & Manuel Luque, 2022. "Teaching Probabilistic Graphical Models with OpenMarkov," Mathematics, MDPI, vol. 10(19), pages 1-20, September.
    20. Steffen L. Lauritzen & Dennis Nilsson, 2001. "Representing and Solving Decision Problems with Limited Information," Management Science, INFORMS, vol. 47(9), pages 1235-1251, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:204:y:2013:i:1:p:223-248:10.1007/s10479-012-1263-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.