IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v47y2001i9p1235-1251.html
   My bibliography  Save this article

Representing and Solving Decision Problems with Limited Information

Author

Listed:
  • Steffen L. Lauritzen

    (Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg, Denmark)

  • Dennis Nilsson

    (Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg, Denmark)

Abstract

We introduce the notion of LImited Memory Influence Diagram (LIMID) to describe multistage decision problems in which the traditional assumption of no forgetting is relaxed. This can be relevant in situations with multiple decision makers or when decisions must be prescribed under memory constraints, such as in partially observed Markov decision processes (POMDPs). We give an algorithm for improving any given strategy by local computation of single policy updates and investigate conditions for the resulting strategy to be optimal.

Suggested Citation

  • Steffen L. Lauritzen & Dennis Nilsson, 2001. "Representing and Solving Decision Problems with Limited Information," Management Science, INFORMS, vol. 47(9), pages 1235-1251, September.
    • Handle: RePEc:inm:ormnsc:v:47:y:2001:i:9:p:1235-1251
    DOI: 10.1287/mnsc.47.9.1235.9779
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.47.9.1235.9779
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.47.9.1235.9779?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
    ---><---

    References listed on IDEAS

    as
    1. Prakash P. Shenoy, 1992. "Valuation-Based Systems for Bayesian Decision Analysis," Operations Research, INFORMS, vol. 40(3), pages 463-484, June.
    2. 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. 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.
    2. Jannie Sønderkær Nielsen & John Dalsgaard Sørensen, 2014. "Methods for Risk-Based Planning of O&M of Wind Turbines," Energies, MDPI, vol. 7(10), pages 1-20, October.
    3. Fernandez del Pozo, J. A. & Bielza, C. & Gomez, M., 2005. "A list-based compact representation for large decision tables management," European Journal of Operational Research, Elsevier, vol. 160(3), pages 638-662, February.
    4. Apiruk Detwarasiti & Ross D. Shachter, 2005. "Influence Diagrams for Team Decision Analysis," Decision Analysis, INFORMS, vol. 2(4), pages 207-228, December.
    5. 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).
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Julia Mortera & Paola Vicard & Cecilia Vergari, 2012. "Object-Oriented Bayesian Networks for a Decision Support System," Departmental Working Papers of Economics - University 'Roma Tre' 0144, Department of Economics - University Roma Tre.
    11. 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.
    12. 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.
    13. Shoshana Anily & Abraham Grosfeld-Nir, 2006. "An Optimal Lot-Sizing and Offline Inspection Policy in the Case of Nonrigid Demand," Operations Research, INFORMS, vol. 54(2), pages 311-323, April.
    14. Chernonog, Tatyana & Avinadav, Tal, 2016. "A two-state partially observable Markov decision process with three actionsAuthor-Name: Ben-Zvi, Tal," European Journal of Operational Research, Elsevier, vol. 254(3), pages 957-967.
    15. Abraham Grosfeld‐Nir & Eyal Cohen & Yigal Gerchak, 2007. "Production to order and off‐line inspection when the production process is partially observable," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(8), pages 845-858, December.
    16. Finn Jensen & Thomas Nielsen, 2013. "Probabilistic decision graphs for optimization under uncertainty," Annals of Operations Research, Springer, vol. 204(1), pages 223-248, April.
    17. Barry R. Cobb, 2021. "Statistical Process Control for the Number of Defectives with Limited Memory," Decision Analysis, INFORMS, vol. 18(3), pages 203-217, September.
    18. Barry R. Cobb, 2007. "Influence Diagrams with Continuous Decision Variables and Non-Gaussian Uncertainties," Decision Analysis, INFORMS, vol. 4(3), pages 136-155, September.
    19. Atefeh Hasan-Zadeh, 2019. "Mathematical Modelling Of Decision-Making Application To Investment," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(2), pages 1-14, June.
    20. 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.
    21. Vincenzo Butticè & Carlotta Orsenigo & Mike Wright, 2018. "The effect of information asymmetries on serial crowdfunding and campaign success," Economia e Politica Industriale: Journal of Industrial and Business Economics, Springer;Associazione Amici di Economia e Politica Industriale, vol. 45(2), pages 143-173, 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. Prakash Shenoy, 1998. "Game Trees For Decision Analysis," Theory and Decision, Springer, vol. 44(2), pages 149-171, April.
    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. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Finn Jensen & Thomas Nielsen, 2013. "Probabilistic decision graphs for optimization under uncertainty," Annals of Operations Research, Springer, vol. 204(1), pages 223-248, April.
    12. Apiruk Detwarasiti & Ross D. Shachter, 2005. "Influence Diagrams for Team Decision Analysis," Decision Analysis, INFORMS, vol. 2(4), pages 207-228, December.
    13. repec:cup:judgdm:v:1:y:2006:i::p:162-173 is not listed on IDEAS
    14. Fernandez del Pozo, J. A. & Bielza, C. & Gomez, M., 2005. "A list-based compact representation for large decision tables management," European Journal of Operational Research, Elsevier, vol. 160(3), pages 638-662, February.
    15. Els Hannes & Diana Kusumastuti & Maikel Espinosa & Davy Janssens & Koen Vanhoof & Geert Wets, 2012. "Mental maps and travel behaviour: meanings and models," Journal of Geographical Systems, Springer, vol. 14(2), pages 143-165, April.
    16. Zitrou, Athena & Bedford, Tim & Walls, Lesley, 2010. "Bayes geometric scaling model for common cause failure rates," Reliability Engineering and System Safety, Elsevier, vol. 95(2), pages 70-76.
    17. 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.
    18. Robert F. Nease JR, 1996. "Do Violations of the Axioms of Expected Utility Theory Threaten Decision Analysis?," Medical Decision Making, , vol. 16(4), pages 399-403, October.
    19. 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.
    20. Lopez-Diaz, Miguel & Rodriguez-Muniz, Luis J., 2007. "Influence diagrams with super value nodes involving imprecise information," European Journal of Operational Research, Elsevier, vol. 179(1), pages 203-219, May.
    21. Oepping, Hardy, 2016. "Ein Bayes-Netz zur Analyse des Absturzrisikos im Gerüstbau [A Bayesian network for analysing the risk of falling from height in scaffolding]," MPRA Paper 73602, University Library of Munich, Germany.

    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:inm:ormnsc:v:47:y:2001:i:9:p:1235-1251. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.