IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v462y2016icp217-221.html
   My bibliography  Save this article

On the Bellman’s principle of optimality

Author

Listed:
  • Gross, Eitan

Abstract

Bellman’s equation is widely used in solving stochastic optimal control problems in a variety of applications including investment planning, scheduling problems and routing problems. Building on Markov decision processes for stationary policies, we present a new proof for Bellman’s equation of optimality. Our proof rests its case on the availability of an explicit model of the environment that embodies transition probabilities and associated costs.

Suggested Citation

  • Gross, Eitan, 2016. "On the Bellman’s principle of optimality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 217-221.
  • Handle: RePEc:eee:phsmap:v:462:y:2016:i:c:p:217-221
    DOI: 10.1016/j.physa.2016.06.083
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843711630351X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2016.06.083?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. Caplin, DA & Kornbluth, JSH, 1975. "Multiobjective investment planning under uncertainty," Omega, Elsevier, vol. 3(4), pages 423-441, August.
    2. Chand, Suresh & Schneeberger, Hans, 1988. "Single machine scheduling to minimize weighted earliness subject to no tardy jobs," European Journal of Operational Research, Elsevier, vol. 34(2), pages 221-230, March.
    3. Robert A. Abrams & Uday S. Karmarkar, 1979. "Infinite Horizon Investment--Consumption Policies," Management Science, INFORMS, vol. 25(10), pages 1005-1013, October.
    4. Eric V. Denardo & Bennett L. Fox, 1979. "Shortest-Route Methods: 2. Group Knapsacks, Expanded Networks, and Branch-and-Bound," Operations Research, INFORMS, vol. 27(3), pages 548-566, June.
    5. Gregory P. Prastacos, 1983. "Optimal Sequential Investment Decisions Under Conditions of Uncertainty," Management Science, INFORMS, vol. 29(1), pages 118-134, January.
    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. Andyn Omanovic & Norbert Zsiga & Patrik Soltic & Christopher Onder, 2021. "Optimal Degree of Hybridization for Spark-Ignited Engines with Optional Variable Valve Timings," Energies, MDPI, vol. 14(23), pages 1-21, December.

    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. Hansen, Paul & Ryan, Jennifer, 1996. "Testing integer knapsacks for feasibility," European Journal of Operational Research, Elsevier, vol. 88(3), pages 578-582, February.
    2. Xuhan Tian & Junmin (Jim) Shi & Xiangtong Qi, 2022. "Stochastic Sequential Allocations for Creative Crowdsourcing," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 697-714, February.
    3. Bachtenkirch, David & Bock, Stefan, 2022. "Finding efficient make-to-order production and batch delivery schedules," European Journal of Operational Research, Elsevier, vol. 297(1), pages 133-152.
    4. A A Namen & C T Bornstein & J Rosenhead, 2009. "Robustness analysis for sustainable community development," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(5), pages 587-597, May.
    5. Yuanzheng Ma & Tong Wang & Huan Zheng, 2023. "On fairness and efficiency in nonprofit operations: Dynamic resource allocations," Production and Operations Management, Production and Operations Management Society, vol. 32(6), pages 1778-1792, June.
    6. Heidenberger, Kurt, 1996. "Dynamic project selection and funding under risk: A decision tree based MILP approach," European Journal of Operational Research, Elsevier, vol. 95(2), pages 284-298, December.
    7. So, Mee Chi & Thomas, Lyn C. & Huang, Bo, 2016. "Lending decisions with limits on capital available: The polygamous marriage problem," European Journal of Operational Research, Elsevier, vol. 249(2), pages 407-416.
    8. Feng Li & Zhi-Long Chen & Zhi-Long Chen, 2017. "Integrated Production, Inventory and Delivery Problems: Complexity and Algorithms," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 232-250, May.
    9. Wan, Guohua & Yen, Benjamin P.-C., 2009. "Single machine scheduling to minimize total weighted earliness subject to minimal number of tardy jobs," European Journal of Operational Research, Elsevier, vol. 195(1), pages 89-97, May.
    10. Alessandro Arlotto & Noah Gans & J. Michael Steele, 2014. "Markov Decision Problems Where Means Bound Variances," Operations Research, INFORMS, vol. 62(4), pages 864-875, August.
    11. Vincent T’kindt & Karima Bouibede-Hocine & Carl Esswein, 2007. "Counting and enumeration complexity with application to multicriteria scheduling," Annals of Operations Research, Springer, vol. 153(1), pages 215-234, September.
    12. Asano, Makoto & Ohta, Hiroshi, 1999. "Single machine scheduling to meet due times under shutdown constraints," International Journal of Production Economics, Elsevier, vol. 60(1), pages 537-547, April.
    13. Anton J. Kleywegt & Jason D. Papastavrou, 1998. "The Dynamic and Stochastic Knapsack Problem," Operations Research, INFORMS, vol. 46(1), pages 17-35, February.
    14. Anton J. Kleywegt & Jason D. Papastavrou, 2001. "The Dynamic and Stochastic Knapsack Problem with Random Sized Items," Operations Research, INFORMS, vol. 49(1), pages 26-41, February.
    15. Grace Y. Lin & Yingdong Lu & David D. Yao, 2008. "The Stochastic Knapsack Revisited: Switch-Over Policies and Dynamic Pricing," Operations Research, INFORMS, vol. 56(4), pages 945-957, August.
    16. Choobineh, F. Fred & Mohebbi, Esmail & Khoo, Hansen, 2006. "A multi-objective tabu search for a single-machine scheduling problem with sequence-dependent setup times," European Journal of Operational Research, Elsevier, vol. 175(1), pages 318-337, November.
    17. Pathumnakul, Supachai & Egbelu, Pius J., 2005. "Algorithm for minimizing weighted earliness penalty in single-machine problem," European Journal of Operational Research, Elsevier, vol. 161(3), pages 780-796, March.
    18. Chen, Wei-Yang & Sheen, Gwo-Ji, 2007. "Single-machine scheduling with multiple performance measures: Minimizing job-dependent earliness and tardiness subject to the number of tardy jobs," International Journal of Production Economics, Elsevier, vol. 109(1-2), pages 214-229, September.
    19. Ouhimmou, M. & D'Amours, S. & Beauregard, R. & Ait-Kadi, D. & Chauhan, S. Singh, 2008. "Furniture supply chain tactical planning optimization using a time decomposition approach," European Journal of Operational Research, Elsevier, vol. 189(3), pages 952-970, September.
    20. H-Y Wong, 2007. "Using Robustness Analysis to structure online marketing and communication problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(5), pages 633-644, May.

    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:eee:phsmap:v:462:y:2016:i:c:p:217-221. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.