IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/62.html
   My bibliography  Save this paper

Linear Programming and Sequential Decision Models

Author

Listed:
  • Alan S. Manne

Abstract

This paper is designed to show how a typical sequential probabilistic model may be formulated in linear programming terms. In contrast with Dantzig and Radner, the time horizon here is an infinite one. For another very closely related study, the reader is referred to a paper by R. Howard. The essential idea underlying this linear programming formulation is that the "state" variable i and the "decision" variable j are introduced as subscripts to the unknowns x_{ij}. These unknowns x_{ij} represent the joint probabilities with which the state variable takes on the value of i and the decision variable the value of j. Although the particular application described is a rather specialized one, there seem to be quite a number of other cases where the technique should be an efficient alternative to the functional equation approach of Bellman.

Suggested Citation

  • Alan S. Manne, 1959. "Linear Programming and Sequential Decision Models," Cowles Foundation Discussion Papers 62, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:62
    Note: CFP 148.
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d00/d0062.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Roy Radner, 1959. "The Application of Linear Programming to Team Decision Problems," Management Science, INFORMS, vol. 5(2), pages 143-150, January.
    2. John D. C. Little, 1955. "The Use of Storage Water in a Hydroelectric System," Operations Research, INFORMS, vol. 3(2), pages 187-197, May.
    Full references (including those not matched with items on IDEAS)

    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. Durmaz, Tunç, 2016. "Precautionary Storage in Electricity Markets," Discussion Papers 2016/5, Norwegian School of Economics, Department of Business and Management Science.
    2. Truchon, Michel, 1988. "Programmation mathématique et théorie économique," L'Actualité Economique, Société Canadienne de Science Economique, vol. 64(2), pages 143-156, juin.
    3. Lamond, Bernard F. & Monroe, Susan L. & Sobel, Matthew J., 1995. "A reservoir hydroelectric system: Exactly and approximately optimal policies," European Journal of Operational Research, Elsevier, vol. 81(3), pages 535-542, March.
    4. Luss, Hanan & Rosenwein, Moshe B., 1997. "Operations Research applications: Opportunities and accomplishments," European Journal of Operational Research, Elsevier, vol. 97(2), pages 220-244, March.
    5. Rusmevichientong, Paat & Van Roy, Benjamin, 2003. "Decentralized decision-making in a large team with local information," Games and Economic Behavior, Elsevier, vol. 43(2), pages 266-295, May.
    6. Andre Luiz Diniz & Maria Elvira P. Maceira & Cesar Luis V. Vasconcellos & Debora Dias J. Penna, 2020. "A combined SDDP/Benders decomposition approach with a risk-averse surface concept for reservoir operation in long term power generation planning," Annals of Operations Research, Springer, vol. 292(2), pages 649-681, September.
    7. Philpott, A.B. & de Matos, V.L., 2012. "Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion," European Journal of Operational Research, Elsevier, vol. 218(2), pages 470-483.
    8. A. Lust & K.-H. Waldmann, 2019. "A general storage model with applications to energy systems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(1), pages 71-97, March.
    9. DAKHLAOUI Ahlem, 2007. "Dynamic games in the wholesale electricity market," LERNA Working Papers 07.21.242, LERNA, University of Toulouse.
    10. C.B. McGuire, 1958. "Some Models of a Sales Organization," Cowles Foundation Discussion Papers 53, Cowles Foundation for Research in Economics, Yale University.
    11. Renée Kidson & Brent Haddad & Hui Zheng & Steven Kasower & Robert Raucher, 2013. "Optimising Reliability: Portfolio Modeling of Contract Types for Retail Water Providers," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(9), pages 3209-3225, July.
    12. Chengjun Wu & Guohua Fang & Tao Liao & Xianfeng Huang & Bo Qu, 2020. "Integrated Software Development and Case Studies for Optimal Operation of Cascade Reservoir within the Environmental Flow Constraints," Sustainability, MDPI, vol. 12(10), pages 1-16, May.
    13. Ignacio Guisández & Juan I. Pérez-Díaz & José R. Wilhelmi, 2016. "The Influence of Environmental Constraints on the Water Value," Energies, MDPI, vol. 9(6), pages 1-21, June.
    14. DAKHLAOUI Ahlem & MOREAUX Michel, 2007. "Trade-off between Hydro and Thermal Power Generation under Uncertainty," LERNA Working Papers 07.13.234, LERNA, University of Toulouse.

    More about this item

    Statistics

    Access and download statistics

    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:cwl:cwldpp:62. 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: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.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.