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Linear Programming and Sequential Decision Models

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  • 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.
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d00/d0062.pdf
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    References listed on IDEAS

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    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.
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