Linear Programming and Sequential Decision Models

Alan Manne

No 62, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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.

Pages: 16 pages
Date: 1959
Note: CFP 148.
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Published in Management Science (April 1960), 6(3): 259-267

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