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Title: Analytic solutions to small scale two level programs with applications to the United States Department of Agriculture grain commodities programs;
United States Department of Agriculture grain commodities programs 
Author: Peterson, Henry Howard
Date: 1986
Abstract: The two level program is a model of a two stage, sequential decision making process involving two decision makers. Neither decision maker has control over all of the variables. The level one decisions are made first. Next, the level two decisions are made using the level one decisions as exogenous data. Various interactions can occur between the two levels and it is thus necessary for the level one decision makers to include in their decision making the possible reactions at level two. The optimal solution simultaneously satisfies both the level one program and the subprogram at level two. Published research to date has been primarily concerned with the search for efficient computer algorithms to two level programs. The main purpose of this research is to investigate analytic solutions to complex, nonlinear programs that are beyond solution by typical computer algorithms. The methodology derived is based on the well known theorems for the necessary and sufficient conditions for the solution of nonlinear programs by Kuhn-Tucker [1951] and by Arrow-Enthoven [1961]. First, the level two solution is derived as a function of the level one decision variables. Next, the level one solution is derived having incorporated the level two solutions. A nonlinear, two commodity model is formulated of the United states Department of Agriculture (USDA) grain commodities support program. Linear and nonlinear price and demand functions are explicitly included as functions of acreage withheld from production under the program. Other inputs include direct and cross elasticites of supply. Input data is from United States government publications. Methodology is derived for estimating the parameters of the price and demand functions. The results of the study indicate the feasibility and usefulness of using analytic methods to solve complex, nonlinear two level programs. Applications to the USDA's grain commodities program provided realistic projections of commodity prices, carryovers and program costs. Similar research should be conducted in other areas involving sequential decision making. The study should be useful as a reference in classroom studies.
Description: Binder's title on spine: United States Department of Agriculture grain commodities programs. Typescript. Thesis (Ph. D.)--University of Hawaii at Manoa, 1986. Bibliography: leaves 100-102. Photocopy. x, 102 leaves 29 cm
Rights: All UHM dissertations and theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission from the copyright owner.
Keywords: Decision making -- Mathematical models, Sequential analysis, Grain trade -- Decision making -- Mathematical models

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