Conservative linear programming with mixed multiple objectives |
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Authors: | AL Soyster B Lev DI Toof |
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Affiliation: | Virginia Polytechnic Institute and State University USA;Temple University, Philadelphia, PA USA;Arthur Young, Washington, DC USA |
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Abstract: | In an ordinary linear program a single objective vector is constructed and one attempts to choose a decision vector to optimize this objective. Often multiple criteria exist or exact estimates for the components of a single objective vector are not entirely clear. For these cases a conservative decision-maker may want to choose an alternative that maximizes the objective value under the worst foreseeable circumstances. Herein we develop a unified framework for applying the maximin criterion to problems with various degrees of uncertainty attached to the objective vector. Three cases are solved via linear programming: (1) Complete Information, (2) Partial Information, and (3) Total Ignorance. It is shown that the functional value of the maximin solution decreases in a convex manner with increasing uncertainty. In addition certain relationships between maximin and efficient solutions are provided. Finally, an extension to integer constrained decision variables is presented. |
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