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Conservative linear programming with mixed multiple objectives

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  • Soyster, AL
  • Lev, B
  • Toof, DI

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.

Suggested Citation

  • Soyster, AL & Lev, B & Toof, DI, 1977. "Conservative linear programming with mixed multiple objectives," Omega, Elsevier, vol. 5(2), pages 193-205.
  • Handle: RePEc:eee:jomega:v:5:y:1977:i:2:p:193-205
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