Date of Award

5-2007

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Mathematical Science

Advisor

Kostreva, Michael M

Abstract

Equitable efficiency in multiple criteria optimization was introduced mathematically in the middle of nineteen-nineties. The concept tends to strengthen the notion of Pareto efficiency by imposing additional conditions on the preference
structure defining the Pareto preference. It is especially designed to solve multiple criteria problems having commensurate criteria where different criteria values can be compared directly.

In this dissertation we study some theoretical and practical aspects of equitably efficient solutions. The literature on equitable efficiency is not very extensive and provides very limited number of ways of generating such solutions. After introducing
some relevant notations, we develop some scalarization based methods of
generating equitably efficient solutions. The scalarizations developed do not assume any special structure of the problem. We prove an existence result for linear multiple criteria problems.

Next, we show how equitably efficient solutions arise in the context of a
particular type of linear complementarity problem and matrix games. The set of equitably efficient solutions, in general, is a subset of efficient solutions. The multiple
criteria alternative of the linear complementarity problem dealt in our dissertation has identical efficient and equitably efficient solution sets.

Finally, we demonstrate the relevance of equitable efficiency by applying it
to the problem of regression analysis and asset allocation.

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