Goal programming models and their duality relations for use in evaluating security portfolio and regression relations

The literature on multiple objective programming contains numerous examples in which goal programming is used to plan a selection of inputs to secure desired outputs that will conform ‘as closely as possible’ to a collection of (possibly conflicting) objectives. In this paper the orientation is changed from selection to evaluation and the dual variables associated with goal programming are brought into play for this purpose. The body of the paper is devoted to an example in portfolio planning modelled along lines like those used by Konno and Yamazaki where closeness to risk and return objective is measured in sums of absolute deviations. An appendix then shows how such a use of dual variables may be applied to evaluate least absolute value regressions relative to their sensitivity to data variation. Simple numerical examples are used to illustrate the potential uses of these dual variable values for evaluation in more complex situations that include determining whether an efficiency frontier has been attained.