GOAL PROGRAMMING-MODELS AND THEIR DUALITY RELATIONS FOR USE IN EVALUATING SECURITY PORTFOLIO AND REGRESSION RELATIONS

The literature on multiple objective programming contains numerous exa mples in which goal programming is used to plan a selection of inputs to secure desired outputs that will conform 'as closely as possible' t o a collection of (possibly conflicting) objectives. In this paper the orientation is changed from selection to evaluation and the dual vari ables associated with goal programming are brought into play for this purpose. The body of the paper is devoted to an example in portfolio p lanning modelled along lines like those used by Konno and Yamazaki whe re closeness to risk and return objective is measured in sums of absol ute deviations. An appendix then shows how such a use of dual variable s may be applied to evaluate least absolute value (LAV) regressions re lative to their sensitivity to data variations. Simple numerical examp les are used to illustrate the potential uses of these dual variable v alues for evaluation in more complex situations that include determini ng whether an efficiency frontier has been attained. (C) 1997 Elsevier Science B.V.