A positive approach to estimating the weights for quadratic multiple objective programming

This paper integrates positive and normative approaches to modelling. The normative approach uses assumptions associated with multiple objective programming. The positive approach uses past observations to estimate the weights associated with each objective criterion. The technique encompasses both linear and non-linear objectives such as profit, cost and risk as well as quadratic calibration terms. The proposed methodology minimizes the sum of squared errors about the ideal multiple objective function, that is one that would reproduce observed results, rather than to minimize errors between fitted and observed activity levels. The technique removes the need to rely upon the use of abstract restraints normally applied to mathematical programming methods and provides a more objective means of testing the appropriateness of a model than previously. The technique has many applications in the field of mathematical modelling such as forecasting and analysing changes in decision-making and behaviour.