An investigation of the use of goal programming to fit response surfaces

This paper deals with the development and implementation of goal programming models for fitting response surfaces where the observed data are characterized by certain peculiarities, such as the existence of ‘outliers’. A factorial statistical experiment is designed to compare (through Multivariate ANOVA) various forms of the goal programming algorithm with the traditional ordinary least squares method. The comparison is based on both the speed of convergence of the proposed algorithms and the accuracy of the estimated optimum solution relative to the true optimum of a pre-specified theoretical response surface. Results indicate that two different goal programming methods – each involving two secondary criteria – achieved a more accurate estimated solution than did the ordinary least squares method. This advantage is realized at the expense of slower convergence speed, however.