A Mixed Integer Linear Programming Model for Finding Optimum Operating Conditions of Experimental Design Variables Using Computer-Aided Optimal Experimental Designs

Computer-aided optimal experimental designs are an effective quality improvement tool that provides insights of information under various quality engineering problems. In the literature, considerable attention has been focused on maximizing the determinant of the information matrix in order to generate optimal design points. However, minimizing the average prediction based on the I-optimality criterion is more useful than commonly used D-optimality criterion for a number of situations. In this paper, special experimental design situations are explored where both qualitative and quantitative input variables are considered for an irregular design space with the pre-specified number of design points and the first-order polynomial model. In addition, this paper lays out the algorithmic foundations for the proposed D- and I-optimality criteria embedded mixed integer linear programming models in order to obtain optimal operating conditions using the first-order response functions. Comparative studies are also conducted. The results show that the proposed model for the D-optimality is able to identify approximately 30% smaller standard deviation value than the traditional counterpart. The proposed model for the I-optimality also provides a feasible solution whereas there is no optimum solution for the traditional counterpart.