Development of a multiple response-based mixed-integer nonlinear optimization model with both controllable and uncontrollable design factors

Response surface methodology (RSM) is an appropriate tool for modeling and analyzing existing or new products. In the literature, considerable attention has been paid to develop RSM models while using controllable design factors. However, there are some situations where uncontrollable design factors are required to conduct an experiment. Therefore, this paper is four-fold. One, an A-optimal design is selected as the appropriate design to generate the design matrix. Two, an exchange algorithm is proposed to construct A-optimal design points while dealing with uncontrollable design factors. In addition, fitted mean and standard deviation response functions are obtained with both controllable and uncontrollable design factors. Three, a multiple response-based mixed-integer nonlinear model and its solution procedure are proposed to find optimum operating conditions of both controllable and uncontrollable design factors. Next, a case study is presented to show the effectiveness of the proposed methodology. It is also reported from the case study that the proposed optimization model may achieve a variance reduction of up to 73% compared to the traditional counterpart. Finally, comparison and validation studies are conducted to verify the optimum operating conditions.