Design variables are important to be conducted the appropriate experiment analyzing and getting the accurate values for integer, discrete, zero-one (binary), and continuous variables. The researchers should classify design factors before the experiment is conducted. In literature, there are several factors such as quantitative, qualitative, discrete, continuous, zero-one (binary), non-zero-one (non-binary), controlled and uncontrolled variables (Sanchez & Wan, 2009).
Quantitative variables get numerical values. On the other hand, qualitative variables do not get numerical values, and they classify the values of the variables. Discrete variables can get only determined ...view middle of the document...
First-order and second-order models can be defined as approximation functions of the models. Firstly, if the response is described by just a linear function of the independent variables, then we call the function as the first-order model (1), and secondly if the response is modelled differ from a linear function of the independent variable, the function is called the second-order model (2).
In literature, a central composite design (CCD) can be also referred to as a rotatable CCD because the CCD should have rotatable property, especially interested in a second order model (Box & Hunter, 1957). The axial point is with , and for the CCD to be rotatable property with . The central composite (CCD) is the most popular class of designs used for fitting a second-order model (2), when (usually is preferred 3 or 4). The CCD with k factors consists of the total number of design points ( ), axial or star points (2k), and the number of runs at the center points ( ) design points, and when , a factorial design is usually used, and then is . When , a fractional factorial design of resolution V is a better choice, and is .
The MINLP can be solved as the relaxed model, and then it can be applied to any well-known algorithm. In this research paper, we are going to propose to apply to the nonlinear branch and bound technique. These kind of problems are observed by Sandgren (1990), Hajela & Shih (1990). Cao & Wu (1997), Kim et al. (1998), Lin et al. (1999), Alighanbari et al. (2005), and De Wit (2005). Because of non-convex property for MIP problems, they have to be gotten the results by some search strategy such as branch and bound method for getting the outcomes of MIP (Tran et al., 2007).
A brief information is given for the readers’ convenience in this study. RSM is also a beneficial quality improvement method for the researchers who can use RSM to find out the optimum factor levels such as maximize or minimize the conditions based on the assumption. The second-order model is used in this research paper because the effects of quadratic and interaction is also observed for the experiment. We also deal with the rotatable CCD which is useful to build the nonlinear programming model, and we should consider the rotatable property constraints for the design variables in the nonlinear model. After the model is built using the rotatable CCD, we apply to nonlinear branch and bound algorithm to get integer, discrete, and binary variables.
2. Literature Review
It is a critical question why we need especially integer, discrete and zero-one (binary) variables applying the design of experiment, and how to solve these kind of problems. In literature, there are many design of experiments using the rotatable CCD applications but a few articles are related to how to deal with the integer, discrete and zero-one (binary) variables using the design of experiment. However, these articles give some limited ideas how to get the integer, discrete and zero-one...