Response surfaces, desirabilities and rational functions in optimizing sugar production

Response surface methods have long been use in various chemical applications, most typically in optimization problems. Very often the problem, in addition to several design variables, has also several response variables to be optimized. A plethora of different approaches to multi-response optimization exists but, in terms of simplicity, it is difficult to beat the desirability function technique. In spite of its simplicity and efficiency, the desirability function technique seems not to be familiar for all chemometricians. This case study of optimizing full-scale sugar production will show how desirability functions were successfully used in response surface modeling (RSM)-based optimization. The optimization was based on ordinary least-squares regression polynomials. In addition to ordinary polynomial modeling, a new method of using rational functions, a linearizing transform and ridge regression is also introduced and discussed. In this study, a freeware computer program, R, for implementing response surface and desirability function methods is used. R plays the same de-facto standard role among statisticians as perhaps does Matlab among chemometricians. R is already used by some chemometricians and contains some chemometrics or chemometrics-related packages (R-packages are analogous to Matlab toolboxes). This study illustrates the use of some common RSM tools and desirability functions. Copyright (C) 2010 John Wiley & Sons, Ltd.