Solving Multi-Response Problem Using Goal Programming Approach and Quantile Regression

Abstract

Response surface methodology (RSM) is a group of mathematical and statistical techniques helpful for improving, developing and optimizing processes. It also has important uses in the design, development and formulation of new products. Moreover, it has a great help in the enhancement of existing products. (RSM) is a method used to discover response functions, which meet and fulfill all quality diagnostics simultaneously. Most applications have more than one response; the main problem is multi-response optimization (MRO). The classical methods used to solve the Multi-Response Optimization problem do not guarantee optimal designs and solutions. Besides, they take a long time and depend on the researcher's judgment. Therefore, some researchers used a Goal Programming-based method; however, they still do not guarantee an optimal solution. This study aims to form a goal programming model derived from a chance constrained approach using quantile regression to deal with outliers not normal and errors. It describes the relationship between responses and control variables at distinctive points in the response conditional distribution; it also considers the uncertainty problem and presents an illustrative example and simulation study for the suggested model.