A Bayesian approach for multiple criteria decision making with applications in Design for Six Sigma

The usual approach to solving the Multiple Criteria Decision Making (MCDM) problem is by either using a weighted objective function based on each individual objective or by optimizing one objective while setting constraints on the others. These approaches try to find a point on the efficient frontier or the Pareto optimal set based on the preferences of the decision maker. Here, a new algorithm is proposed to solve a MCDM problem based on a Bayesian methodology. At a first stage, it is assumed that there are process responses that are functions of certain controllable factors or regressors. At a second stage, the responses in turn influence the utility function of one or more decision makers. Both stages are modelled with Bayesian regression techniques. The advantages of using the Bayesian approach as opposed to traditional methods are highlighted. The methodology is applied to engineering design problems, providing a rigorous formulation to popular “Design for Six Sigma” approaches.