A new methodology based on multistage stochastic programming for quality chain design problem

In multi-stage manufacturing/service systems, quality of final products depends on several decision variables and design factors from several stages of operations as well as environmental and operational nuisance factors. Typically, the effects of factors in one stage might remain significant at the next stages. Due to a high degree of interdependencies among the variables in/between the stages, multistage quality control methods have recently attracted special attentions. Multi-response optimization is a well-grounded method for an offline quality design that can consider several inputs and outputs. This study introduces a new multiresponse surface methodology by proposing two different modeling approaches for quality optimization in multistage systems with multiple response variables. Several stochastic parameters, including response surfaces and covariates, are to be considered the proposed models. In order to cope with the uncertainty, multistage stochastic programming is applied with a scenario generation algorithm based on Nataf transformation for correlated parameters. Also, a comprehensive numerical analysis is done to give more insights into the application of the proposed approach.