Developing a two‐stage stochastic programming model in tolerance optimization using a guard band approach

Abstract

An alternative way of looking at tolerance optimization is presented through a stochastic perspective by accounting for both manufacturing process uncertainty as well as uncertain market conditions. This can be accomplished by looking at a two‐stage stochastic programming model where the decision maker takes a course of action in the first stage, such as setting the product selling prices based on product quality, after which a random event occurs, leading to a recourse decision in the second stage. Production processes face uncertainties which impact product characteristics. The recourse decisions are the specification limits and upper and lower guard bands are necessary to monitor the process. This leads to the binning of a product based on its quality, uncertain market demand, and uncertain production process. The selling prices, the specification limits and the guard bands are then determined based on these uncertain conditions. The model presented is based on chance‐constrained programming, utilizing sample average approximation methods to solve the problem.