A multi-objective mathematical optimization model for process targeting using 100% inspection policy

The selection of the optimal process target is an important problem in production planning and quality control. Such process targeting problems are usually modeled in the literature using a single objective optimization model. In this paper multi-objective optimization is introduced in the process targeting area. The quality characteristic under consideration is normally distributed with unknown mean and known standard deviation, and has two market specification limits. 100% inspection is used as the mean of product quality control. Product satisfies the first specification limit is sold in a primary market at a regular price and products fails the first specification limit and satisfies the second one is sold in a secondary market at a reduced price. The product is reworked if it does not satisfy both specification limits. The developed multi-objective optimization model consists of three objective functions, which are to maximize profit, income and product uniformity using Taguchi quadratic function as a surrogate for product uniformity. An algorithm is proposed to obtain and rank the set of Pareto optimal points. The utility of the model has been demonstrated using a numerical example from the literature with some additional data the new model requires. Sensitivity analysis was conducted and showed that the results of the model are sensitive to changes in process variance. In addition the optimal objectives of the profit function and product uniformity are more sensitive to changes in model parameters than the income function.