Lot sizing and quality investment with quality cost analyses for imperfect production and inspection processes with commercial return

This study examines an imperfect production and inspection system with customer return and defective disposal. We develop an optimal lot sizing model with production and inspection quality investment, incorporating all the quality costs. We find the optimal lot size, rework frequency, defective proportion, and Type I and Type II inspection error proportions which minimize the total quality cost and maximize the total profit. We further analyze the solutions for no, partial, sequential and joint investment decisions on production and/or inspection processes in terms of quality costs using numerical analyses. The result provides important managerial insights into practice.