A New EPQ Model for Imperfect Production, Screening, and Rework With Backorders Under Grey Uncertainty

The occurrence of imperfect products that are studied at a specific rate during production holds a significant and comprehensive position in the literature. The fundamental premises underlying the research on the EOQ and EPQ models are as follows: there exists a specific percentage of imperfect production; that the defective rate of production is in line with a certain probability distribution; and that defective products are in themselves defective, repairable (rework), and defective (selling at a low price) etc. The studies of EPQ models that consider the inspection rate and production rate hold significant significance in the literature. This work presents the development of a novel EPQ model to handle the issue of reduced production time to eliminate backorders. The model's functioning is described by including uncertainty modeling, specifically using grey values to represent production rate, costs and prices.