Production inventory policies for defective items with inspection errors, sales return, imperfect rework process and backorders

In order to sustain the challenges of maintaining good quality and perfect screening process, rework process becomes a rescue to compensate for the imperfections present in the production system. The proposed model attempts to explore the existing real-life situation with a more practical approach by incorporating the concept of imperfect rework as this occurs as an unavoidable problem to the firm due to irreparable disorders even in the reworked items. Hence, a production inventory model is formulated here to study the combined effect of imperfect quality items, faulty inspection process and imperfect rework process on the optimal production quantity and optimal backorder level. An analytical method is employed to maximize the expected total profit per unit time. Moreover, the results of several previous research articles namely Chiu et al (2006), Chiu et al (2005), Salameh and Hayek (2001), and classical EPQ with shortages are deduced as special cases. To demonstrate the applicability of the model, and to observe the effects of key parameters on the optimal replenishment policy, a numerical example along with a comprehensive sensitivity analysis has been presented. The pertinence of the model can be found in most of the manufacturing industries like textile, electronics, furniture, footwear, plastics etc. A production lot size model has been explored for defectives items with inspection errors and an imperfect rework process.