International Journal of Mathematical, Engineering and Management Sciences Vol. 2, No. 4, 242–258, 2017 ISSN: 2455-7749 242 Inventory Modeling for Imperfect Production Process with Inspection Errors, Sales Return, and Imperfect Rework Process Aditi Khanna 1 , Aakanksha Kishore 2 , Chandra K. Jaggi 3* Department of Operational Research Faculty of Mathematical Sciences University of Delhi, Delhi 110007, India 1 dr.aditikhanna.or@gmail.com, 2 kishore.aakanksha@gmail.com, 3 ckjaggi@yahoo.com * Corresponding author (Received November 15, 2016; Accepted January 16, 2017) Abstract In real life, due to certain machine problems, process deterioration and many other factors, production processes deliver imperfect quality items. So, the effect of these defectives cannot be ignored in terms of ensuring good customer service. In order to sustain today’s cut-throat competition, rework process of defective items becomes a rescue to compensate for the imperfections present in the production system. The present model attempts to explore the traditional imperfect environment with a more practical approach by incorporating the concept of inspection errors, along with an imperfect rework process. By considering human errors as unavoidable, Type-I and Type-II errors are also incorporated in the study. To prioritize on the customer satisfaction level, Sales returns are given full price refunds. An analytical method is employed to maximize the expected total profit per unit time to study the combined effect of aforementioned factors on the optimal production quantity. A numerical example along with a comprehensive sensitivity analysis has been presented to demonstrate the applicability of the model and also to observe the effects of key parameters on the optimal production policy respectively. The pertinence of the model can be found in most manufacturing industries like textile, electronics, furniture, footwear, crockery etc. Keywords- Inventory, Production, Imperfect Items, Inspection, Reworking 1. Literature Overview A common unrealistic assumption in the manufacturing sector is that all the items produced are of good quality. This has led many researchers to study the classical EPQ extensively and relax the traditional assumption of perfect quality. The first study in this field can be dated back a century ago and was projected by Taft (1918). (Schrady, 1967; Porteus, 1986; Rosenblatt and Lee, 1986; Lee and Rosenblatt, 1987) were some other researchers to study the effect of imperfect quality items on EPQ models and hence laid the foundation of vast research in this direction. Very soon, the need for incorporating human errors along with imperfect quality was taken into account. In view of this, Liou et al. (1994), Makis (1998) first studied the effects of inspection errors in the imperfect EMQ model. Some other researchers emphasized on reworking of defective items in order to compensate the losses incurred due to errors. Salameh and Jaber (2000) carried out an important research by considering that the whole lot contains a random percentage of defective items with known p.d.f. They also assumed that whole received lot goes through 100% screening process and the sorted out defective items are sold as a single batch at a discounted price. Furthermore, Hayek and Salameh (2001) first examined the relevance of rework on imperfect quality items in finite production model with allowable shortages. They assumed that all the defectives enter the rework process and emerge as perfect items after rework. So, there are no scrap items produced in their model. However, Chiu (2003) considered the emergence of scrap items before the beginning of rework process and considered that a random proportion, with