In practices, not only production but inspection processes are often not perfect, thereby generating defects and inspection errors. Previous imperfect-quality inventory studies, however, have mostly focused on developing cost-minimizing models that do not consider imperfect inspection processes and related defect sales return issues despite their practical significance. Thus, this study proposes a profit-maximizing economic production quantity model that incorporates both imperfect production quality and two-way imperfect inspection, i.e., Type I inspection error of falsely screening out a proportion of non-defects and disposing of them like defects and Type II inspection error of falsely not screening out a proportion of defects, thereby passing them on to customers, resulting in defect sales returns. We also consider rework and salvage in disposing of screened and returned items. Then we solve the model optimally and present numerical sensitivity analyses to provide important managerial insights into practices.
In a typical manufacturer–customer supply chain, the manufacturer's production process quality is often not perfect and hence produces imperfect-quality defective items. Since the pioneering work by Rosenblatt and Lee (1986) and Porteus (1986), many researchers have developed various imperfect-quality inventory models for this important problem involving an imperfect production process.
In detail, previous imperfect-quality inventory models can be divided into two streams in terms of an inspection method of defects related to different imperfect production processes (see also Yano and Lee, 1995 for a review). One stream of research has examined a production system which deteriorates in every cycle as run cycles progress after an initial state involving no error, and thus produces defects. In this deteriorating process situation, most of the researchers have examined an inspection method of defective items based on regular intervals (Rosenblatt and Lee, 1986; Porteus 1986; Lee and Rosenblatt, 1987 and Lee and Rosenblatt, 1989; Lee and Park, 1991; Liou et al., 1994; Vickson, 1998; Kim et al., 2001; Chen et al., 2008; Jaber et al., 2009), while others have explored an inspection based on an interval with a constant integrated hazard (Rahim, 1994; Rahim and Ben-Daya, 2001), an entire lot inspection at the end of a process (Guu and Zhang, 2003), and an inspection of the last k units ( Yeh and Chen, 2006). On the other hand, the other line of research has investigated an imperfect production process with no deterioration over time. In this non-deteriorating case, the inspection was mostly done by an entire lot screening ( Cheng, 1989, Cheng, 1991a and Cheng, 1991b; Anily, 1995; Lee et al., 1996; Salameh and Jaber, 2000; Hayek and Salameh, 2001; Chiu, 2003; Tripathy et al., 2003; Chiu et al., 2006; Leung, 2007; Jaber et al., 2008), except for Zhang and Gerchak (1990) involving an inspection of a fraction of a lot.
In practices, often both production and inspection processes of a manufacturer are not perfect, thereby producing and passing some defects to customers causing subsequent defect sales returns or falsely screening out some non-defects. Most of the existing imperfect-quality inventory models, however, have not dealt with such important practical situations involving both imperfect production and imperfect inspection processes. Therefore, we present a profit-maximizing imperfect-quality inventory model with two types of inspection errors and defect sales return that determines an optimal production lot size. The inspection errors consist of a Type I inspection error of falsely screening out a proportion of non-defects regarded as defects, incurring unnecessary additional costs, and a Type II inspection error of falsely not screening out a proportion of defects, thereby passing them on to customers and consequently resulting in customers’ defect sales returns due to quality dissatisfaction. Our model extends an EPQ model by incorporating defect proportion, proportions of Type I and Type II inspection errors, and proportions of rework and salvage in handling screened and returned items that follow known pdf's.
