تعیین اندازه دسته تولید و کیفیت سرمایه گذاری با تجزیه و تحلیل هزینه های کیفیت برای تولید و بازرسی فرآیندهای ناقص با بازده تجاری

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.

In a closed-loop supply chain, we frequently discover firms producing defective items and passing some to customers due to imperfect quality in both production and inspection processes. This imperfect process reliability then causes customers to return defective items for exchange or refund. For example, the average return rate in the apparel and the consumer electronics industry amounts to 19.44% and 8.46%, of which 49.45% and 35.71% are due to defects, respectively (Reverse Logistics Executive Council, 1999). The annual value of product returns is estimated at $100 billion (Stock et al., 2002 and et al.,) and commercial returns in online retailing and e-commerce are recorded up to 25% of sales (Krikke et al., 2004). In addition, imperfect inspection incurs an opportunity loss by falsely screening out non-defective items and disposing of them as defectives. Thus, it is important for firms to understand both internal and external effects of defective production and inspection failure on lot sizing, inventory, quality costs and profit. There have been a vast number of studies that deal with imperfect production, inspection and reverse logistics issues. Most studies focused mainly on developing cost-minimizing models for either internal effects of defective production and process quality improvement, or recycling and rework of reusable item returns. The imperfect production and inspection system in practice, however, incurs not only internal failure costs related to rework, salvage and scrap, but also external failure costs from defective item return, reverse logistics, resolution of customer quality problems, and refund or exchange, negatively affecting the firm’s profit. Thus, to reduce these negative effects, the firm often invests in prevention activities to improve process capability, worker skills, inspection and test equipment design, as well as appraisal activities to determine the degree of conformance and internally screen out defectives. Consequently, it is imperative for a firm to carefully consider the tradeoff relationships among the internal and external aspects of quality costs (i.e., prevention, appraisal, internal failure and external failure) in the optimal investment decision along with lot sizing (Juran and Gryna, 1988). In this light, this study explores internal and external issues of defective production, inspection failure (Type I and Type II errors), and related quality improvement investment for a firm in a closed-loop supply chain with commercial return. Specifically, we develop a profit-maximizing model that jointly determines the optimal production lot size, rework frequency, and defective production and inspection error proportions related to respective investment. We solve the model optimally using differential calculus and nonlinear programming. We also analyze our model in terms of four quality cost components to discover their tradeoff relationships in lot sizing and quality investment decision making. Moreover, we investigate the solutions and quality cost structure of different decisions in practice with no, partial, sequential and joint investment in production and inspection process reliability, in order to provide important managerial insights and help managers make well-informed decisions. The significance of this study may lie in building a more practical model, quantifying and analyzing quality costs and comparing different investment decision-making situations, thereby extending the current body of knowledge on imperfect-quality inventory and quality management. The rest of the paper is organized as literature review and analysis, basic imperfect-quality inventory model and solution approach, extended quality investment model and quality cost decomposition, and optimal solution and quality cost analysis for different investment decisions, followed by conclusions.

In this study, we investigated an imperfect-quality inventory problem in practice in which imperfect production and inspection processes cause a firm to take actions of internal prevention and external reverse logistics of customer defective returns. Most previous studies, however, partially examined cost-minimizing aspects of internal defective production, inspection and/or prevention, or external reverse logistics of used items, without considering imperfect inspection, defective delivery to customers, returns for exchange and refund, and reselling to the second market, which affect the firm's profit. Moreover, few imperfect-quality inventory studies performed a quality cost analysis despite its significance of helping managers understand the effect of quality improvement activities and determine the optimal investment level. Therefore, we incorporated all the above issues into our inventory model, in which the profit is decomposed into non-quality-related components and total quality cost components (i.e., prevention, appraisal, internal failure and external failure). The objective of the model was to determine production lot size, rework frequency, defective proportion, and Type I and Type II inspection error proportions dependent on the production and inspection process reliability investment, which maximize the total profit and minimize the total quality cost. We examined and compared the optimal solutions among the basic model and the models with various investment decisions (partial, sequential and joint) in production and/or inspection processes. Based on the analytical models along with numerical analyses, we provided important managerial implications to practices. First, the net inventory depletion rate to satisfy customer demand and exchange requests for defective items varies by not only demand rate, but also by defective proportion, Type I and II inspection error proportions, customers’ return choice for exchange, and multiple defective disposal options of rework and salvage. Second, firms need to incorporate not only internal but also external effects of defective items in their production and inspection process reliability investment decisions, by considering reverse logistics aspects of defective returns, subsequent exchange and refund, and various defective disposal options, as they are affected by defective proportion, and Type I and II inspection error proportions. Third, as joint investment yields superior profit performance to partial and sequential investment, it is important to integrate and jointly consider investment decisions in production and inspection process reliability improvement for quality activities. Fourth, understanding the effect of each failure proportion on firms’ total profit or total quality cost is very crucial for practicing managers. The effects of defective proportion and Type I inspection error on the internal and external failure proportions and the quality cost structure are similar, but Type II inspection error behaves inversely and produces different results. Fifth, when investing in process reliability partially or sequentially as in practice, a firm first needs to consider production process reliability and/or Type I inspection process reliability. Enhancing only Type II inspection process reliability cannot guarantee the balanced quality cost structure. Finally, as the difference in the total profit from different investment decisions comes from that in the total quality cost, it is crucial for managers to measure and quantify the size of quality problems, based on the quality cost analysis presented, to accurately justify control and improvement efforts, guide their development and track progress in quality management activities by clearly understanding the tradeoff relationships and the best balance among quality costs. The significance and contribution of this study may lie in developing a more realistic and comprehensive model by integrating and extending the past research, including internal and external aspects of defective production and two types of inspection errors, and providing richer managerial insights into practices through the decomposition and analysis of the total quality cost. For future research, it is desired to extend further the present quality investment model with lot sizing by investigating a deteriorating production process and by examining more complicated multistage production or supply chain systems along with lead time and capacity issues besides quality to further close the gap between practice and academia.