سیاست تکمیل دوباره بهینه برای یک سیستم موجودی یکپارچه شده با قطعات معیوب و کمبود مجاز تحت اعتبار تجاری

This study proposes a single-supplier, single-retailer integrated inventory model that accounts for defective items that arrive in a retailer's order under a full-lot inspection policy. All defective items are returned to the supplier in next delivery. After receipt of the returned items, the supplier will classify them into two types: items that still have some worth and waste items. For those items that still have some worth, the supplier will offer customers a discount in order to minimize losses arising from these defective items. The supplier needs to pay a disposal fee for those items classified as waste items. Shortages are allowed and are fully backlogged. To encourage sales the supplier offers trade credit to the retailer. A two-echelon inventory model is established, and the decision variables include: replenishment cycle time, the time taken to run out of stock and the number of lots delivered from the supplier to the retailer. An algorithm is developed to determine the optimal supply chain strategy and numerical examples are provided to show the solution procedure. Also, a sensitivity analysis is conducted on the main parameters of the model.

The ultimate objective of effective supply chain management is the reduction of costs, improvement of cash flow and increased operational efficiency across the entire business through connecting inventory control, purchasing coordination and sales order processing with market demand. In a competitive business environment the ability to integrate one's supply chain is essential for company success. The joint optimization concept for the supplier and retailer was initiated by Goyal (1976). Banerjee (1986) extended Goyal's (1976) model and assumed that the supplier followed a lot-for-lot shipment policy with respect to a retailer. Later, Goyal (1988) relaxed the lot-for-lot policy and illustrated that the inventory cost could be significantly reduced if the supplier's economic production quantity (EPQ) was an integer multiple of the retailer's purchase quantity. Lu (1995) then generalized Goyal's (1988) model by relaxing the assumption that the supplier could supply the retailer only after completing the entire lot size. Many researchers (Goyal, 1995, Goyal, 2000, Ha and Kim, 1997, Viswanathan, 1998, Hill, 1999, Goyal and Nebebe, 2000, Woo et al., 2001, Pan and Yang, 2002, Khan and Sarker, 2002, Kim and Ha, 2003, Kelle et al., 2003, Yao and Chiou, 2004, Siajadi et al., 2005, Hoque, 2008, Sarker and Diponegoro, 2009, Glock, 2011 and Glock, 2012) continued to propose more batching and shipping policies for integrated inventory models. The above inventory integration models commonly adopt the unrealistic assumption that all units received by a retailer are of good quality when studying strategic production/transportation decisions. In reality, imperfect production process, flaws in the goods transportation process and many other factors inevitably lead to a certain proportion of defective items being received during a production run. Over the years, several different economic order quantity (EOQ) models that account for defective items have been developed. For example, Rosenblatt and Lee (1986) and Porteus (1986) initially considered the effects of an imperfect production process on quality imperfection and on lot size. Salameh and Jaber (2000) extended the traditional EPQ/EOQ model by accounting for imperfect quality items. They considered the issue of poor-quality items being sold as a single batch by the end of a 100% screening process. Wu and Ouyang (2000) considered the potential for an arrival order lot to contain some defective items and the number of defective items in a sampled sub-lot to be a random variable. Currently, several relevant papers exist that study EPQ models for items with imperfect quality such as Ouyang et al. (2002), Chiu (2003), Chang (2003), Balkhi (2004), Hou and Lin (2004) and Papachristos and Konstantaras (2006). These models determine an optimal policy from the perspective of either the retailer or the supplier only. Integrated vendor–buyer models that consider defective items have also been presented (see, for example Affisco et al., 2002, Singer et al., 2003, Comeaux and Sarker, 2005, Huang, 2004, Lo et al., 2007, Chung and Wee, 2008, Maddah and Jaber, 2008, Chiu et al., 2011 and Khan et al., 2011). Enterprises and academic bent on the improvement of production process to eliminate defectives and reduce waste. However, in practice defective is inevitable (Schwaller, 1988). Facing growing levels of competitive and economic pressures, more and more enterprises have begun to view the defective treatment as a process that may be used to manage costs and drive additional revenues. Also, the growing global concern for the environment has led to increased interest in the treatment of defective. In this paper, a common defective treatment for manufactures of clothing, shoe, accessory, furniture, electronics, toys and bedding is involved. For example, a famous clothing company produces middle and top grade women's apparel. Their brands are sold in China's major cities more than 300 stores. All returns from retailers will be check and classed. While the returned clothes with minor production defects, such as stain, skipped or dropped stitches, wavy bottom hem, sewing thread not matching, etc., will be cut label and sold to wholesalers with discount price. If the defects affecting the usability and salability, such as: fabric hole, shading among panel, wrong measurement, dye patches etc., then the returns will be scraped. The above integrated inventory models for items with imperfect quality failed to account for the effect of trade credit on optimal policies. Trade credit is a widespread tool and represents an important proportion of company finance. Businesses, especially small businesses with limited financing opportunities, may be financed by their suppliers rather than by financial institutions (Petersen and Rajan, 1997). Furthermore, offering trade credit to retailers may improve supplier sales and reduce on-hand stock levels (Emery, 1987). Goyal (1985) was the first to establish an EOQ model with a constant demand rate under the condition of a permissible delay in payments. Aggarwal and Jaggi (1995) extended Goyal's (1985) model to include deteriorating items. Jamal et al. (1997) further generalized this issue with allowable shortages. Kim et al. (1995) examined the effects of a credit period on the ordering policies from the supplier's viewpoint. Teng (2002) modified Goyal's (1985) model by considering the difference between the selling price and purchase cost, and found that the economic replenishment interval and order quantity decreased under the permissible delay in payments in certain cases. Numerous relevant papers have been produced relating to trade credit such as Huang (2003), Ouyang et al., 2005 and Ouyang et al., 2009, Teng et al. (2005), Su et al. (2007), Chen and Kang (2010a) and Yu (in press). By taking the considerations of imperfect-item and trade credit as described above, Li et al. (2009) developed a model to determine the retailer's optimal replenishment policy with defective items under conditions of permissible delay of payments. Further, Chen and Kang (2010b) investigated the issue of defective items with a permissible delay in payment from the perspective of both the vendor and buyer. However, in their models the occurrence of shortage in the inventory system is overlooked. In real life, many famous products or modern goods, for example Apple's iPad and iPhone, may cause a situation in which customers may prefer to wait for back orders while shortages occur. Inventory shortage problems can interfere with a company's profits and customer service. Therefore, for inventory managers of manufacturing and retail organizations how to control inventory in the supply chain that enable them to minimize inventory costs and meet customer demand is worth discussing. This paper proposes a single-supplier, single-retailer integrated inventory model that accounts for defective items that arrive in a retailer's order under a full-lot inspection policy. All defective items are returned to the supplier and classified into two types: items that still useful and waste items. The former are sold to customers in a discounted price and the later cost a disposal fee. Shortages are allowed and are fully backlogged. For the retailer, trade credit is permissible. A two-echelon inventory model is established and the decision variables include: replenishment cycle time, the time taken to run out of stock and the number of lots delivered from the supplier to the retailer. An algorithm is developed to determine the optimal strategy and numerical examples are provided to show the solution procedure. Furthermore, a sensitivity analysis is conducted on the main parameters of the model. Finally, conclusions and possible future research topics are provided.

In this study an integrated inventory model is proposed that accounts for defective items in a retailer's arrival order lot under a full-lot inspection policy and also accounts for shortages. It is assumed that retailers are permitted trade credit. All defective items delivered by the supplier will be returned and classified into two categories: those that still have some worth and those that are waste items. For study purposes, a two-echelon inventory model is built and the average cost function is formulated. By employing a novel algorithm, the optimal duration of the replenishment cycle time, the time taken to run out of stock and the number of lots delivered from the supplier to the retailer is determined. Additionally, a sensitivity analysis is conducted on the main parameters of the model. Through mathematical analysis it is shown that whilst the extension of supplier credit terms will allow retailers to take advantage of trade credit more frequently, the retailer may order a smaller quantity to shorten the replenishment cycle length. Conversely, if the allowable delay in payment time is sufficiently long, then the retailer is unlikely to reduce their order quantity because there is a trade-off with transportation costs. A shorter replenishment cycle length resulting from a smaller order size incurs higher transportation costs which the retailer will try to avoid. This study provides a useful managerial insight that suppliers should critically evaluate their credit terms carefully in order to avoid a strategic mismatch and unnecessary losses. The results illustrate that to improve the system effectively members of the supply chain are required to work carefully to improve market demand through increased product quality. Future research could modify or extend the present model in several ways. First, in this study a single-supplier and a single-retailer for a single product were considered. This foundation could be further extended to more practical situations, such as considering multiple retailers or multiple items, or taking raw material supply into account. Other possible extensions are to formulate the demand as a function of the length of the allowable payment delay time and the other factors, or to examine the interactions between the supplier and the retailer from the perspective of game theory. Finally, it would be of significant interest to relax the deterministic assumptions, such as demand rate, defective rate, and backorder rate; and thus extend the methodology to operate in an uncertain or stochastic environment.