مدیریت موجودی فروشنده(VMI) با قرارداد محموله انبار (CS) برای زنجیره تامین در سطح دو با فرایند تولید ناقص با یا بدون وقفه بازسازی

A vendor managed system with the Consignment Stock agreement is a business practice where a buyer׳s inventory remains the property of the vendor until its withdrawal by the final customer demand. Such an agreement has shown to be a profitable stock management approach, especially when operating in uncertain environments where delivery lead times and/or market demand vary over time. One main issue that has been addressed in the literature on supply chain coordination is when a vendor׳s production process is imperfect; i.e., it generates defective items that are either reworked or scrapped. From the available works that investigated coordinating orders between a vendor and a buyer with imperfect production, to the authors׳ knowledge, no one has considered a Vendor Managed Inventory (VMI) with the Consignment Stock (CS) agreement as a policy where the vendor's production process is imperfect. This paper also introduces various managerial decisions pertaining to imperfect items, specifically, reworking items and applying minor-setups for restoration. A mathematical model is developed to determine the optimal production-inventory policies for various possible scenarios. The managerial decisions incorporated in this model give it the flexibility required to adapt to a firm's production situations and needs as may arise due to the nature of different industries and businesses. Significant findings include that accounting for imperfect items with Consignment Stock practice increases the batch size, reduces the number of batch shipments per cycle, and reduces the overall cycle time. Further, introducing minor setups for restoration reduces the overall cost of the system.

Inventory systems have various supply chain coordination policies (Jaber and Zolfaghari, 2008). Vendor Managed Inventory (VMI) with Consignment Stock (CS) agreement is one of these policies that has been observed in the automotive industry (Valentini and Zavanella, 2003) and studied by researchers (Braglia and Zavanella, 2003). This study introduces VMI with the Consignment Stock agreement as well as the consideration of an imperfect production process in a supply chain context. Inventory consignment is a business arrangement where a ‘buyer’ holds items in its inventory without ‘owning’ them (Simchi-Levi et al., 2000). The buyer makes appropriate payments for the purchase of consumed items. That is, within the CS inventory model the ‘change of ownership’ of the items is unrelated to the shipment of the items from one party (the vendor) to the other (the buyer). This is contrary to the basic design of classical inventory systems (e.g., Jaber and Zolfaghari, 2008 and Glock, 2012). Braglia and Zavanella (2003) considered a single-vendor and a single-buyer scenario to help in understanding the behavior and aptitude of the Consignment Stock policy in the supply chain coordination context. Although the concept of VMI with CS agreement is not new, it is the work of Valentini and Zavanella (2003) that provided an initial foundation for most of the later work regarding this policy. The mathematical model of Braglia and Zavanella (2003) is considered the base-case model, which this study builds and extends upon. Furthermore, Braglia and Zavanella (2003) provided a comparison with the classical model of Hill, 1997 and Hill, 1999 and concluded with a proposal for identifying situations in which the CS policy׳s implementation could be advantageous. They also concluded that the CS policy might be a strategic and profitable approach for supply chain coordination when delivery lead times or market demands vary with respect to time. Zanoni and Grubbström (2004) developed an explicit form of the implicit analytical solution given in Braglia and Zavanella (2003), while Persona et al. (2005) proposed an analytical model to take into account the effects of obsolescence. Wallin et al. (2006) identified and explained the critical factors that steer a firm׳s decision when making choices regarding inventory speculation, inventory postponement, inventory consignment and reverse inventory consignment. Srinivas and Rao (2007) developed four stochastic versions of the CS model which are (1) a basic CS model, (2) CS with delays, (3) CS with information sharing and delays, and (4) CS with controllable lead-time. Battini et al. (2010) extended the work of Persona et al. (2005) by considering demand variability, stock-out risk and limited warehouse space for low unit cost, high demand and small size (easy to store) items. To the authors׳ knowledge, there is no available work in the literature that explores a two-level supply chain operating under a CS agreement for the case when the vendor׳s production process is imperfect with defective items generated and where different alternative scenarios for managing scrap and/or rework are considered. VMI and CS are commonly misperceived as the same; however, the underlying difference is that in the VMI the replenishment of orders at the buyer׳s side is generated by the vendor (Holweg et al., 2005). VMI systems in general are perceived to have substantial success in inventory studies (Sari, 2007 and Claassen et al., 2008), but further investigations showed that adopting a VMI policy or a CS agreement is profitable (Chen et al., 2010) and demonstrated that there are benefits from combining the two (Gümüş et al., 2008). Sui et al. (2010) also showed success from the implementation of a VMI system with a consignment inventory. Their simulation-based approach allowed them to relax simplifying assumptions more common with analytical modeling of similar systems. Other advantages that can be gained from a VMI model with CS agreement are discussed in Zanoni et al. (2012). They compared different policies that the vendor may adopt when the vendor׳s production process is subject to learning effects. The assumptions that the equipment and machinery used in a production process are not subject to failures and that the output produced from the process has no defects are not realistic (e.g., Agnihothri and Kenett, 1995 and Khan et al., 2011). Porteus (1985, 1986) and Rosenblatt and Lee (1986) were the first to independently modify the economic order/production quantity (EOQ/EPQ) model by assuming that a production process, which starts in a control state, may shift with a specified probability to an out-of-control state. They also assumed that the process remains in that state until the entire lot is produced. Their work has provided a foundation for some inventory and supply chain models (e.g., Urban, 1998, Khouja, 2003, Jaber and Zolfaghari, 2008 and Khan et al., 2011). One of the interesting works that stemmed from that line of research is the one that considers interruptions to restore the production process into an in-control state at a cost (minor setups). Khouja (2005) extended the work of Porteus (1986) by assuming that a production process can be interrupted and restored. The more frequent the interruptions the less the number of defects generated, but the cost of restoration is higher. The policy is to determine the optimal number of interruptions in a cycle and the lot size that minimize the total system cost. The model of Khouja (2005) was later investigated in a two-level (vendor–buyer) supply chain with reworks (El Saadany and Jaber, 2008). The concept of imperfect production with process restoration has not been investigated in a VMI with CS agreement context. The advantages of VMI with CS agreement are prevalent for specific considerations. Many suppliers are attracted to the VMI policy because it mitigates uncertainty of demand and that items are readily available to the buyer when needed (Piplani, 2006). Organizations should always ensure smooth and efficient running of their operations (Hayek and Salameh, 2001), and having imperfect items in the system will counteract these advantages. Moreover, VMI material is stored at the buyer׳s warehouse, which is usually associated with lower holding costs. Shipping imperfect items to the buyer to have them scrapped or then returned to the vendor for rework may not seem to be economical and may counteract the benefits of applying VMI with CS agreement. The popularity of VMI has been seen from the 1980s through their introduction in Walmart and Procter & Gamble, and later initiatives by other companies including Campbell Soup, Johnson & Johnson and by European firms as well (Waller et al., 1999). The application of VMI and the concerns aforementioned are considered motivations to perform this study. Furthermore, there is no work in the literature that investigates imperfect production in a two-level supply chain with CS policy (Jaber and Zolfaghari, 2008 and Glock, 2012), which makes this paper the first. Hereafter, the paper is organized as follows. Section 2 presents the mathematical model developed. Section 3 tests the model using numerical examples and discusses the results. The paper is summarized and concluded in Section 4 with insights into future work.

This paper considered a two-level (vendor–buyer) supply chain operating a VMI with CS agreement with a vendor׳s production process that is imperfect; i.e., it may go out-of-control and generate nonconforming items. It extended the model of Braglia and Zavanella (2003) by assuming that the vendor׳s production process to be imperfect generating defective items that are scrapped and/or reworked. The paper considered the scenario of interrupting the vendor׳s production process to restore it to an in-control state. This reduces the number of imperfect and scrap items per lot and incurs additional (minor) setup costs each time the production process is interrupted, restored and resumed. The developed model is a flexible model. It can expand to a comprehensive one, which includes the possibility to rework a production batch of imperfect items, or collapse to a basic model (Braglia and Zavanella, 2003). The results showed that introducing the concept of process restoration and reworking defective items improved the system׳s performance. It is understandable that not all production situations operate under the suggested parameters, and hence may not all yield the same results. However, the advantage of the model is in its simplicity and ease of use. In essence, the model can be implemented to assist in making managerial decisions for a VMI with CS agreement policy in two-fold: (1) determines the optimum values of the production batch sizes and the number of shipments per a vendor׳s cycle; and (2) suggests alternative options for a given vendor regarding its scrapping policy, rework policy, production process restoration policy, or any combination of the three policies. In general, the model can be used as a decision tool for management to determine production policies for different production scenarios based on data input from management. The paper also developed two simple mathematical models, classical coordination and VMI with CS, and showed that the latter is a better policy when the vendor׳s production process is imperfect; i.e., it produces defective items that are either rework or scrapped. Although seen as a successful exploration of the CS agreement, the proposed model is not without limitations. Future work may address some of these limitations such as stochastic rather than deterministic demand, and performing process restoration is not restricted to the time when shipment is made to the buyer. For further investigations, the above assumptions can be relaxed. Moreover, there are a number of lines worthy of further exploration and study. A multi-buyer or a multi-level supply chain (or a combination of both) with the consignment policy coordination mechanism provides an intriguing opportunity to better understand and explore models of VMI with CS agreement from a practical perspective. Finally, an interesting extension to this work could be by accounting for learning and forgetting in production, in setups and in quality (Jaber et al., 2010).