بهبود عملکرد زنجیره تامین از طریق اعتبار تجاری تحت تقاضای وابسته به موجودی و ظرفیت ذخیره سازی محدود

The present paper develops a performance-improving model through trade credit for a two-echelon supply chain, where a supplier sells a single product through a retailer who has limited storage space and faces an inventory-dependent end demand. We consider the non-integrated and integrated optimizing model. Under the non-integrated optimizing model, we present how the supplier determines the trade credit period to induce the retailer ordering more so as to reduce the supplier's operating cost and enhance sales volume of products as well. The proposed model shows that the presented trade credit policy can increase each member's profitability but also the profitability of the whole channel. Furthermore, we develop a theorem to efficiently determine the optimal inventory and trade credit policy for the integrated optimizing model.

In the classical EOQ model, it is assumed that a retailer must pay for items once he/she received them from a supplier. However, many suppliers usually allow in practice their retailers a trade credit for settling the account without any interest charged. For example, Wal-Mart, the largest retailer in the world, has used trade credit as a larger source of capital than bank borrowings. Also, Aaronson et al. (2004) reported that “60.8 percent of firms had outstanding credit from suppliers”. This type of trade credit is equivalent to offering the retailers short-term interest-free finance in stock. Hence, the trade credit should affect the retailer's conduct of order significantly. In this regard, a lot of research papers discussed the inventory problems with trade credit. For example, researchers like Haley and Higgins (1973), Goyal (1985) studied the effect of trade credit period on the optimal inventory policy. Zhou (1997) discussed the impact of different rules for delay in payment on the retailer's order policy. Recently, by using a DCF approach, Chung and Liao (2009) developed an inventory model where trade credit is dependent on the quantity ordered. However, these papers assumed that the demand was a known constant. They ignored the effects of price on the demand volume. In order to reflect it in inventory models with trade credit permitted, Teng et al. (2005), Sheen and Tsao (2007) have employed price-sensitive demand. Tsao and Sheen (2008) studied the problem of dynamic pricing, promotion and replenishment for a deteriorating item subject to the supplier's trade credit and the retailer's promotional effort. In their paper, they adopted a price- and time-dependent demand function to model the finite time horizon inventory for deteriorating items. Besides price and promotion, many marketing researchers, such as Levin et al. (1972) and Silver and Peterson (1985), noted that holding higher inventory level in the retail industry would probably make retailers sell more items. It implies that the inventory level of items also affects their marketing demand. Since a delay of payments directly reduces inventory cost, trade credit policy actually encourages the retailer to order a larger lot size of items, and ultimately leads to a greater sales volume. Hence, from retailers' side, a key question is how to determine their order batch size for a given trade credit policy if demand is stock-dependent. Under ignoring capacity limitation of warehouses, Sana and Chaudhuri (2008) analyzed a kind of EOQ model with a current-stock-dependent demand rate where a supplier gives a retailer both a credit period and a price discount on the purchase of merchandise. Soni and Shah (2008) developed the optimal ordering policy for retailers who face a stock-dependent demand and two progressive credit periods offered by suppliers. Recently, Min et al. (2010) developed a lot-sizing model for deteriorating items with a current-stock-dependent demand and delay in payments. In reality, however, the available capacity of warehouse is always limited. In this paper, we will further consider under any given trade credit policy how retailers determine their order batch sizes when they face limited storage capacity and an inventory-level-dependent demand. All the researches mentioned above are implemented from the perspective of the retailer. However, to the best of our knowledge, only limited researches have been done from the perspective of the supplier. Kim et al. (1995) formulated a model to determine the optimal credit period for the supplier and the optimal sales price and corresponding order quantity for the retailer. In their model, they restricted their analysis to non-cooperative leader–follower relationship and the supplier's order decision to the lot-for-lot (LFL) policy. Abad and Jaggi (2003) reconsidered Kim et al.'s problem, and developed a model for determining optimal supplier and retailer policies. Luo (2007) considered a two-echelon inventory-coordinated model where the supplier entices the retailer increasing order quantity through a permissible trade credit. Arkana and Hejazi (2011) designed a coordination mechanism based on a credit period in a two echelon supply chain. However, these models consider a constant demand or a price-sensitive demand only. Moreover, they assumed that retailers had unlimited storage space. Recently, Zhou et al. (2012) developed a two-echelon supply chain model with trade credit, in which the retailer faces limited display shelf space, but can stock the remaining to the backroom. Our paper also focuses on how the supplier designs the trade credit policy to maximize his/her own profits when the retailer faces the inventory-dependent demand and limited storage space, but cannot rent the warehouse to stock the remaining. The above models consider the objective from either the retailer's or the supplier's perspective. However, in the global competitive marketplace, the retailer and the supplier should cooperate as a whole and establish a long-term cooperative relationship. Goyal (1976) first studied a seller–customer inventory model. After that, many researchers discussed ordering/pricing issues for an integrated supply chain, such as Banerjee (1986), Wee and Yang (2007). Abad and Jaggi (2003) further considered a supplier–buyer integrated model under trade credit policy. Recently, Ho et al. (2008) and Chen and Kang (2010) discussed the operational impact of a “two-part” trade credit policy in an integrated inventory model. To compare with the decentralized setting, we also develop in this paper an integrated supply chain model, in which the retailer faces the inventory-dependent demand and limited storage space. The remainder of the paper is organized as below. Section 2 presents assumptions and notations used in the paper. In Section 3, we construct the retailer's and supplier's objective function in a decentralized setting. In Section 4, we specify the condition under which the supplier can get benefits from offering the retailer trade credit, and provide the method of how to set such a trade credit policy. While Section 5 gives the integrated optimizing model with trade credit, Section 6 shows numerical analysis of parameters of the proposed models. The paper ends with Section 7.

In this paper, we first construct the model with inventory-dependent demand and limited storage space to analyze how trade credit affects the retailer's order decision, and how the supplier maximizes his/her own average profit through designing the trade credit policy under the supplier-Stackelberg game structure. To compare with the decentralized setting, we also develop in this paper an integrated supply chain model and a theorem to efficiently determine the optimal inventory and trade credit policy. Finally, we show the sensitivity analysis of parameters and gain some management insights.