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In this paper, a single-vendor, single-buyer supply chain for fixed lifetime product is considered. We propose models to analyze the benefit of coordinating supply chain through quantity discount strategy. Under the proposed strategy, the buyer is requested to alter his current order size such that the vendor can benefit from lower costs, and quantity discount is offered by the vendor to compensate the buyer for his increased inventory cost, and possibly provide an additional savings. In addition, the centralized decision-making model is formulated to examine the effectiveness of the proposed quantity discount model. It is proved that the quantity discount strategy can achieve system optimization and win–win outcome. At last, a detailed numerical example is presented to illustrate the benefit of the proposed strategy.

Perishability of either raw materials or finished products is a major problem in some industries such as agro-food industry, drug industry. Due to the limited product lifetime, an ineffective inventory management at each stage in the supply chain from production to consumers can lead to high system costs including ordering costs, shortage costs, inventory holding costs, and outdating costs. Moreover, the quality of products (freshness) may be unacceptable, thus reducing customer satisfaction. Liu and Shi (1999) classified perishability and deteriorating inventory models into two major categories, namely decay models and finite lifetime models. Decay models deal with inventory that shrinks continuously and proportionally with time, while finite lifetime models assume a limited lifetime for each item. Furthermore, the finite lifetime models can be generally classified into two subcategories, namely common or fixed finite lifetime models and random finite lifetime models. Items with common finite lifetimes, usually referred in the literature as perishable items (Liu and Lian, 1999), perish at the same age if not used by demand. Fresh products, cans of fruit, foodstuffs, and drugs are examples of the items having fixed finite lifetimes. The random finite lifetimes, on the other hand, are treated as random variables with certain probability distributions, such as exponential and Erlang. Items with random lifetimes, thus, spoil at different ages. Past researches on the Fixed-Life Perishable Problem (FLPP), such as Fries (1975), Nandakumar and Morton (1993), Liu and Lian (1999), and Lian and Liu (2001), mainly addressed single-stage inventory systems. Fujiwara et al. (1997) studied the problem of ordering and issuing policies in controlling finite-life-time fresh-meat-carcass inventories in the supermarket. Kanchana and Anulark (2006) investigated the effect of product perishability and retailers’ stockout policy on system total cost, net profit, service level and average inventory level in a two-echelon inventory system, and a periodic review inventory-distribution model was proposed to deal with the case of fixed-life perishable product. Because members of a supply chain are different entities with their own interests, active cooperation and close coordination play an important role in supply chain management. Therefore, some efficient mechanisms are necessary to enforce coordination between parties in the supply chain. Examples of such mechanisms include quantity discount (Goyal and Gupta, 1989), revenue sharing (Giannoccaro and Pontrandolfo, 2004), sales rebate (Wong et al., 2009), trade credit (Chen and Kang, 2010). Among these mechanisms, quantity discount is a commonly used scheme. Goyal and Gupta (1989) reviewed the literatures on the quantity discount models. For fixed lifetime items, there are few literatures on the coordination mechanisms. In this paper, a single-vendor, single-buyer supply chain for item with fixed lifetime is considered. We develop models to analyze the benefit of coordinating supply chain by quantity discount strategy. If coordination is not introduced, given buyer's EOQ order quantity, the vendor's order size is an integer multiple of the buyer's that minimizes his own inventory cost. Under the proposed coordination strategy, the vendor requests the buyer to alter his current EOQ, and the vendor's order size is another integer multiple of the buyer's new order quantity such that the vendor can benefit from lower setup ordering and inventory holding costs. To entice the buyer to accept this strategy, the vendor must compensate the buyer for his increased inventory cost, and possibly provide an additional saving by offering the buyer a quantity discount, which depends on his order size. The rest of this paper is organized as follows. In Section 2, the decentralized models with and without coordination, and centralized model are formulated. The analytically tractable solutions to these models are obtained. It is proved that the quantity discount strategy can achieve system optimization and win–win outcome. A numerical example is presented in Section 3 to illustrate the effectiveness of the proposed quantity discount strategy. The summary and concluding remark are presented in the last section.

In this paper, a quantity discount coordination strategy for a single-vendor, single-buyer supply chain of product with fixed life time is investigated. The analytical method as to how to determine the optimal strategy is proposed, and analytically tractable solutions are obtained. It is indicated that the buyer's order size is larger at cooperation against the non-cooperation (K>1)(K>1) if h2≥h1h2≥h1. The vendor's total cost as well as that of the total system can be reduced no matter how much the parameters change. The vendor can not only compensate the buyer for his increased inventory cost by offering the buyer an order size dependent discount, but also provide the buyer an additional saving of View the MathML sourceα(TCv¯(n*)−TCv(m*)), where αα is determined through negotiations between the vendor and the buyer, and is generally dependent upon the existing balance of power between them. In addition, to validate the efficiency of the proposed quantity discount strategy, the system optimization problem under centralized decision-making is discussed analytically. We prove that the decentralized quantity discount strategy can achieve system optimization and win–win outcome. As a result, both the vendor and the buyer will benefit in the long run. At last, a numerical example is presented to illustrate the performance of the strategy. The sensitivity analysis of cost savings on parameters is conducted. The computational results reveal that the total cost can be reduced no matter how much the parameters change. Moreover, the costs of the supply chain can be reduced significantly if the vendor's unite holding cost is high. On the other hand, if the buyer's holding cost is high, the costs of the supply chain cannot be reduced much. With an attempt to propose an interesting strategy for the common single-vendor single-buyer supply chain system of fixed lifetime product, and to make a contribution to this important research area, we hope this paper can serve as the initial point to the study of other extensions of the problem.