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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : International Journal of Production Economics, Volume 111, Issue 2, February 2008, Pages 543–561
We consider a supplier and a customer operating under a service agreement that requires the supplier to cover the random customer demand with high probability. To fulfill the service agreement, the supplier carries a certain amount of safety stock. The customer has some bearing on its demand variability, possibly through activities such as acquiring advance demand information, employing more sophisticated forecasting techniques or smoothing its product consumption, but these activities bring an extra cost to the customer. Since a reduction in the customer demand variability helps the supplier reduce its safety stock, the supplier is willing to offer a price discount in exchange for reduced demand variability. We examine a pricing scheme where the supplier assesses its potential cost savings from a reduction in the customer demand variability and returns a fraction of these cost savings back to the customer through a price discount. We show that both parties realize cost savings under such a pricing scheme, examine the efficiency issues and consider the case where the customer does not reveal certain cost components accurately.
Although conventional inventory models treat the customer demand as an exogenous random process, there are many situations where the customer can affect certain aspects of its demand process through activities such as acquiring advance demand information, employing more sophisticated forecasting techniques or smoothing its product consumption. Essentially, the outcome of these activities is to reduce the customer demand variability, which, in turn, benefits the customer through increased fill rates and the supplier through reduced inventories. However, although both the supplier and the customer benefit from these activities, the costs associated with them are usually born only by the customer. Consequently, the customer may pursue these activities in a much more limited scope than the supplier desires, and the supplier may have to share the costs of these activities with the customer or provide other incentives. In this paper, we consider a supplier and a customer operating under a service agreement that requires the supplier to cover the random customer demand in each time period with high probability. The customer has some bearing on its demand variability, but this requires the customer to incur an extra cost. Early in the paper, we do not explicitly specify how the customer can affect its demand variability, but we later give a specific example where the customer can do this through advance demand information acquisition. A reduction in the customer demand variability helps the supplier reduce the safety stock that it needs to fulfill the service agreement, and the supplier is willing to offer a price discount to motivate the customer. We propose a pricing scheme that is motivated by the idea that the supplier should return a fraction of its potential cost savings that can be realized by the reduction in the demand variability back to the customer through a price discount. The result is a pricing scheme where the price charged to the customer is a linear function of the standard deviation of the customer demand. We show that both the supplier and the customer realize cost savings under such a pricing scheme. We examine the efficiency issues and consider the case where the customer does not reveal certain cost components accurately. Our work is motivated by the relationship between a just-in-time manufacturer and its raw material supplier. In each time period, the supplier faces the demand for the raw material that the manufacturer needs for production in the current time period. Through better planning and forecasting techniques, the manufacturer can anticipate the need for the raw material in the future and reduce its demand variability, which, in turn, decreases the safety stock of the supplier. In our setting, the price discount is initiated by the supplier with the goal of reducing its safety stock requirements. Price discounts initiated by the suppliers often occur in industries where there are only a few suppliers and a few consumers of some raw material, and a specific supplier-consumer pair operates in a close relationship. Such situations are common in high-tech industries. As pointed by Lal and Staelin (1984), a large supplier may also initiate a price discount when supplying many small consumers. Our results may also be applicable in this setting by interpreting the customer demand in this paper as the total demand from all consumers. The literature on exploiting different forms of information to increase the efficiency of inventory systems is quite rich. Several papers quantify the value of real-time demand information coming from the retailers in a supply chain. Lee et al. (2000) consider a two-stage supply chain where the customer demands at different time periods are correlated and show that the value of real-time demand information is significant especially when the demand quantities in different time periods are highly correlated. Cachon and Fisher (2000) study a distribution system with one warehouse and multiple retailers, and point out that the value of real-time demand information can be small when compared with the benefits of reducing the lead times or batch sizes. Gavirneni et al. (1999) quantify the value of real-time demand information in capacitated production and distribution systems. Bourland et al. (1999) consider a setting where the ordering cycles of the supplier and the retailer are not aligned. They show that the supplier can make better ordering decisions if it knows the amount of demand that occurs at the retailer between the time of the last order of the retailer and the time that the supplier places an order. Another form of information that is used to increase the efficiency of inventory systems is the forecast updates. Gullu, 1996 and Gullu, 1997 studied production and distribution systems where the demand forecasts get more accurate over time and show that the inventory costs can be reduced if one explicitly takes the forecast updates into consideration. There is also work on quantifying the value of advance demand information. Hariharan and Zipkin (1995) consider a continuous-time inventory control model where the customer demand becomes known ττ time periods in advance. They refer to ττ as the “demand lead time” and show that the effect of increasing the demand lead time is exactly the same as the effect of decreasing the supply lead time. Karaesmen et al., 2002 and Karaesmen et al., 2004 study production systems with advance demand information where the main difference from Hariharan and Zipkin (1995) is the limited production capacity modeled through a single-server queue. Ozer (2003) studies the value of advance demand information in distribution systems. Gilbert and Ballou (1999) examine the reductions in the inventory costs due to advance customer commitment and give a queueing model to assess the impact of advance customer commitment on the capacity requirements. Van Donselaar et al. (2001) and Thonemann (2002) consider the value of advance information in a project environment. Several companies submit proposals for projects. If a company manages to get a project, then it needs raw materials from its suppliers. The companies are able to share information about their proposals with their suppliers, although it is not certain that they will get the project. These papers quantify the value of such imperfect advance demand information to the suppliers. Smoothing the orders is another method to increase the efficiency of inventory systems. Balakrishnan et al. (2004) and Disney et al. (2006) consider models where the retailer computes its order quantity according to a base-stock policy, but its actual order quantity is a convex combination of the order quantities computed in a certain number of past time periods. The goal is to reduce the variability of the orders that the supplier receives. Graves et al. (1998) describe a similar idea in a materials requirement planning environment with limited capacity. Boute et al. (2007) investigate the benefit from smoothing the orders in a make-to-order environment where the production lead time for the supplier depends on the orders placed by the retailer. An interesting point raised by this paper, and also by Bertrand (1986), is that although smoothing the orders is beneficial to the supplier, it may not be beneficial to the retailer since it restricts the ordering pattern of the retailer. Closely related to this body of research is the work on using sophisticated forecasting methods to deal with the bullwhip effect by reducing the variability of the orders that the supplier receives. Zhang (2004) characterizes the effect of different forecasting methods on the magnitude of the bullwhip effect. Dejonckheere et al. (2003) show that the bullwhip effect is inevitable as long as one uses a base-stock policy and propose alternative policies. Lastly, the literature on setting up optimal price discounts is related to our work. Monahan (1984) studies a setting where a customer places orders to a supplier according to the economic order quantity and shows that the supplier can realize cost savings by offering price discounts to persuade the customer to place larger orders. Monahan (1984) assumes that the supplier and the customer have the same ordering cycles, but Lee and Rosenblatt (1986) generalize this model to allow the customer to order more frequently than the supplier. These two papers focus on maximizing the cost savings of the supplier. The supplier sets up the price discount scheme so that the customer, after the price discount, is only not worse off than it was before the price discount. Lal and Staelin (1984) and Dada and Srikanth (1987), on the other hand, consider the total cost of the supplier and the customer. They show how to set up a price discount scheme under which the ordering decisions of the supplier and the customer jointly minimize the total system cost. Weng (1995) extends this work by assuming that the demand is sensitive to price. An important point is that the papers mentioned in this paragraph do not provide a natural mechanism through which the cost savings from the price discount are shared between the supplier and the customer. Chen (2001) and Cheung (1998) present models that are useful when deciding how much price discount should be given to the customers who are willing to wait for the fulfillment of their orders. Klastorin et al. (2002) consider a case where the supplier is willing to offer a price discount if the customer plans the timing of its orders to coincide with the timing of the inventory replenishments of the supplier. In this paper, we make the following research contributions. (1) We analyze a model that captures the relationship between a supplier and a customer where the supplier is willing to reduce the price if the customer reduces its demand variability. We propose a pricing scheme under which both parties realize cost savings. (2) We show that the cost savings of the supplier are larger than those of the customer under the proposed pricing scheme. In this pricing scheme, the supplier decides how the price will be adjusted according to the customer demand variability. Consequently, the supplier can be viewed as the dominant party and this dominance is reflected in its cost savings. (3) We show that if the supplier and the customer repeatedly use the proposed pricing scheme, then the customer eventually keeps the standard deviation of its demand at the level that minimizes the total system cost. (4) Realizing that setting up the proposed pricing scheme requires the supplier to know all cost parameters of the customer, we consider the case where the customer does not reveal a crucial cost component accurately. We show that both parties continue to realize cost savings under certain assumptions, and if the two parties repeatedly use the proposed pricing scheme, then the motivation for the customer to distort the cost component diminishes. In Section 1, we formulate the model and derive the cost functions of the supplier and the customer. Section 2 describes the pricing scheme and shows that both parties realize cost savings under this pricing scheme. Section 3 considers the case where the customer does not reveal a crucial cost component accurately and presents results similar to those in Section 2. Section 4 shows the application of our model to a case where the customer can reduce its demand variability by acquiring advance demand information. In Section 5, we present numerical examples.
نتیجه گیری انگلیسی
This paper considered the relationship between a supplier and a customer operating under a service agreement. The supplier carries a certain amount of safety stock to fulfill the service agreement, whereas the customer is able to reduce its demand variability, albeit by incurring an extra cost. Since a reduction in the customer demand variability reduces the safety stock of the supplier, the supplier is willing to offer a price discount. We studied a pricing scheme where the supplier returns a fraction of its potential cost savings from a reduction in the customer demand variability back to the customer through a price discount. We showed that both the supplier and the customer benefit from such a pricing scheme and the cost savings of the supplier are larger than those of the customer. If the two parties repeatedly use our pricing scheme, then the customer eventually keeps the standard deviation of its demand at the level that minimizes the total system cost. Our pricing scheme continues to provide cost savings to both the supplier and the customer even when the customer does not reveal the cost component C(·)C(·) accurately. Numerical illustrations showed that our pricing scheme is especially beneficial to the supplier and the customer when the uncertainty in the customer demand costs highly either to the supplier or to the customer, or when the cost of reducing the uncertainty in the customer demand is small. Furthermore, the customer can significantly increase its cost savings by not revealing the cost component C(·)C(·) accurately.