Coordination mechanisms of supply chain systems

Transcription

1 European Journal of Operational Research 179 (2007) 1 16 Invited Review Coordination mechanisms of supply chain systems Xiuhui Li, Qinan Wang * Nanyang Business School, Nanyang Technological University, , Singapore Received 23 November 2005; accepted 13 June 2006 Available online 28 August Abstract Supply chain management (SCM) has become an important management paradigm. As supply chain members are often separate and independent economic entities, a key issue in SCM is to develop mechanisms that can align their objectives and coordinate their activities so as to optimize system performance. In this paper, we provide a review of coordination mechanisms of supply chain systems in a framework that is based on supply chain decision structure and nature of demand. This framework highlights the behavioral aspects and information need in the coordination of a supply chain. The identification of these issues points out several directions of future research in this area. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Review; Coordination mechanisms; Supply chain management; Inventory management 1. Introduction Supply chain management (SCM) is to apply a total systems approach to managing the entire flow of information, materials, and services in fulfilling a customer demand (Chase, 1998). This philosophy has brought fundamental changes to the field of business management. Traditionally, managers focus on the management of their internal operations to improve profitability. However, SCM calls for the integration of their operational activities with decisions and activities of their external business partners. * Corresponding author. Tel.: ; fax: addresses: xiuhui@pmail.ntu.edu.sg (X. Li), aqnwang@ntu.edu.sg, fengling@cs.rmit.edu.au (Q. Wang). Numerous studies have demonstrated that substantial benefits can be obtained from SCM. However, SCM provides tremendous challenges to managers. A supply chain system is comprised of all organizations that are involved in transforming raw materials to a final product. These organizations are often separate and independent economic entities. Although a completely integrated solution may result in optimal system performance, this solution is not always in the best interest of every individual member in the system. As a result, independent supply chain members are usually more keen in optimizing their individual objectives rather than that of the entire system. A key issue in SCM is then to develop mechanisms that can align the objectives of independent supply chain members and coordinate their decisions and activities so as to optimize system performance /$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi: /j.ejor

2 2 X. Li, Q. Wang / European Journal of Operational Research 179 (2007) 1 16 From an operational perspective, SCM is to effectively integrate suppliers, manufacturers, warehouses, and stores, so that merchandise is produced and distributed at the right quantities, to the right locations, and at the right time, in order to minimize system wide cost while satisfying service requirements (Simchi-Levi et al., 2000). In this sense, a supply chain coordination mechanism is an operational plan to coordinate the operations of individual supply chain members and improve system profit. When supply chain members are separate and independent economic entities, this action plan has to include an incentive scheme to allocate the benefits from coordination among them so as to entice their cooperation. This article provides a review of coordination mechanisms of supply chain systems. There has been a great deal written on SCM. Tsay et al. (1998) reviewed the recent literature on supply chain contracts. Ganeshan et al. (1998) provided a taxonomic review of the SCM research in three categories: competitive strategies, firm-focused tactics, and operational efficiency. Tan (2001) provided a review of the evolution of the SCM philosophy. Sahin and Robinson (2002) provided a review of the prior research on information and physical flow coordination. We focus on coordination mechanisms that can align the objectives of individual supply chain members. The review is organized in a framework that is based on supply chain decision structure and nature of demand. This framework highlights the behavioral aspects and information need in the coordination of a supply chain. The identification of these issues points out several directions of future research in this area. The rest of the review is organized as follows. Section 2 discusses the roles of coordination in SCM. Section 3 reviews the literature on the coordination of a centralized supply chain where decisions can be made by a centralized body. Subsequently, Section 4 considers the coordination of a decentralized supply chain where each member is a separate economic entity and makes its operational decisions independently. Finally, Section 5 summarises the directions of future research. 2. Roles of supply chain coordination Consider a prototype two-echelon supply chain whereby a supplier sells a product to a group of buyers or retailers. The supplier may be a wholesaler/distributor who obtains its supply from an external source of supply or a manufacturer who produces the product internally under capacity limits. Demand generates only at the retailers, and each retailer replenishes its inventory from the supplier. Traditionally, production and inventory decisions are made locally at the site of activity. The supplier or a retailer adopts the deterministic EOQ policy or an installation policy to replenish its inventory (Silver and Peterson, 1998; Zipkin, 2000). As these policies are results of local optimization, they typically do not optimize system performance. The benefits of centralizing the demand and lot-size decisions have been shown to be very significant when demand is deterministic (Wang, 2001, 2004; Wang and Wu, 2000). Although similar evaluations are not available when demand is stochastic, the benefits of demand/lot-size coordination should be similar. Inventory management at a single location consists of two fundamental decisions: how much to order and when to order (Zipkin, 2000). Inventory management at a supply chain, however, consists of replenishment decisions at different firms. There are three dimensions on which the operational activities of a supply chain can be coordinated in order to maximize system profits or minimize system costs. First, order quantities that optimize individual performance are often not able to optimize system performance. This issue has long been realized. There is a vast literature on discount policies that suppliers can use to entice buyers to increase their order quantities so as to improve profits (Dolan, 1987; Chen et al., 2000; Wang, 2005). Second, orders can be synchronized to reduce system inventory. Consider the case of a supplier and two separate but identical buyers. Let the demand at the buyers be deterministic. If the two buyers are coordinated to place orders at the same point in time, the supplier may adopt a lot-for-lot policy and carry no inventory. If the two buyers are not coordinated on the timing of their orders, the supplier s inventory replenishment cost is double that under the lot-for-lot policy (Klastorin et al., 2002; Wang et al., 2006). Finally, accurate, timely and easily accessible information can improve decisions. In the context of SCM, a supplier is able to better match inventory supply with demand when information is available on the buyer s inventory status. Recent studies have reported significant cost savings from information

3 X. Li, Q. Wang / European Journal of Operational Research 179 (2007) sharing (Lee et al., 2000; Moinzadeh, 2002). The reported benefits, however, vary considerably from study to study, ranging from zero to nearly 35%. This wide variation can be attributed to two factors. First, the benefit of information sharing is context dependent. That is, information is more useful in certain situations than others. Second, the benefit of information depends on how it is used. Although this issue is obvious, it raises an important challenge: optimal policies may change with the information structure. With the existing literature, the issue is obviously no longer whether collaboration is beneficial. Rather, it is how to achieve such benefits. Ideally, a decision in a supply chain can be made by a centralized decision maker with access to all available information to optimize system performance. This is possible when the entire supply chain is under the control of a single decision maker, or the coordination benefits can be fairly distributed among the individual members by a central body. When such a solution can be implemented, the system is referred to as a centralized system. However, in general, neither a supplier nor a buyer can control the entire supply chain. Each supply chain member has its own state of information and decisions that can be made use to optimize its own interest. When the supply chain members are separate and independent economic entities, they will act independently and opportunistically to optimize their individual benefits. In this case, an action plan has to be complemented with an incentive scheme that can allocate the benefits of coordination among the supply chain members so as to align their objectives of coordination. Such a system is regarded as a decentralized supply chain system. In view of the above discussion, we review the literature on the coordination of supply chain inventory systems under a framework that is based on supply chain decision structure and nature of demand. Table 1 presents a brief summary and some examples of the literature in the four categories. The literature in each category will be further reviewed based on time coordination and/or demand and information structure. In general, a supply chain is a network of organizations and its network topology can take various formats by extending from two levels to many levels, from one supplier to many suppliers, and from one product to many products (Roundy, 1986, 1989, 1990, 1993; Maxwell and Muckstadt, 1985). Network structures that have been defined for a large-scale production/inventory system can be used to describe the structure of a supply chain system. For simplicity of exposition, we use the two-echelon supply chain system that is described at the beginning of the section as a base system for the review. Unless stated otherwise, the prototype two-echelon system is the supply chain structure under consideration without further elaboration. 3. Centralized supply chain systems A centralized supply chain system is viewed as one entity that aims to optimize system performance. Various production/inventory policies have been developed to optimize the performance of a Table 1 Supply chain coordination models Decision Structure Nature of demand Deterministic Centralized 1. The classic lot-sizing problem for multi-echelon inventory systems (e.g., Wagner and Whitin, 1958; Zangwill, 1969; Schwarz, 1973) 2. Power-of-two and integer-ratio coordination policies (e.g., Roundy, 1985, 1986) 3. The classic joint replenishment problem (e.g., Goyal, 1973; Silver, 1976; Chakravarty, 1985; Federgruen and Zheng, 1992) Decentralized 1. Quantity discount models (e.g., Dolan, 1978; Monahan, 1984; Lal and Staelin, 1984; Parlar and Wang, 1994; Wang, 2002) 2. Profit-sharing models (e.g., Goyal, 1976; Banerjee, 1986b; Joglekar and Tharthare, 1990) Stochastic 1. Installation policies (e.g., Clark and Scarf, 1962; Deuermeyer and Schwarz, 1981; Svoronos and Zipkin, 1988) 2. Echelon stock policies (e.g., Clark and Scarf, 1960; Chen and Zheng, 1994a,b, 1998) 3. Information sharing models (e.g., Zheng and Zipkin, 1990; Cachon and Fisher, 2000; Moinzadeh, 2002) 1. Supply chain game models (Porteus and Whang, 1991; Cachon and Zipkin, 1999; Caldentey and Wein, 2003)

4 4 X. Li, Q. Wang / European Journal of Operational Research 179 (2007) 1 16 centralized supply chain system. We first discuss the deterministic case, and then review models with stochastic demand Deterministic systems The objective is to develop a production/inventory policy to minimize system cost. It is typically assumed that demand occurs at a buyer/retailer continuously at a constant rate, and no backlogging, lost sales, or transshipment is permitted anywhere in the system. Early studies have focused on the existence and development of optimal policies. However, such policies are usually difficult to characterize and implement. Recent studies have focused on approximate policies that are nearly optimal and practically useful No time coordination The problem of optimizing a multi-echelon inventory system is a classical one. When the planning horizon is finite, an optimal lot-sizing policy exists. This optimal policy is typically non-stationary. Previous studies have developed various algorithms to solve the discrete-time lot-sizing problem (Veinott, 1969; Zangwill, 1969; Kalymon, 1972). The continuous-time version of the problem can be solved approximately by a discrete-time algorithm with a very small base planning period. We refer to Clark (1972) for a review of the early work on multi-echelon inventory systems. When the planning period is infinite, however, an optimal policy is very difficult to characterize when there is more than one buyer. Schwarz (1973) has proven that an optimal policy for the continuoustime infinite-horizon lot-sizing problem, if it exists, must have the following necessary properties: (i) zero-inventory: deliveries should be made to the warehouse or a retailer only when its inventory is zero; (ii) last-minute ordering: deliveries should be made to the warehouse only when its inventory is zero and at least one retailer places an order; and (iii) stationary replenishment interval: deliveries are made to a retailer in equally-spaced intervals between two consecutive orders. The zero-inventory property was proven for the finite-horizon discrete-time lot-sizing problem first by Wagner and Whitin (1958) for a single-facility and subsequently by Zangwill (1966) and Veinott (1969) for many facilities. The stationary property was proven by Carr and Howe (1962) in the finitehorizon case Time coordination The optimal replenishment policy of a multi-echelon inventory system, however, typically entails a very complex non-stationary structure and thus is difficult to obtain and of little practical use. As such, previous studies have considered heuristic policies by restricting the timing of orders for the supplier and buyers so as to meet the above necessary properties for an optimal solution. Specifically, early studies have focused on stationary-nested or single-cycle policies. A policy is called stationary if each facility orders at equally-spaced points in time and in equal amounts. A policy is nested if each facility orders every time any of its immediate suppliers does, and perhaps at other times as well (Veinott, 1969). Policies that are both stationary and nested are called stationary-nested or singlecycle. Studies on inventory policies for multi-level production inventory systems before the seminal work of Roundy (1985, 1986) have typically considered stationary-nested policies (Schwarz, 1973; Schwarz and Schrage, 1975; Maxwell and Muckstadt, 1985). Stationary and nested policies are attractive because they are easy to implement. However, such policies may result in very bad results in some cases. Roundy (1985) demonstrated that the effectiveness of the optimal nested policy can be arbitrarily close to zero. Consequently, Roundy (1985, 1986) developed power-of-two and integer-ratio policies. Let T 0 and T i denote the replenishment interval for the supplier and buyer i, respectively, i =1,...,N. A nested policy requires T i = (1/n i )T 0, where n i is a positive integer. A power-of-two or integer-ratio policy is a generalization of a nested policy. Namely, a power-of-two policy requires T i ¼ 2 ni T 0, where n i, is an (positive, zero, or negative) integer. An integerratio policy is a further generalization such that T i = n i T 0 or T i = (1/n i )T 0, where n i, is a positive integer. For a given T 0 a power-of-two or integer-ratio policy can pffiffiffi be found pffiffiffi such that the system cost is within 2 þ 1= 2 =2 1:06 of the minimum system cost. When optimization can be pcarried ffiffi out on T 0, a system cost that is within 1= 2 ln 2 1:02 of the minimum system cost can be achieved under the optimal solution. Muckstadt and Roundy (1993) discussed the rationale of using order intervals T i as variables.

5 X. Li, Q. Wang / European Journal of Operational Research 179 (2007) These results have been extensively studied and extended to other versions of lot-sizing problems: finite assembly rates (Atkins et al., 1992), individual capacity constraints with more general cost structures (Federgruen and Zheng, 1993), backlog (Mitchell, 1986; Atkins and Sun, 1995, 1997; Chen, 1998), and capacitated lot-sizing problems (Jackson et al., 1988; Roundy, 1989; Federgruen and Zheng, 1993; Herer and Roundy, 1997). Jackson et al. (1988) obtained efficient heuristics for the general capacitated version (with bounds of the type R i T i 6 C), using the structural results for the uncapacitated version of the problem. However, no worst-case bound is known for their heuristics, and there is no guarantee of feasibility of the solution produced by the heuristic. For the case with a linear ordering cost and a single capacity constraint, Roundy (1989) obtained a 94% efficient heuristic. A special case of the above model is the classical joint replenishment problem (JRP). Consider an inventory system in which multiple items are ordered from a common source. A major ordering cost is incurred each time an order is placed to the common source, independently of the number of items that are included in the order, and a minor ordering cost is incurred for each item that is included in the order. Obviously, ordering cost savings can be obtained when several items are replenished jointly. The key issue is then how to group these items. Many studies adopted group replenishment at constant intervals of time. Goyal (1973) developed sub-optimal solutions to the problem of determining economic order quantities for items furnished by a single supplier. For a similar problem of determining the optimal packaging frequency of jointly replenished items, Goyal (1974a,b) presented a systematic procedure which guarantees the optimum solution. Silver (1976) presented a much simpler non-iterative approach at rather small cost penalties. Chakravarty (1985) suggested an efficient heuristic to create groups, under the condition that there always exists an optimal grouping in which the items are arranged in an increasing order of h j d j /K j, where h j >0, d j >0 and K j > 0 denote the holding cost, demand and setup cost of item j at a unit time, respectively. An efficient approximation has also been developed for the joint replenishment problem by rounding off the policies that are obtained from the relaxation of the problem (Jackson et al., 1985; Federgruen and Zheng, 1992; Muckstadt and Roundy, 1993). This class of stationary policies is highly effective: within 94% and 98% of the optimum, respectively, for the fixed base model and the variable base model. The classic JRP model has been extended in several directions. Anily and Federgruen (1990a) introduced vehicle routing cost into the model for a capacitated multi-product distribution system. They restricted the number of products in the distribution system to one and proposed two heuristics to solve this problem (Anily and Federgruen, 1990b). Anily and Federgruen (1993) considered an extension of the model to situations in which inventory of the product is kept at the retailers as well as at the warehouse. Federgruen and Zheng (1992) and Federgruen et al. (1992) considered inventory systems with sub-modular joint setup cost structures but without any capacity restrictions on the replenishment quantity. Fumero and Vercellis (1999) considered an integrated optimization model for production and distribution planning with the aim of optimally coordinating important and interrelated logistic decisions such as capacity management, inventory allocation, and vehicle routing. The integrated model was solved via Lagrangean relaxation and both lower bounds and heuristic feasible solutions were obtained Stochastic systems In reality, a stochastic model that specifies demand as a stochastic process is often more accurate than its deterministic counterpart the economic order quantity (EOQ) model (Zheng, 1992). However, a barrier to the application of a stochastic model is that the optimal policy does not have a simple structure, and is not easy to implement even if it does exist (Clark and Scarf, 1962). This implies that appropriate coordination mechanisms are especially necessary. Moreover, information sharing contributes another dimension for coordination when demand is stochastic. Following the developments of multi-level production/inventory systems, two classes of inventory control policies have been used for supply chain inventory management. Traditionally, members in a supply chain have little communication about their demand and inventory activities. The control of inventory is decentralized in the sense that each member makes its inventory decision separately based entirely on the local inventory position (inventory on-hand plus outstanding orders minus

6 6 X. Li, Q. Wang / European Journal of Operational Research 179 (2007) 1 16 backorders). This inventory policy is referred to as an installation policy. An installation policy is operationally simple because it does not require any information about the inventory situations at other members in the system. However, it does not optimize system performance. Most previous research on distribution and serial systems under continuous inventory review has adopted an installation stock policy. Deuermeyer and Schwarz (1981) considered a distribution inventory system consisting of one supplier and multiple identical retailers and developed an installation stock policy by approximating each facility as a single-location inventory system and using decomposition as an adaptation of the METRIC technique. Moinzadeh and Lee (1986), Lee and Moinzadeh (1987a,b), Svoronos and Zipkin (1988) and Axsater (1993) examined the same problem by employing secondmoment information in the approximations. Forsberg (1997) and Axsater (2000) generalized the results to the case of non-identical retailers under simple and compound Poisson demand. Badinelli (1992) put forward a descriptive model of a serial inventory system in which each member adopts an installation stock (R, Q) policy. Alternatively, the inventory at a supply chain member can be controlled according to an echelon stock policy that replenishes inventory based on the echelon inventory position (the sum of the local inventory position and the inventory positions at all its downstream members) instead of the local inventory position. Echelon stock policies were first introduced by Clark and Scarf (1960). They showed that echelon base-stock policies are optimal in a periodic-review finite-horizon setting when there are no economies of scale in placing orders at all the stages except the most upstream stage in a serial inventory system. This result was later generalized to an infinite-horizon setting (Federgruen and Zipkin, 1984) and assembly systems (Rosling, 1989). Nevertheless, optimal echelon stock policies are extremely difficult to characterize when there are economies of scale in placing orders at all stages. Because of this difficulty, most previous studies have considered heuristic policies for serial inventory systems (De Bodt and Graves, 1985; Chen, 1999a; Chen and Zheng, 1997, 1998), although Chen and Zheng (1994a) derived some exact results. Chen and Zheng (1994b) also established lower bounds for serial, assembly and distribution systems with setup costs at all stages. Capacitated multi-echelon systems were also studied (Glasserman and Tayur, 1994, 1995; Kapuscinski and Tayur, 1998). Obviously, as the echelon stock policy incorporates downstream agents inventory information for inventory control, it is superior to an installation policy. Axsater and Rosling (1993) demonstrated this fact analytically by comparing these two policies for serial and assembly systems. However, the implementation of an echelon policy requires a centralized information system that enables a supply chain member to have access to the demand and inventory information at all its downstream supply chain members in order to continuously monitor its echelon stock. Unfortunately, neither the installation stock nor the echelon stock completely characterizes the inventory state of a supply chain. Obviously, an installation policy at the supplier utilizes no inventory information from the buyers and an echelon stock policy at the supplier utilizes only the echelon stock (i.e., the total inventory at all the buyers) information. If the supplier is able to devise its inventory replenishment policy according to the exact inventory position at each buyer, it may be able to better match its stocks with orders from the buyers. In this sense, to optimize system performance, inventory should be replenished at the supplier based on the exact inventory positions at the buyers. Nonetheless, this requires that demand and stock information at each stocking point be shared on a real time basis between the supplier and buyers in the supply chain. With the recent advances in information technology such as electronic data interchange (EDI) and other related developments, this is now possible. In fact, these developments have had a substantial impact upon SCM. As the time and cost to process orders are substantially lowered, impressive improvements in supply chain performance have been obtained. It is now a general belief that capturing and sharing real-time demand and stock information is the key to improving supply chain performance. Information sharing has a direct impact on production scheduling, inventory control and delivery plans of individual members in the supply chain. Systematic distortions in demand information occur as it passes along a supply chain in the form of orders. As a result, production and replenishment orders do not match with actual demand. This effect is commonly known as the bullwhip effect, and has a great negative impact on supply chain performance. Sharing sales information and inventory data has been viewed as a major strategy to counter this

7 X. Li, Q. Wang / European Journal of Operational Research 179 (2007) effect. Swaminathan and Tayur (2003) provided an overview of relevant analytical research models that have been developed for supply chains in E-business. We briefly review in the following models that quantify the benefits of information sharing Independent and exogenously determined demand process Zheng and Zipkin (1990) was probably one of the earliest studies that attempted to quantify the benefits of information sharing. They analyzed the value of information flow in a two-item competing for a single production facility setting, and showed that using information about outstanding orders of both products could result in improvements of system performance. Subsequently, Zipkin (1995) extended the analysis to a multi-item production facility. Bourland et al. (1996) examined a simple twolevel system that is composed of a supplier and a single retailer who adopt periodic-review inventory systems. It was found that the supplier could improve its order replenishment decision by making use of information about the inventory level at the retailer at the time of its order review when their review periods were not synchronized. Subsequently, Gavieneni et al. (1999) and Gavieneni (2002) measured the benefit of sharing the parameters of a retailer s ordering policy with the manufacturer in a capacitated setting of a typical supply chain. Three situations were considered from the degree of information sharing among the members. The studies demonstrated the relationships between capacity, inventory and information at the supplier level, as well as how they are affected by the retailer s (S-s) values and end-item demand distribution. Cachon and Fisher (2000) studied the value of sharing information in a model with one supplier and N identical retailers. In particular, they contrasted the value of information sharing with faster and cheaper order processing, which leaded to shorter lead times and smaller batch sizes, respectively, and found that implementing information technology to accelerate and smooth the physical flow of goods through a supply chain was significantly more valuable than to expand the flow of information. More recently, Moinzadeh (2002) proposed a heuristic replenishment policy for a supplier facing a group of multiple identical retailers by incorporating information about the inventory positions of the retailers, compared the performance of the model with those that do not use information in their decision making, and identified the parameter settings under which information sharing is most beneficial for the supplier. Lee et al. (1997) analyzed four sources of the bullwhip effect, namely, demand signal processing, rationing game, order batching and price variations, and found that information sharing could be used to counter the bullwhip effect. However, no quantitative measurement of the benefit of information-sharing was given in the study. More recently, Chen et al. (2000) first quantified the effect of forecasting and lead times on the bullwhip effect for a simple two-stage supply chain that consists of one supplier and a single retailer, and then extended the results to multiple-stage supply chains with and without centralized customer demand information. It was demonstrated that centralized demand information could reduce, but not completely eliminate the bullwhip effect. Hariharan and Zipkin (1995) considered the value of sharing customers advance warning information about their demands and concluded that demand lead times improved performance, in the same way that replenishment lead times degraded it. Iyer and Ye (2000) assessed the value of a retailer s promotion plan information in a two-level logistics system. They showed that (1) it may be optimal for the retailer to eliminate retail promotions as the decreasing of predictability of the sales impact of a promotion; (2) increased stockpiling tendency of customers increases retailer profits and decreases manufacturer profits; and (3) retail promotion information sharing can make retail promotions change from being less profitable to being more profitable than no promotions for the manufacturer. The benefits of vendor managed inventory (VMI) systems have also been studied. Cetinkaya and Lee (2000) assumed that the supplier has the option of delaying a delivery in anticipation of orders from other retailers, and used the information about the retailers inventory positions to coordinate shipments from the supplier to enjoy economies of scale in shipments and for eventual unloading of the shipments to the retailers to rebalance their stocking positions. This assumption was later relaxed by Cheung and Lee (2002) Correlated demand process The studies reviewed above assume that the demand processes are independently and identically distributed over time. Under this condition, the benefit of information sharing lies in a supplier s capa-

8 8 X. Li, Q. Wang / European Journal of Operational Research 179 (2007) 1 16 bility to react to a retailer s needs via the knowledge of the retailer s inventory levels to help reduce uncertainties in the demand process. Recently, Lee et al. (2000) considered a two-level supply chain that consists of a manufacturer and a single retailer who faces a non-stationary auto-correlated demand process, and showed that the manufacturer would experience great savings when demand information was shared by the downstream member. The analysis was subsequently extended by Aviv (2002) to a setting in which companies could observe early market signals to improve their forecasting performance. However, Raghunathan (2001) pointed out later that the finding of Lee et al. (2000) depends on the critical assumptions that the manufacturer uses only the most recent order information from the retailer to forecast its future orders and that the parameters of the demand process are only accessed by the retailer. If the parameters of the auto-correlated demand process are known to both parties, sharing of demand information is actually of limited value. As the manufacturer can forecast the demand by using the retailer s order history and the accuracy of forecast increases monotonically with each subsequent time period, the value of information decreases monotonically with each time period and converges to zero. Since the entire retailer order history is available to the manufacturer, the manufacturer is in a position to use the data in its forecasting process. These discussions illustrate a fundamental problem with studies that evaluate the benefits of information: the value of information depends on how it is utilized. The benefit of demand information has also been studied by using the history of the demand process to more accurately forecast the demand distribution using Bayesian updates (Iglehart, 1964; Azoury, 1985; Lovejoy, 1990; Milner and Kouvelis, 2002). 4. Decentralized distribution system A decentralized supply chain differs from a centralized system in that members act independently to optimize their individual performance. Although more and more firms have realized that collaboration with their supply chain partners can significantly improve their profits, the centralization of inventory and production decisions for a decentralized supply chain is often unrealistic. The challenge, then, is to devise coordination mechanisms that are not only able to coordinate the activities but also able to align the objectives of independent supply chain members (Chen et al., 2000) Deterministic systems Previous research on the coordination of decentralized deterministic systems has focused on using quantity discounts to induce independent buyers to increase their order quantities. Crowther (1964) was probably the first to consider quantity discounts as a mechanism for a supplier to entice buyers to increase their order quantities so as to improve channel efficiency. Dolan (1987) provided an excellent synopsis about the rationales and conditions for a supplier to offer quantity discounts to buyers. Many studies have been done independently from the viewpoints of inventory and production management and marketing channel coordination. The studies in the two areas differ in their focuses and model assumptions. Specifically, previous studies in the inventory and production management literature have typically focused on improving channel efficiency in managing inventory and production activities under the assumption that annual demand is exogenously determined. In contrast, studies in the marketing literature have typically focused on sales profit maximization under the assumption that inventory and production costs are independent of the pricing decision. Various discount pricing policies have been developed. As Dolan (1987) reviewed the early quantity discount literature, we review the more recent developments in this area in the following. In general, it is assumed that the external demand rate, which could be constant or price-sensitive, occurs at a retailer continuously over an infinite horizon, and the supplier has symmetrical information about the annual demand and relevant cost parameters of a buyer. The objective is to determine the inventory and quantity discount policies to minimize cost or maximize profit The case of a single retailer Many existing studies have analyzed quantity discount policies in the setting of a supplier and a single buyer. Although a supplier normally faces many buyers in reality, this setting has been adopted for simplicity of analysis. Under the assumption of a fixed demand, Dolan (1978) adopted an approximation for the supplier s

9 X. Li, Q. Wang / European Journal of Operational Research 179 (2007) inventory related cost and analyzed quantity discounts as a mechanism for the supplier to induce buyers to purchase in quantities that minimize system cost. Subsequently, Monahan (1984) assumed a lot-for-lot replenishment policy for a vendor and derived the vendor s optimal quantity discount policy. It was shown that the vendor could earn higher profits by offering a buyer a quantity discount. The model was later extended by Banerjee (1986a) by incorporating the vendor s inventory carrying costs when the product is manufactured internally (i.e., the vendor is a manufacturer) and by Rosenblatt and Lee (1985), Lee and Rosenblatt (1986) and Goyal (1987) by relaxing the lot-for-lot assumption. Banerjee (1986b) also considered pricing and lot-sizing decisions as part of a sequential negotiation process or a cooperative game between the buyer and the supplier. Adopting the approximation formulation of Dolan (1978), Dada and Srikanth (1987) characterized the range of order sizes and prices which reduce costs for the supplier and buyer, and developed feasible pricing schemes to allocate the cost savings between the supplier and buyer. Chakravarty and Martin (1988) determined the optimal discount price and replenishment interval under periodic review for the vendor. When demand is price elastic, a buyer has to determine its retail price and lot size jointly in order to maximize its profit (Abad, 1988). Weng and Wong (1993) studied some managerial issues related to using all-unit quantity discount policies under a constant or price-elastic demand. Parlar and Wang (1994) studied the quantity discount pricing decision of a supplier and the ordering decisions of homogeneous buyers whose annual demand is a linear function of price as a Stackelberg game, and characterized the conditions in which the supplier would offer quantity discounts. Extending the model by Parlar and Wang (1994), Weng (1995) showed that quantity discounts alone are not sufficient to guarantee joint profit maximization. However, perfect coordination that maximizes system profit could be achieved by simultaneously implementing quantity discounts and a franchise fee (i.e., a fixed payment per period from the buyer to the supplier) in a system in which the annual demand rate is a decreasing function of price. Abad (1994) characterized Pareto efficient solutions and Nash bargaining solutions. Viswanathan and Wang (2003) extended traditional quantity discounts that are based solely on buyers individual lot sizes, to volume discounts that are based on buyers annual volume, and showed that a unified discount policy is able to achieve system optimality. In addition to quantity discount policies, profit sharing mechanisms have also been proposed. Under this proposal, the system performance is first optimized and the resultant benefit is then shared between the supplier and the buyer. This solution can be considered as a cooperative solution. Its implementation, however, depends on the development of a profit sharing scheme that is acceptable to both parties. Goyal (1976) proposed for the supplier and buyer to share the coordination benefit proportionally according to their costs. Banerjee (1986b) developed a joint economic-lot-size model under a lot-for-lot replenishment policy together with an appropriate price adjustment, which is economically beneficial for both parties. Goyal (1988) relaxed the lot-for-lot assumption of Banerjee (1986b) and suggested a more general joint economic-lot-size model. He showed a lower or equal joint total relevant cost as compared to the model of Banerjee (1986b). Joglekar and Tharthare (1990) allocated the profit by making the buyers pay for the order processing cost they impose on the vendor every time they order and, in return, the supplier lowers its price per unit The case of heterogeneous retailers When there are many buyers, an important issue for the coordination of a decentralized supply chain is whether incentive schemes can be designed on an individual basis. According to Section 2(a) of the Robinson Patman Act of the United States, it is unlawful... either directly or indirectly, to discriminate in price between different purchasers of commodities of like grade and quality... Consequently, individual payments are not always lawful. However, a coordination mechanism with a unified incentive scheme is difficult to develop. There are two reasons. First, as discussed previously in Section 3.1, a supplier s optimal inventory replenishment policy when facing a group of heterogeneous buyers typically entails non-stationary replenishment intervals and, thus, does not admit an explicit formulation. Second, a unified discount policy must be designed according to buyers cost and demand structures, as well as their economic behaviors, so as to fully exploit the benefits of coordination. When individual incentive schemes are permissible, a straightforward solution to the problem that is able to optimize system performance is for the supplier to negotiate a separate discount policy with

10 10 X. Li, Q. Wang / European Journal of Operational Research 179 (2007) 1 16 each buyer, fixing the lot size and annual volume at the quantities that optimize system profit and selecting a price that is agreeable to both parties. Alternatively, Chen et al. (2001) demonstrated that optimal system profit can be achieved with a common quantity discount policy when demand is not price elastic. However, the supplier has to offer very high price discounts and would incur a substantial loss under this discount policy in an effort to maximize system performance. To implement this solution, Chen et al. (2000) proposed that a franchise fee (a fixed payment per period) from each buyer to the supplier is negotiated between the supplier and each buyer to reallocate the benefits. Nevertheless, a straightforward solution as discussed above seems to be more desirable in such situations. Suppliers in reality usually offer a common pricing policy that contains multiple break points to all buyers. Other than legal considerations, a common pricing policy is desirable not only for fairness of trade but also for ease of implementation. Multiple break points are offered to accommodate different cost and demand structures of heterogeneous buyers. However, a general discrete quantity discount is difficult to develop. As such, early studies adopted continuous approximations. Lal and Staelin (1984) first developed a unified quantity discount policy for a group of heterogeneous retailers, assuming that the supplier uses a lot-for-lot policy to replenish its inventory and adopts a continuous price function that decreases exponentially with order size. Rosenblatt and Lee (1985) analyzed the problem under similar conditions assuming that price is a linear (negatively sloped) function of order quantity. Kim and Hwang (1988) also analyzed the problem under the same channel conditions and lot-for-lot replenishment policy assuming that the supplier provides a single incremental discount policy to all buyers. Optimal general discrete quantity discount policies have been developed recently by Wang (2002). Under the approximate formulation for the supplier s inventory related cost that was developed by Dolan (1978), it was found that a larger buyer is generally willing to exchange a higher order quantity for a higher price discount. Under this condition, the optimal general discrete quantity discount policy can be easily developed. It was also shown that a continuous approximation severely impairs the ability of quantity discounts to improve system performance. Recently, Wang and Wang (2005) extended this research to situations whereby each buyer faces a price-sensitive demand. It was found that, in general, quantity discounts that are based on buyers order quantities and developed as Stackelberg equilibrium strategies for the supplier are not able to optimize system performance. Improvements have been made in two aspects. Wang and Wu (2000) showed that the effectiveness of a unified general all-unit quantity discount schedule can be enhanced significantly if the price discounts are offered based on percentage increase, rather than unit increase, from a buyer s order quantity before discount. On the other hand, Wang (2005) extended traditional quantity discounts that are based solely on buyers individual lot sizes, to volume discounts that are based on buyers annual volume, and showed that a unified discount policy is able to achieve nearly optimal system profit. The models above, however, suffer from a common weakness that a heuristic inventory policy or simply an approximation of the inventory related cost function is assumed for the supplier. Obviously, neither a lot-for-lot policy nor a heuristic replenishment policy is desirable for the supplier. To overcome this problem, Wang (2001) combined time coordination and quantity discounts, and developed a supplier s optimal quantity discount policy when the replenishments of the supplier and buyers are coordinated according to a power-of-two policy. However, Wang (2004) found later that a powerof-two policy is not always able to provide a stable equilibrium coordination mechanism and an integer-ratio policy is always able to do so when buyers act independently and opportunistically. Furthermore, when a power-of-two policy is able to provide a stable equilibrium solution, an integer-ratio policy is more, or at least equally, effective. As such, an integer-ratio time coordination scheme should be used for the coordination of a decentralized supply chain. In the meantime, Viswanathan and Piplani (2001) considered a simplified scenario whereby the supplier specifies common replenishment periods and requires all buyers to order only at those time periods. The supplier offers a single price discount to entice the buyers to comply with the coordination scheme. In contrast, Klastorin et al. (2002) assumed an exogenously determined replenishment period for the supplier and adopted a stationary-nested replenishment policy for the system. They developed the supplier s minimum single price discount to entice buyers cooperation. Recently, Wang et al. (2006) developed a general model that places no restrictions on the supplier s replenishment interval (i.e., treating

11 X. Li, Q. Wang / European Journal of Operational Research 179 (2007) it as a decision variable) and the buyers replenishment periods (i.e., allowing them to integer or integer-ratio multiples of the supplier s replenishment interval), and showed that time coordination is able to gain a significant benefit Stochastic systems In view of the difficulties in managing centralized stochastic multi-echelon inventory systems, it is an understatement that it is a challenge to coordinate a decentralized supply chain with stochastic demand. It is then not surprising that the literature in this category is scattered. As most real supply chain inventory systems fall into this category, this of course represents challenges and opportunities for future research. A few important studies that largely fall into this category are briefly reviewed in the following. Porteus and Whang (1991) described the conflicts of interests between the manufacturing and marketing divisions of a firm (which can be interpreted loosely as a supply chain) over the production capacity decision, and showed that these conflicts can be reconciled by establishing an internal futures market for capacity. Lee and Whang (1999) considered the problem of coordinating a decentralized version of the Clark Scarf serial system. While each member incurs a holding cost, only the end member faces a shortage cost. Consequently, the upstream members will carry less buffer inventory than may be best for the system as a whole and the member furthest downstream tends to carry extra inventory, which is inefficient since finished goods usually are most costly to hold. The paper proposed rules for performance measurement and accountability, which have the following desirable properties: (i) cost conservation (i.e., all costs can be traced to individual members without the need for subsidies or taxes from the central planner), (ii) incentive compatibility (i.e., what is optimal for each individual member is also optimal for the system as a whole), and (iii) information decentralizability (i.e., the rules can be implemented using local information only). This scheme involves a consignment policy for redistributing inventory carrying costs among the members, an additional backlog penalty paid to an upstream member by its direct customer, and a shortage reimbursement paid to a downstream member by its direct supplier. No markups are added to the transfer prices. However, implementing this scheme requires common knowledge about the demand distribution. For the same model as Lee and Whang (1999), except with delays between the transmission and receipt of orders between sites, Chen (1999b) restored system-optimal performance using a measurement scheme based on accounting inventory. A division s accounting inventory is its on-hand stock minus backlogs of orders placed by the downstream site, under the assumption that the upstream division is perfectly reliable. Moses and Seshadri (2000) showed that given a review period, unless the manufacturer agrees to share the cost of carrying a fraction of the safety stocks at the retailer, the two will not agree upon the level of stocks to be carried in the store. They proved that there is an equilibrium value for this fraction. Different from the information sharing in a centralized system, in which retailers usually cannot get any value from sharing information with the supplier, benefits for retailers could be significant in a decentralized system. Cheung and Lee (2002) discussed the value of sharing information about the retailers inventory positions which could be used to coordinate shipments from the supplier to enjoy economies of scale in shipments, and for eventual unloading of the shipments to the retailers to rebalance their stocking positions. Cachon and Zipkin (1999) discussed Nash equilibrium that differs from the optimal solution. However, by using simple linear transfer payments, Nash equilibrium can achieve the optimal profit. Axsater (2001) considered a Stackelberg game with the warehouse being the leader. If the game is played repeatedly, the system will approach Nash equilibrium but not necessarily the centralized optimal solution. Caldentey and Wein (2003) characterized the optimal centralized and Nash solutions, and showed that a contract with linear transfer payments replicates a cost-sharing agreement and coordinates the system. They also compared the total system costs, the agents decision variables, and the customer service levels of the centralized versus Nash versus Stackelberg solutions. 5. Conclusions and discussion In a nutshell, a coordination mechanism for a centralized supply chain system is an action plan that coordinates the decisions and activities of all supply chain members to optimize system performance. However, this is inadequate for a decentralized supply chain system whereby members are separate economic entities acting opportunistically to optimize their individual performance. This is because an action plan is often not in the best inter-