Financial Globalization: A Glass Half Empty?

Since the 1970s, the world has embarked on a new financial globalization era. Cross-country capital flows have significantly increased in developed and developing countries. However, the characteristics of financial globalization differ from what was originally expected. Various examples illustrate this point. Although the literature predicted large gains from financial globalization (such as additional funding, broad diversification, and deeper financial systems), the positive effects have been more limited. In developed and developing countries, financial globalization has manifested in increasing gross capital flows (inflows and outflows) rather than larger net flows. Capital markets are segmented and only a few large firms access international markets. International institutional investors do not seem to have played a stabilizing role, helping to exacerbate and transmit crises across countries. Although financial globalization has brought several beneficial changes, its net effects and spillovers to the overall economies participating in it have yet to be understood.


Introduction
Enterprises can be non-cooperative and cooperative in a supply chain since they individually try to maximize their own profits. For a VMI (Vendor Managed Inventory) -type supply chain, the manufacturer and its retailers cooperate with each on their inventory control. The manufacturer decides on the appropriate inventory levels of each of the products for all enterprises, and the appropriate inventory policies to maintain these levels (Simchi-Livi et al. 2000). A VMI system has been widely adopted by many industries for years. The classical success story for VMI system is found in the partnership between Wal-Mart and Procter & Gamble (P&G). In 1985, the partnership had dramatically improved P&G's on-time deliveries and Wal-Mart's sales, and both of their inventory turns also increased (Buzzell and Ortmeyer 1995). Besides retailing industries, VMI is adopted by leading chemical companies to increase supply chain efficiency and to enhance customer and supplier relationships (Challener 2000). High-tech industries such as Dell, HP and ST Microelectronics also operate efficient supply chains through VMI to reduce inventory levels and costs (Shah 2002, Tyan andWee 2003). In this system there are manufacturers ( P&G, Dell, HP etc.) and retailers, such as Wal-Mart, and all kinds of products sold, for example, HP selling printers, computers and scanners etc, P&G manufacturing cosmetics, household cleaners and paper products etc.
integrated supply chain inventory model, those on integrating marketing policies into inventory decisions, and those on Stackelberg games in supply chains.
Early researches based on simple supply chain inventory involved a single vendor and single retailer, as used by Goyal (1977) for studying a joint economic lot size (JELS) model to minimize the total relevant costs. Banerjee (1986) generalized Goyal's model (Goyal 1977) by incorporating a finite production rate for the vendor to obtain the optimal joint production or order quantity. Goyal (1988) extended Banerjee's model (Banerjee 1986) again by relaxing the lot-for-lot production assumption and argued that the economic production quantity is an integer multiple of the buyer's purchase quantity and showed that its model provides a lower or equal joint total relevant cost. Kohli and Park (1994) investigated joint ordering policies as a method to reduce transaction costs between a single vendor and a homogeneous group of retailers. They presented expressions for optimal joint order quantities assuming all products are ordered in each joint order. Lu (1995) considered a one-vendor multi-buyer integrated inventory model and gave a heuristic approach for joint replenishment policy. Banerjee and Banerjee (1992) considered a VMI system in which the vendor makes all replenishment decisions for its buyers to improve the joint inventory cost. Woo et al. (2001) and Yu and Liang (2004a) extended their discussions to three level supply chain in which only one raw material is considered. Recently, VMI is widely studied by other researchers, such as Achabal et al. (2000), Dong and Xu (2002), Disney and Towill (2003), Toni and Zamolo (2005), and Rusdiansyah and Tsao (2005) etc. How to give an optimal inventory policy for maximizing the joint inventory cost is the main objective for these literatures. Note that in the above VMI setting (Woo et al. 2001, Yu andLiang 2004a, etc.), in order to streamline the supply chain, vendors are expected to synchronize its production cycles with buyers' ordering cycles, such as common replenishment cycles/epochs adopted (Viswanathan and Piplani 2001, Woo et al. 2001, Mishra 2004, Yu and Liang 2004a, so that the total inventory cost for the entire chain can be reduced (Woo et al. 2001).
Many researchers have considered how to integrate marketing policies into inventory control decisions. For example, Kotler (1971) incorporated marketing policies into inventory decisions and discussed the relationship between economic ordering quantity and price decisions for infinite time horizon. Ladany and Sternleib (1974) studied the effect of price variations on demand and consequently on EOQ (economic order quantity). Roslow et al. (1993) and Yu and Liang (2004b) studied co-op advertisement or pricing. Chen and Chen (2005) and Anjos et al. (2005) established a pricing and inventory policy that maximizes the revenue from selling a given inventory of items with continuous decay. These papers mainly discuss how the end market policies influence system wide profit to show the importance of market parameters.
Stackelberg games for analyzing the game in supply chains are studied by quite a lot of researchers. In recent years, Weng (1995) studied the supply chain with one manufacture and multiple identical retailers, shows that Stackelberg game is used to guarantee perfect coordination considering quantity discounts and franchise fees. In the setting studied by Weng (1995), Chen et al. (2001a) showed that when the retailers are not identical, such a scheme is not guaranteed to perfectly coordinate the channel. They consider two Stackelberg games with the supplier as the leader and the retailers as followers. In one, the supplier sets a constant wholesale price, and in the other, the supplier offers an order-quantity discount scheme with one breakpoint. Viswanathan and Wang (2003) studied a similar setting with one manufacturer and one retailer by Stackelberg game with three price discount schemes, namely, (1) volume discounts, (2) quantity discounts, and (3) quantity discounts and simultaneous offer of volume discounts when demand is constant but pricesensitive. It is shown that quantity discount schemes help the supplier achieve economies in order processing and inventory costs by encouraging buyers to increase the size of each of lot. However, quantity discounts tend to raise the cycle inventory of the supply chain. With demand that is price-sensitive, Qin et al. (2006) considered volume discounts and franchise fees as coordination mechanisms in a system consisting of a supplier and a buyer. The problem is analysed as a Stackelberg game. The competition/coordination mechanism in supply chains with Stackelberg game was also discussed by Huang and Li (2001), Viswanathan and Rajesh (2001), Chen et al. (2001b), Sarmah et al. (2005) , and Parlar and Weng (2006) etc. A critical assumption made throughout this literature, though, is that the supplier has full information, and can design the quantity discount/franchise scheme without giving a reasonable reason. Most of these researchers took quantity discounts or/and franchise fee with a contract as incentive schemes s to influence buyers' ordering behaviour, thus reducing the supplier's (and the total supply chain's) costs. In the above literature, none of them take the wholesale price and retail price as a decision variables in the setting with one vendor and multiple different retailers. The game in VMI system is few concerned.

Problem description
In this paper, we consider one manufacturer and multiple retailers in a VMI setting in which: (1) The manufacturer produces one type of product with a limited production capacity, and supplies it to its multiple retailers.
(2) The retailers are geographically dispersed to serve the markets in their own regions. The demand function for every retailer is the decreasing and convex function with respect to its retail price. (3) The manufacturer is a leader in the supply chain. The retailers' response is available to the manufacturer (vendor) who determines the inventory replenishment plan and wholesale price. The manufacturer produces the product with fixed product rate and its production capacity is limited. (4) The retailers are assumed to be followers in the supply chain. However, they have the right to make decisions on their own retail prices. (5) The manufacturer is responsible for the chain-wide inventory control with the policy of VMI in which the manufacturer provides the product to its multiple retailers with a common replenishment cycle, and thus incurs all inventory related costs in order to eliminate the influence of the variations of the common replenishment cycle and backorder rate of every retailer on its retailers. Each retailer bears some inventory cost by repaying it to the manufacturer, and the cost for each retailer is in direct proportion to its demand rate. The inventory cost per unit is a constant that is previously negotiated by the manufacturer and its retailers.

Notations
Parameters Definition m Total number of retailers i Index of retailers or markets, 1, 2,..., Fraction of backlogging per unit time for retailer i , decision variables for the manufacturer

Game model
This section models the leader-follower relationship between the manufacturer and the retailers as a Stackelberg game with the manufacturer as the leader and retailers as its followers. In this game, the manufacturer maximizes its net profit by giving its optimal wholesale price and inventory control policy for the VMI system. All retailers decide their optimal retail prices to maximize their own net profits.
Here we consider a two-echelon supply chain with a supplier distributing a single product to m separated retailers who in turn sell the product on their own markets. The demand at each retailer is described by a general demand function of the retail price. The demand functions are, almost invariably, downward sloping and a convex function with respect to i p . We have This common demand function can go back to Samuelson (1947), see also Vives (1990) and often be described as Cobb-Douglas demand function as follows: , (2) ( ) 1, 2,..., in which i K and represents the market scale of retailer i and the demand elasticity of retailer i with respect to its retail price respectively. Following the problem description that is a decreasing and convex function in the 2 i p e ( ) i i D p nd point in Subsection 3.1, we have e . 0 i p > It is assumed that the supply chain adopts a VMI strategy where the manufacturer is responsible for the chain-wide inventory control and each retailer pays its inventory cost again to the manufacturer in proportion to its demand rate and thus the inventory cost per unit that is a constant i D i ζ negotiated by the manufacturer and its retailers. Retailer i 's inventory cost then is Therefore, the net profit for retailer i is given as Equation (3): Consider the transfer payment from a retailer to the manufacturer in our model. According to the 5 th point of the problem description in Subsection 3.1, the payment consists of two components; a wholesale price and an inventory charge p c i ζ . The reason is that a) any VMI system, of course including our VMI setting, is established under the setting that the manufacturer and its retailers have the long time cooperation of inventory control. In this case, it is not acceptable for a retailer to buy its product from the manufacturer at a higher price than that of the other retailers. The manufacturer must sell the same product at the same price to its retailers. So the first component, the wholesale price, as the manufacturer's decision variable, occurs. b) The second component i ζ occurs in our manuscript is also necessary since each retailer may have differences each other, such as inventory holding cost, ordering cost and demand rate, distance etc. So for the manufacturer, it is reasonable to charge different inventory costs from different retailers according to their inventory condition and demand rate.
After the net profit function for individual retailers is established as above, let us consider the net profit function for the manufacturer. Consider the components of the total inventory cost first. Figure 1 shows the inventory levels for all retailers and the manufacturer. As indicated in the 5 th point of the problem description in Subsection 3.1, the inventory cost spent for all retailers consist of two parts, one is paid by all retailers and the other is paid by the manufacturer. According to the given VMI policy, retailer i pays inventory cost by demand rate only, that is ( ) , and the manufacturer pays the rest of the total inventory cost. So what the manufacturer spent is equal to abstracting the inventory cost paid by all retailers from that paid by the whole VMI system. To manage the product inventory in retailer i , VMI system spends on fixed order cost, = on holding cost, and L D on backorder cost per unit time according to Figure 1. Thus the inventory cost for the manufacturer managing all retailers' product inventory is given by Equation [Insert Figure 1 about here] The manufacturer's capacity is limited and produces the product with a fixed production rate. When the sum of all retailers' demand rate is less than the production rate, it means that capacity is redundant and the production process is not continuous. The setup cost occurs at every beginning of the common replenishment cycle, and 1 x = . Otherwise and the production capacity is used up. The whole production process being continuous without production setup cost . Thus, the manufacturer's total inventory cost at its own side for the product can be expressed by Equation Leader-follower game in VMI system The total indirect cost of the manufacturer is rearranged in Equation (6): .
The direct cost per unit time which consists of manufacturing cost and transport cost is formulated in Equation (7): As the total revenue for the manufacturer is given as We have now obtained the net profit functions for the retailers and the manufacturer in Equations (3) and (8) respectively. Then the lead-follower relationship for the manufacturer and its retailers can be formulated as the Stackelberg game model below: subject to , 1, 2, , .
Here Equations (10) and (11)  The game mechanism: the manufacturer is treated as the leader who first determines the common replenishment cycle, the backorder fraction and wholesale price, etc. The retailers are treated as the followers who take the manufacturer's decision results as the given input parameters in determining the retail prices i p in their markets when they maximize their net profits respectively. The results of the retailers then influence the net profits of the manufacturer. Then the manufacturer adjusts its optimal decisions in order to maximize its net profit. The process continues until the manufacturer can't increase its profit by changing its decision variables, and then the equilibrium, called Stackelberg equilibrium, obtained. That is to say, during this process, as the leader in the game, the manufacturer knows all retailers' reactions and therefore considers them when it maximizes its profit by working out the common replenishment cycle C , the backorder fraction , wholesale price and x . Every retailer takes the manufacturer's results as its input parameters in determining its retail price i p 1, 2, , i m = … .

Analysis of the Stackelberg equilibrium
From the game mechanism in the preceding section, in order to determine the Stackelberg equilibrium, we first solve the reaction functions of all retailers in the lower level of the proposed Stackelberg game model, and then give the manufacturer's optimal decisions considering the reaction functions of its retailers.

Let us replace in Equation
with Equation (16), and we obtain Equation (17): Taking the first derivative of Equation (17) If 0 1, , the optimal solution is at .
This is impractical. Therefore, we must ignore the situation where 0 < ≤ 1. Let us focus on the situation where >1 by setting Equation From Equation (19), it can be seen that retail i 's price is determined by its price elasticity , wholesale This indicates that Equation (15) is satisfied naturally for a retailer to maximize its net profit. By substituting (19) into (17) Leader-follower game in VMI system

The manufacturer's decisions
The manufacturer determines the optimal common replenishment cycle C for the VMI system, wholesale price , and the backorder fraction etc. to maximize its own net profit subject to the constraints imposed by Equations subject to: (10)- (13) and (19). Since x is a binary variable, so the Stackelberg game model can be discussed with 1 x = and 0 x = separately. Firstly we analyse the model with 1 x = from Equations (23) to (29) below. When 1 x = , because the second derivative of (22) with respect to Thus, is a concave function of for any other given and Set the first derivative of (22) with respect to equal to zero, then can be obtained as It can be seen that is in the feasible area of the manufacturer's model. And is the optimal solution of the manufacturer.
The second derivative of (25) with respect to C is (26) ( , ) m NP C c is a concave function of C for any given . p c Thus, from , the optimal value of is obtained as In the radical sign of Equation (27) This is similar to that of the EOQ model in terms of overall demand rate and relevant cost components; The optimal increases when , Equation (28) is a continuous function of variable cp. Since the capacity of the manufacturer is enough ( 1 x = ) and the maximal of (28) does exist, the optimal cp to maximize (28) is to satisfy Let us denote the solution of Equation (29) that maximizes Equation (28) as .
* p c From the analysis from Equation (23) to (29), all optimal variables are determined with 1 x = . Now we discuss the optimal results with . 0 x =

When
, Equations 0 x = (10) and (11) The only solution is denoted by here. Through the similar analysis we can obtain optimal which is the same as Equation which is similar to Equation (27) From the above analysis, we can obtain the algorithm steps to calculate the equilibrium of the Stackelberg game as the following section.
The base example shows that retailer 1's market is worse than retailer 2', but better than retailer 3'. By applying the above solution procedure in Section 6, the corresponding results for the base example and sensitivity analysis with some selected parameters are shown in 1. The market related parameters have significant influence on the manufacturer' and all retailers' profits. For example, when increases from 1.4 in the base example to 1.5, the manufacturer's and retailer 1's profits go down from 68255 to 60090 and 66808 to 31728, decreased by 11.96% and 52.51% respectively. However 1 p e retailer 2's and 3's profits remain relatively stable, going up slightly from 181391 to 182806 and 23490 to 23796, increased by 0.78% and 1.3% respectively. It can be seen that retailer 1's related parameters have a significant influence on its own profit, and then on its vendor's/the manufacturer's profit. The other retailers' profit is not much influenced. 2. Retailer 1's parameters not only have impacts its own retail price and the manufacturer's wholesale price, but also on the other dispersed retailer's retail prices via the change of the manufacturer's decisions. For example, if increases from in the base example to , retailer 1 changes its retail price from original 2114 to 1924, and the manufacturer decreases its wholesale price from 597.11 to 542.63, deduced by 9.12%, and this reduced wholesale price then makes retailer 2 and retailer 3 have the opportunity to decrease their retail prices, from 2618 to 2382 and 1812 to 1649 respectively. The improvement of the retailer 1's market makes the manufacturer change its market strategy from the strategy of high price with low demand rate to that of low price with high demand rate. The change of the strategy not only lets retailer 1 and the manufacturer enjoy the increased profits, but also lets the other retailers benefit from added profits from the decreased wholesale price from 597 to 543. 1 K 6 2 10 × 6 3 10 × 3. In VMI system, the inventory cost i ζ 1, 2,..., i m = per unit paid by retailer i is decided by the negotiation between retailer i and the manufacturer. At the first glance, the manufacturer would get more profit with the increase of i ζ . Here the result from the example is opposite. When 1, 2,..., i m = 1 ζ increases from 2 to 12, retailer 1 is willing to pay more inventory cost for per unit product, then enhances its retail price from 2102 to 2127, and then its net profit decreases from 66972 to 66644. In order to cope with this kind of change, the manufacturer takes the measure f reducing the wholesale price from 598.43 to 595.83, and its profit also decreases from 68263 to 68248. That is to say, an unreasonable value for i ζ 1, 2,..., i m = in VMI system may cause both manufacturer's and retailer i 's profits to drop. This has the important managerial insight that the manufacturer ought to treat i ζ i as market policy carefully to maximize their profits. 1, 2,..., m = 4. The mutual competition or promotion exists among retailers. For example, from the first conclusion, when increases from 1.4 in the base example to 1.5, retailer 1's profit goes down from 66808 to 31728, reduced by 52.51%, but retailer 2's and 3's profits go up from 181391 to 182806 and 23490 to 23796, increased by 0.78% and 1.3% respectively. That is, the mutual competition among retailers occurs at this setting. However, with the improvement of increasing from in the base example to the mutual promotion occurs; since three retailers get added profits, from 66808, 181391 and 23490 to 104073, 186608 and 24627, increased by 55.78%, 2.88% and 4.84% respectively. In the leader-follower game, the manufacturer maximizes its profit considering the retailers' maximizing their own profits. In order to illustrate the validity of the leader-follower game to the manufacturer, with the given parameters for the base example, we assume that the manufacture only negotiate a wholesale price with its retailers at a fixed value. As an illustration, we fix the wholesale price at different levels between 200-1000, calculate the corresponding results, and compare them with that of the base example, as shown in Figure 2. The series denoted by and in Figure 2 represent the manufacturer's net profits corresponding to different fixed wholesale price, the base example respectively. "Decrease" represents the profit reduction and is measured by . From Figure 2, we conclude that: (a) The leader-follower game benefits the manufacture in VMI setting; the deviation of wholesale price from the optimal point 597.11 will bring a loss to the manufacturer. For example, when =200, the decrease of the manufacturer's profit is up to 85%. p c (b) For a given deviation of the wholesale price from 597.11 (the Stackelberg equilibrium), the minus deviation has greater influence on the manufacturer's profit than that of the plus deviation. For example, setting the deviation=200, the manufacturer's profit decreases around 27% at = 397.11, while it decreases only around 2% at = 797.11. p c p c

Conclusion
This paper has discussed a VMI supply chain where a manufacturer and multiple retailers play a game with each other under the partial cooperation in the inventory control with VMI policies in order to determine mutually optimal product marketing (retail price and wholesale price) and inventory policies by maximizing their individual net profit. The retailers determine the optimal local retail prices and the manufacturer gives its wholesale price and the product's inventory replenishment in the supply chain level. This supply chain problem is modeled as a Stackelberg game model where the manufacturer is the leader and retailers are followers. An algorithm has been proposed to solve this game model. A numerical study is conducted to understand the Stackelberg equilibrium and significant influence of market related parameters on optimal policies and profits of the manufacturer and its retailers. The result of numerical example also shows that: (a) the competition or promotion still exists among the different retailer's markets via changed wholesale price even if they only sale the product in dispersed and independent product markets; (b) the Stackelberg equilibrium benefits the manufacturer; any deviation of the manufacturer from the equilibrium will bring a loss to the manufacturer. However, this paper has the following limitations which may be extended in further research. The paper does not consider the horizontal competition among different retailers with one retailer's demand is the function of the other retailers' retail prices. Secondly, although the Stackelberg equilibrium benefits the manufacturer's profit, it can not guarantee that the system-wide profit is maximized. Thirdly, only a single product is assumed in the discussion. It is more realistic to include multiple product variants of a single product family. Finally, this paper has focused on a supply chain dominated by a manufacturer. Many supply chains may be dominated by retailers and the manufacturer may be just a follower. This is an interesting scenario for further research.
George Q. Huang received the BEng and Ph.D. degrees in mechanical engineering from Southeast University in China and Cardiff University in the UK in 1983 and 1991, respectively. Dr. Huang joined Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong in 1997 after a few years of researching and teaching at British universities. His main research interests include agent-based collaborative environments for complex engineering and business systems and computational game theory. He has published extensively in these topics, including over 80 journal papers, two monographs entitled Cooperating Expert Systems in Mechanical Design and Internet Applications in Product Design and Manufacturing respectively, and an edited reference book entitled Design for X: Concurrent Engineering Imperatives. Dr. Huang is a Chartered Engineer, and a member of IEE (UK), HKIE, IIE and ASME. He is editor in chief of International Journal of Mass Customization and editor for Asia Pacific of International Journal of Computer Integrated Manufacturing