This work extends the two-echelon supply chain models by considering two upstream manufacturers and their common retailer. A different interactive game structure is applied to the duopolistic manufacturers and their responses are discussed. By changing the degree of substitutability of the two products, some numerical results are presented. The supply chain members on the pricing policies and related profits distribution are also analyzed.
As a downstream leader in the supply chain, the retailer profit will be more than the upstream manufacturers. In R-S and C-S models, the retailer predominate supply chain profits across the four cases. The C-S model, by depressing the sales volume and increasing in retail price, makes the upstream manufacturers win back small part benefits from R-S model. By the game theory interactive structure, the downstream leader has the advantage over the upstream followers in our study.
The L-F model is what we applies the leader-follower interactive mechanism in upstream members. The upstream leader demonstrates his advantage over the follower indeed. Even so, the downstream retailer is overwhelming in most of the situations. In our cases, that happens only in the condition of the vendor who supplies something which has large demand in the market. At that time, the upstream manufacturer obtains the largest share in the channel profits.
The M-D model, which is to contrast previous three models, has the common setting with R-S model except in the interactive structure. So the M-D demonstrates the identical retail prices and sale volume with R-S model. However, as the dominant situation changes, the wholesale prices vary to impact the channel profits distribution. The retailer who gets big share in profit, as in the downstream member-led model, is no longer seen in the M-D model.
In addition to developing various interactive models of supply chain members, some cases related to manufacturers and their products are conducted. The manufacturer who makes the product with high demand or less elasticity outperforms competitor in profit percentage.
Among R-S, C-S and M-D models, such a rise in profit percentage mainly comes from the trade-off with his counterpart, with little variation of the share to downstream retailer. The market demand helps the dominant manufacturer to get the biggest profit percentages in L-F model, whose increments are from the other manufacturer and downstream retailer.
The case about manufacturing cost difference shows little variation of the profit share to downstream retailer among R-S, C-S and M-D models, likewise the cost advantage manufacturer deprives the share from his opponent. Cost advantage to dominant manufacturer in L-F model does not reveals to reach top profit share in our numerical result.
Among the downstream firm-led models, consumer surplus and welfare exhibit identical order across cases. Upstream members compete with each other facilitates the great welfare, on the contrary, upstream members act in union lead to the worst welfare.
The power structure of the supply chain has gradually shifted from upstream to downstream member. As the downstream firms are closer to the consumer, their bargaining power on profit is over the supply chain participants. In some cases, it is possible for retailers to price products directly from the voice of consumers, rather than on a wholesale price basis.
Such a situation would impact deeply on the vendors. The manufacturers in upstream have to control the production budget wisely and improve their efficiency in order to maintain the position in the supply chain. That is totally different from the past of their roles in supply chain.
However, it contributes to the allocation of resources and benefits the society according to the previous analysis. Besides, most of the downstream retailers favor multi-vendors instead of
single-vendor to avoid the risk of shortage. In our models settings, the similarity of goods that produced by upstream manufacturers will influence on the supply chain members’ decision.
Our work should not be narrowed to the retailer industry only. Instead, it provides sufficient interpretation for why upstream manufacturers in a supply chain struggle in cost-down world nowadays. Pressed by patent fees and endless consumer calls for lower prices and higher quality, the personal computer industries, or even the supply industries such as motherboards and DRAM manufacturers, suffer from the decreasing marginal profits. The downstream structure of personal computer manufacturing determines the tragic fate of the producers, regardless of whether they are American, Japanese, Korean, or Taiwanese (Fuller et al., 2003). In the supply chain issues, we cannot ignore the power that comes from the downstream members.
As the story mentioned in the research background, the building of an advantageous retailer supply chain, or a dominant downstream supply chain, is a key factor to Wal-Mart’s success. Fishman (2006) points out that with its enormous bargaining power Wal-Mart forces vendors to meet its low price policy. Wal-Mart provides big sales/purchasing volume to attract suppliers to accept the contract with little profit. Many cases show that businesses have declared bankruptcy after their long-term relationship is over with Wal-Mart (Norman, 2004).
In contrast, the upstream manufacturers should find their way out to cope with the emerging retailer-dominating condition. Reports show that in countries where Wal-Mart failed to establish advantageous bargaining power over manufacturers, such as in Germany and Japan with manufacturer-oriented cultures (Christopherson, 2007; Aoyama, 2007). Fishman (2006) also points out the case that Snapper Inc. to disconnect with Wal-Mart by devoting product differentiation and improving product quality. By our numerical example, such situation is likely to happen. The upstream manufacturer should gather more information from the market
and devote innovation in the product or manufacturing process to improve its weak spot in a supply chain. From our numerical case analysis, if supply chain members can realize what he play the role in the supply chain, no matter in upstream or downstream, he can expect what he may deserve in the overall supply chain benefits.
In this study, we employ game theory to discuss the interactions of the two-echelon supply chain. As to the complicated of the closed-form solutions, numerical examples are applied in our study; however, some of the solutions boundaries are worth further explored. Our work can extend to multi-level supply chain model, but the tedious process of deriving solutions is anticipated. Moreover, the demand curve applied in the supply chain can also be relaxed to specific product category, which would help to understand the upstream and downstream members’ interactions in different industry.
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Appendix A. Analytical Solutions of L-F Model
The analytical solution of L-F model in retail prices are expressed below:
)
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Appendix B. Second-Order Condition of Profit Functions
The second-order conditions of profit functions are shown below. The Hessian matrix, represented in H, reveals that each principal submatrix is negative (or semi-negative) definite such that the concavity of profit functions is guaranteed.
(1) R-S model
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