Pricing, coalition stability, and profit allocation in the pull assembly supply chains under competition

We consider a pull assembly supply chain consisting of an assembler and its multiple upstream component suppliers/subsidiaries, in which the former buys complementary components from these upstream component suppliers, assembles them into a final product, and sells the final product competing against another assembly firm (rival). The assembler decides the retail price competing with its rival and with the upstream component suppliers can freely decide whether or not to cooperate with another, which can eliminate horizontal and vertical inefficiencies within supply chain members. Using a stylized duopoly model, we study the optimal retail prices of the assembler and the optimal wholesale prices of these component suppliers under different alliance structures and analyze the coalition stability and profit allocation scheme via a proper transfer price for the assembly supply chain. We show that when the upstream suppliers are not allowed to form coalitions, the increase in the number of the upstream component suppliers trading with their assembler are a good thing for the two assemblers. In addition, increasing the intensity of price competition in the market induces the two assemblers to decline the retail prices and the upstream subsidiaries to cut down the wholesale prices; however, all the parties’ profits are not necessarily monotonic in this intensity. In environments in which the upstream subsidiaries can freely form coalitions, the above two results remain unchanged. We also find that the cooperation between the assembler and its upstream subsidiaries can always bring more profit and eliminate inefficiencies for the assembly supply chain. Importantly, we show that the constructed cooperative game has a non-empty core and can design a profit allocation scheme for the grand coalition based on the Shapley value. We identify the transfer prices of the assembler to the upstream subsidiaries to realize the profit allocation scheme that is fair and show that increasing the intensity of price competition can reduce the proposed Shapley values of the upstream suppliers and transfer prices.