Abstract: A supply chain involves multiple enterprises. It is often complicated to deal with the relationship between the benefits of member enterprises and the overall benefit of the supply chain. There are even conflicts of interest between the upstream and downstream, resulting in the decline of the overall benefit. Only by optimizing the overall benefit and designing an effective profit distribution mechanism to achieve the coordination of member enterprises, can the supply chain achieve the optimality. The nonparametric method for efficiency evaluation has been widely used in this field. However, the simple optimization of efficiency does not consider the substitutability and reallocation of resources, and ignores the optimization space released by the adjustment of input and output structures. For efficiency decomposition, the compromise or unilateral optimal solution is not in line with enterprises’ goal of maximizing their own interests. Based on the nonparametric modeling method, a general analysis framework is established for the profit optimization of a two-echelon supply chain, considering the impacts of both technical advancement and resource substitutability. How the cooperative game can promote the supply chain to realize the optimality under the centralized case is discussed. The distribution of the optimized overall profit of the supply chain is studied via a profit game of member enterprises. The game relations between member enterprises are established based on their individual profit baselines. It is identified that there may be multiple equilibrium schemes for profit distribution. To obtain an optimal profit combination of member enterprises, a bargaining model is proposed. The pricing of intermediate products to achieve the optimal equilibrium distribution scheme is given. An illustrative example is provided to examine the above analysis on supply chain profits. The profits of the ten supply chains involved as a result of technical efficiency improvement and resource reallocation are compared with their current profit levels. Also, the profit distribution results without bargaining are compared to that with bargaining. It is shown that the proposed model is effective to realize the profit optimization of supply chains and the equilibrium profit distribution to member enterprises with the appropriate pricing of intermediate products. A modeling framework is thus provided for a preliminary quantitative analysis on the improvement of supply chain profits through cooperative games. The proposed model for a two-echelon structure can be extended to multi-echelon or even network structures.

Key words: supply chain; profit; game; Nash equilibrium; pricing