Traditional supply-chain management methods often treated the given system as a whole, without considering the conflicting interests of its participants. Game theory was adopted in a number of prior studies to identify fair prices and throughputs of the intermediates so as to maintain sustainable operations. In particular, the mathematical frameworks of a series of fictitious systems have already been proposed in the literature. The proper designs of distributed processing systems were generated to facilitate implementation of a decentralized optimization strategy. In these supply chains, the supplier-produced intermediates were bought by consumers to manufacture the final products. However, when the total profit of a supply chain is maximized without constraints, the maximum total profit may not be divided and allocated to every actor fairly. This deficiency could lead to various negative impacts, including dissatisfaction of actors, instability of coalition, loss of markets, and reduction in revenue. For this reason, a cooperative game theory has already been applied to generate fair-profit allocation plans among the supplier(s) and consumer(s) so as to establish a long-term working relationship. The present work developed a two-step approach addresses this issue. Finding the maximum total profit of the whole chain is the primary task of the first step, while the Nash cooperative bargaining approach is adopted in the second step so as to distribute the total profit among the actors fairly. Consequently, the corresponding intermediate prices and throughputs can also be estimated as well. Various case studies in fictitious systems and the petroleum supply chain are provided as examples to demonstrate the feasibility of the proposed approach. It can be observed from the optimization results of various case studies in fictitious systems and the petroleum supply chain that the goal to get the fair profit allocation plans can be achieved while still maintaining the maximum total profit of the whole chain.

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