Abstract:

The production capacity sharing problem was studied in this paper. Considering that the game is composed of a capacity provider and customers, in which the capacity provider and customers are self-interest, with different demands and different market relations. Nash bargaining theory was adopted to explore the sharing strategy of the production capacity. To be specific, the classic scheduling model and the asymmetric Nash bargaining model were combined to develop a production capacity sharing model, which was essentially a nonlinear integer program. To address the computational issue, a solving method based on Lagrangian relaxation was designed, and then, the bargaining results of production capacity sharing were given. Simulation analysis shows that the proposed algorithm performs well in most cases. It is found that when the capacity provider has a min-sum objective function, the capacity provider pays attention to the performance indicators of all customers, and the conflict between the capacity provider and customers are particularly significant. With the increase of bargaining power of the capacity provider, the capacity provider index is optimized, but the customer performance index becomes worse. However, when the bargaining power of the capacity provider is very strong, it will lead to the fluctuation of the overall efficiency of the system. Therefore, the game parties need to maintain a reasonable bargaining power.

Key words: production capacity sharing, single machine scheduling, asymmetric Nash bargaining, Lagrangian relaxation