以制造业产能共享为背景, 考虑自利的产能提供方与需求方诉求不一致和市场关系不对等因素, 采用Nash讨价还价理论研究共享产能分配策略。为此, 首先将传统调度模型与非对称Nash讨价还价模型相结合, 构建出本质为非线性整数规划的产能共享模型。继而, 设计了基于拉格朗日松弛的求解算法, 给出了产能共享的讨价还价分配结果。仿真分析表明, 本文方法在大部分情况下能够获得理想的讨价还价结果。当产能提供方目标为min-sum型, 其关注所有客户的自利且异质的时效要求, 其与客户方的冲突尤其显著; 随着其讨价还价能力的增强, 其改善是以牺牲客户时效要求为代价的。然而当其讨价还价能力再继续增加, 反而导致系统整体效益的波动。因此, 博弈各方需要保持合理的讨价还价强度。

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.