Asymmetric Nash bargaining model for the eastern route of south-to-north water diversion supply chain cooperative operations

The eastern route of south-to-north water diversion (SNWD) project is a large-scale multi-source, multi-objective and multi-project inter-basin system. Constructed to pump, store and supply water to achieve rational water distribution in North China, the project is close to completion currently, and faced with optimal operations management problems. Based on the project practice, this article develops a supply chain system for the SNWD project, where a Stackelberg game model under decentralized decisions, an asymmetric Nash bargaining model, and an asymmetric Nash bargaining model with risk of breakdown and discount are respectively built, and numerical analysis are carried out for managerial insights. This study suggests that: (i) asymmetric Nash bargaining provides a more efficient mechanism for south-to-north water diversion supply chain to achieve cooperative operations through non-cooperative way; (ii) the Agent's sharing profit earned is positively related to his bargaining power, and the optimal wholesale price and the sharing profit of the supplier increases as the bargaining power increases; (iii) due to the existence of the discount factor and the risk of breakdown, both sides in the bargaining game will make a concession to achieve a stationary solution for asymmetric Nash bargaining problem, which is beneficial for both sides of the SNWD supply chain; (iv) the optimal wholesale price increases as the probability of breakdown in disagreement increases; the supplier's optimal profit increases and the external distributor's optimal profit decreases as the probability of breakdown in disagreement increases.