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

Abstract

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.

南水北調東線工程是多水源、 多目標和多工程的大型跨流域調水工程 ， 該工程主要是為了中國北方地區缺水問題而通過調水、 蓄水和供水從而達到水資源合理配置。 目前 ， 該工程即將完工 ， 面臨著優化運營管理問題。 基於工程實際 ， 本文構建了南水北調東線水資源供應鏈系統 ， 進而分別建立了分散決策下的斯塔克爾伯格博弈模型、 非對稱討價還價模型及帶有談判破裂風險和貼現的非對稱討價還價模型 ， 並進行了相應的數值分析 ， 從而得出一些管理啟示和策略。 研究表明 ： （1） 非對稱納什討價還價通過非合作方式 ， 提供了一種更為有效的南水北調供應鏈合作運營機制 ； （2） 參與主體的利潤份額與討價還價能力正相關 ， 最优的批發價和供應商的利潤份額隨著討價還價能力的增加而增加 ； （3） 由於貼現因數和談判破裂風險的存在 ， 談判雙方會相互做出讓步來達到一個穩定的批發價及利潤配置方案 ， 這對於南水北調供應鏈的談判雙方來說都是有益的 ； （4） 隨著談判破裂概率的增加 ， 最優的批發價隨之增加 ， 供應商的最優利潤隨之增加 ， 而外部分銷商的利潤隨之減少。

(*聯絡人： [email protected])

Keywords:

• Stackelberg game
• asymmetric Nash bargaining model
• south-to-north water diversion
• cooperative operations

Keywords:

• 關鍵詞 ： 斯塔克爾伯格博弈;非對納什稱討價還價模型; 南水北調; 合作運營

Acknowledgements

This research is supported in part by: (1) the National Social Science Foundation of China under Grant 10AJY005; (2) the National Natural Science Foundation of China (NSFC) under Grant 50979024, 90924027 and 41101509; (3) the Fund for 2009 Graduate Students research and innovation projects of Jiangsu Province under Grant CX09B_057R; (4) the Fundamental Research Funds for Outstanding Scholars of Hohai University, the International Academic Cooperation Team Development Foundation of Business School, Hohai University. The authors are grateful for the helpful comments and constructive suggestions made by the Editors and two anonymous referees.

Notes

(*聯絡人： [email protected])