Traditional global supply chain models often prioritize profit maximization while neglecting the fair profit distribution among stakeholders and the dynamic challenges of demand uncertainty, leading to cooperative conflicts and inefficiencies. This study bridges this gap by proposing a two-stage stochastic programming framework, which simultaneously addresses demand uncertainty and fair profit distribution. By integrating the Nash bargaining method into the stochastic model, collaborative decision-making that balances fairness and global optimality under uncertain conditions is achieved. To address the computational complexity of large-scale scenario trees, a hybrid strategy combining scenario reduction and Lagrangian relaxation is proposed, which improves the solution efficiency without affecting the accuracy. A real supply chain case study demonstrates the effectiveness of this framework, indicating that fair distribution based on the Nash bargaining method enhances overall performance, stability, and multi-agent coordination in volatile markets. The research results emphasize that fairness based on the Nash bargaining method can enhance multi-agent collaboration in an uncertain environment. This framework provides a practical decision-making tool for the global supply chain, promoting the efficiency and fairness of dynamic markets.
Citation: Zijing Yang, Songsong Liu, Boya Yu. Fair profit distribution in global supply chains under demand uncertainty[J]. Journal of Industrial and Management Optimization, 2026, 22(4): 1789-1823. doi: 10.3934/jimo.2026066
Traditional global supply chain models often prioritize profit maximization while neglecting the fair profit distribution among stakeholders and the dynamic challenges of demand uncertainty, leading to cooperative conflicts and inefficiencies. This study bridges this gap by proposing a two-stage stochastic programming framework, which simultaneously addresses demand uncertainty and fair profit distribution. By integrating the Nash bargaining method into the stochastic model, collaborative decision-making that balances fairness and global optimality under uncertain conditions is achieved. To address the computational complexity of large-scale scenario trees, a hybrid strategy combining scenario reduction and Lagrangian relaxation is proposed, which improves the solution efficiency without affecting the accuracy. A real supply chain case study demonstrates the effectiveness of this framework, indicating that fair distribution based on the Nash bargaining method enhances overall performance, stability, and multi-agent coordination in volatile markets. The research results emphasize that fairness based on the Nash bargaining method can enhance multi-agent collaboration in an uncertain environment. This framework provides a practical decision-making tool for the global supply chain, promoting the efficiency and fairness of dynamic markets.
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Figures(13) / Tables(4)
Zijing Yang, Songsong Liu, Boya Yu. Fair profit distribution in global supply chains under demand uncertainty[J]. Journal of Industrial and Management Optimization, 2026, 22(4): 1789-1823. doi: 10.3934/jimo.2026066
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