Abstract: To obtain Nash equilibrium pattern which will lay the foundation for decision making theories on production and operation,the various decision makers'optimal behavior was modeled. A supply chain network dual channel equilibrium problem which consisted of multiple mutual competition manufacturers, distributors and multiple mutual competition retailers with random market demand was studied. Based on variational inequality theory, a supply chain network dual channel equilibrium model with manufacturers　 production capacity constraints and demand market's restricted price ceiling was established. Through logarithmic quadratic proximal prediction-correction method, an algorithm for solving the equilibrium pattern was designed. The impact of production capacity constraints and price ceiling on the network equilibrium pattern was analyzed by combining with a numerical example. The results demonstrated that when the government restricted the price ceiling on competitive markets，the goods of demand market would cause a shortage, which led the manufacturers, the distributors and the retailers-total profit decrease. However, when existed capacity limitation, the goods equilibrium price without price limitation would be higher, and goods shortage of demand market would be more.

Key words: supply chain network, production capacity constraints, price rigidities, Nash equilibrium, variational inequality, dual channel, logarithmic-quadratic proximal prediction-correction method

摘要： 为获得各Nash均衡量以便为网络各成员生产运营决策提供理论依据，刻画了各决策者的最优行为。研究由多个相互竞争制造商、多个相互竞争分销商与面临随机市场需求的多个相互竞争零售商组成的供应链网络双渠道均衡问题。借助变分不等式理论，建立制造商存在生产能力限制以及需求市场中存在限制性价格上限的供应链网络双渠道均衡模型。利用变分不等式的对数二次逼近的预测校正法，设计供应链网络双渠道均衡解的求解算法。结合算例分析生产能力限制和限制性价格上限对网络双渠道均衡的影响。结果表明，当政府对竞争市场实行限制性价格上限时，将造成需求市场中的商品短缺，导致制造商、分销商和零售商的总利润减少；当存在产能限制时，将导致无价格限制的商品均衡价格更高，以及需求市场中商品短缺量更大。

关键词: 供应链网络, 产能约束, 价格干预, Nash均衡, 变分不等式, 双渠道, 对数二次逼近的预测校正法