中文摘要：

研究了制造商通过分销商实体链和电子商务直销渠道,将其产品经由零售商销售给具有随机需求的消费市场的供应链网络双渠道均衡问题.利用有限维变分不等式理论,分别刻画了存在生产能力限制的供应市场、分销市场、零售市场以及存在限定性价格上限的消费市场的均衡,建立了整个供应链网络双渠道均衡模型,并且设计了供应链网络双渠道均衡的投影收缩算法.数值算例结果表明：当政府对竞争市场实行限制性价格上限时,将造成消费市场中的商品短缺,并导致制造商、分销商以及零售商的总利润减少,当存在产能约束时情况更为严重.

英文摘要：

A dual channel network equilibrium problem is investigated, in which manufacturers＇ products are sold to the consumer market with random demand via the retails by physical transactions of the distributors and directly by electronic transactions. Moreover, the production capacity constraints of the manufacturers and the price ceiling of the consumer market are considered comprehensively. The equilibrium conditions of the supply market, the distributor market, the retailer market and the consumer market are modeled via finite-dimensional variational inequality respectively, and then the dual channel equilibrium pattern of the entire supply chain network is established. The projection and contraction algorithm is designed to solve the dual channel network equilibrium problem. The numerical examples＇ results show that when the government imposes a binding price ceiling on competitive markets, a shortage of the good arises, the total profit of manufacturers and the distributors and the retailers decreases, which is more serious in the existence of production capacity constraints.