中文摘要：

针对多个生产商、多个零售商和需求市场组成的多商品流供应链网络，假定生产商和零售商分别在全国市场和区域市场进行产品广告宣传，分析了其对产品随机需求的影响。通过基于随机效用理论的Logit模型刻画消费者的产品选择，运用Nash均衡方法和变分不等式理论得到生产商和零售商之间的竞争均衡模型，进而建立了考虑广告效应的随机需求多商品流供应链网络均衡的变分不等式模型。最后的数值算例验证了模型的合理性，表明广告宣传是把双刃剑：刺激需求增长，但成本增加，需做好二者间的平衡。

英文摘要：

We considered a multi-ommodity flow supply chain network, consisting of multi-manufacturer, multi-retailer and demand market. The influence of advertisement on random demand was analyzed under the assumption that manufacturers and retailers advertised in domestic and regional markets,respectively. The Logit model based on stochastic utility theory was selected to analyze the product choice of consumers. Meanwhile, the competitive equilibrium models of manufacturers and retailers were studied separately by using Nash equilibrium method and variational inequality theory. A variational inequality equilibrium model for the multi-commodity flow supply chain network with stochastic demand and advertisement effect was set up accordingly. The final numerical example revealed the rationality of the model. It showed that advertisement was a double-edged sword.it would prompt between the two sides become very important. the demand, but as a result,increase the cost. Balance