朱军辉　程春蕊

摘要：研究了直销供应链网络动态均衡模型，分别对制造商、零售商和需求市场的决策者的多期独立决策行为及其相互作用进行了分析，利用变分不等式构建了各层均衡模型以及系统均衡模型，得到了系统达到均衡的条件，给出了具体算例并进行了求解.构建的供应链网络动态均衡模型具有更好的适用性及普遍性，为供应链的各层成员保持供应链的稳定和长期均衡提供决策依据和决策方法.

关键词运筹学；多期决策；变分不等式；均衡模型；直销

中图分类号F224文献标识码A

AbstractA threelevel competitive supply chain network was presented， in which both time and inventory are considered. We analyzed the multiperiod independent decisions of the manufactures， retailers and demand markets as well as the effect of their interaction. Each level's equilibrium model and the whole supply chain network equilibrium model were obtained by variational inequality. The equilibrium conditions of the supply chain network were given. A numerical example was given and solved. The establishment of the supply chain network dynamic equilibrium model has better applicability and universality， which provides the decisionmaking basis and decisionmaking method for the stability and the longterm equilibrium of the supply chain.

Key wordsoperations research； multiperio decisionmaking； variational inequality； equilibrium model； direct marketing

1引言

Anna，Dong，Zhang（2002）首先通过市场均衡的概念，运用变分不等式研究了单一商品流的供应链系统中各层市场成员的个体独立决策行为以及网络成员之间的交互影响，建立了多层供应链网络均衡模型[1]. Anna，Fuminori （2003）给出了电子商务环境下决策者面临多目标决策的供应链网络建模和分析的框架[2].陈兆波、滕春贤、姚锋敏（2008）针对产品的品牌和产地存在的差异性，研究了供应链网络的均衡模型，构建了具有随机需求的多种差异产品的供应链网络均衡模型[3]. Liu，Anna（2012）运用变分不等式刻画多期竞争供应链网络的均衡状态，枸建了有库存的多期供应链网络模型[4].周庆新（2011）建立了有直销单商品流供应链网络均衡模型，导出了有直销单商品流供应链网络达到均衡的条件[5]. 黄斌、朱宏泉（2013）研究了随机需求下有直销多商品流供应链网络均衡模型，导出了供应链网络达到均衡……