Abstract: To solve the impact of node enterprise behavior's uncertainty on supply chain system's performance, a stochastic analysis method for node enterprise behavior of supply chain by using Pi-calculus method was proposed. Interactive diagram was used to describe the uncertainty of node enterprise behavior. Through building the mapping relationship between interactive diagram and Pi-calculus, the Pi-calculus formal specification of node enterprise behavior was acquired. With the operational semantic rule of Pi-calculus, the state transition diagram of node enterprise behavior was formed, which was corresponded to a homogeneous Markov chain. The theory of Markov chain was applied to conduct quantitative analysis on randomness of node enterprise behavior. It was found that the relative impact of customer orders operation's success rate in overall supply chain was determined by order processing capability of each node enterprise. The simulation experiments showed that the proposed method could evaluate the node enterprises with maximum impact on supply chain operations, thus guide improvement of supply chain's operational efficiency.

Key words: supply chains, Pi-calculus, node enterprise behavior, stochastic analysis, Markov chain

摘要： 为解决节点企业行为的不确定影响供应链系统性能的问题，提出一种应用Pi-演算对供应链的节点企业行为进行随机分析的方法。利用交互图描述了节点企业行为的不确定性；通过建立交互图与Pi-演算的映射关系得到节点企业行为的Pi-演算形式规约，利用Pi-演算的操作语义规则构造出节点企业行为的状态转移图；将该状态转移图与一个齐次马尔科夫链对应起来；借助马尔科夫链中的相关理论来定量分析节点企业行为的随机性，发现各节点企业订单处理能力的强弱可以决定其对供应链上客户订单操作成功率的相对影响的大小。仿真实验表明，该方法能够评价出对供应链运作影响最大的节点企业，从而可以指导供应链运作效率的改善。

关键词: 供应链, Pi-演算, 节点企业行为, 随机分析, 马尔科夫链