由于需求的不确定性及网络的复杂性,使得供应链网络上各企业缺货概率的计算变得非常棘手.将供应链网络模型成Markov过程,利用排队理论提出了供应链网络各企业缺货及因满货而待送货的稳态概率的计算公式；对于较大的供应链网络,提出了将系统分解成2级供应链网络集合求各企业缺货概率的近似方法.这种方法是通过修正各制造商的批量送货间隔时间、各销售商及各零售商的批量销售间隔时间参数,把分解后的子系统与多级供应链网络连接起来,利用子系统求出各企业的缺货和因满货而待送货的稳态概率的近似值.数值试验表明所提出的近似解法具有很高的精度.

As the uncertainty of the demand and the complexity of the supply chain net-work, the calculation of the short supply probability becomes very difficult to nterprises inthe supply chain network. This paper models the supply chain network into Markov process.We provide the formulas for calculating the probabilities of short supply and full inventory by using queuing theory. For the larger system, we propose the approximate method to eval-uate short supply probabilities of enterprises by decomposing the supply chain network into the collection of 2 level supply chain networks. This approximate method connects the sub-systems decomposed and the multi-stage supply chain network by modifing the parameters of each manufacturer’s batch delivery interval, each vendor’s batch delivery interval and each re-tailer’s batch delivery interval, and uses the subsystems to calculate the approximations of the steady-state probabilities of the short supply and the full inventory in enterprises. Numerical experiments illustrate that the proposed approximate method has very high accuracy.