单个生产商和多个零售商缺货概率的计算法

Solution of Short Supply Probability for One Manufacturer and Several Retailers

由于需求的不确定性,容易造成缺货,如何计算缺货概率却是一个棘手的问题。本文把由单个制造商和多个零售商构成的供应链模型成M arkov过程,利用排队理论分析供应链上各状态间的转移关系,以单个制造商和三个零售商为例澄清状态转移矩阵的内部结构,并对一般模型提出计算缺货和满货概率的计算公式。在此基础上分析了各状态概率对库存总成本的影响,为系统的优化决策提供分析的依据。数值实验表明所提出的方法是行之有效的。

The uncertainty of the demand,results in being out of stock.How to calculate the probability of being out of stock is a difficult issue.This paper models the supply chain.into Markov process;which is composed of a manufacturer and several retailers.It analyzes the transition relationship of all the states of the supply chain by using the queuing theory,and takes one manufacture and three retailers as an example to clarify the internal structure of the matrix which describes the transitions among the states.It also gives the formula for calculating the probability of being out of stock and full of stock in the general model.On the basis of this,the effect of the probability of all the states on the total inventory cost is analyzed.It lays the foundation of analysis for the optimization of the system.Numerical experiments illustrate that the proposed method is effective.