基于三站点库存组织的备件转运策略分析

基于三站点库存组织研究了备件转运策略对于系统期望延期交货量（EBO）的影响。首先，依据三站点库存组织中备件和故障件的消耗与补给过程以及库存控制策略，给出了考虑保障站点供应优先级的手边现货、应得备件数和延期交货量之间的状态方程。其次，通过定义站点延期交货量与应得备件数之间的比例系数，将原非线性方程组转化成线性方程组，然后借助线性方程组解的判定法则对方程组解的唯一性进行判定，并结合不动点原理构造柯西列逼近原方程的解。最后，在算例分析中借助MATLAB对2种转运策略（按固定概率转运和按优先级约束转运）下系统EBO的数值大小进行对比。结果表明：按优先级约束进行备件转运能够在大部分情况下提高备件利用率同时降低系统EBO。此外，通过分析还可以发现，不同备件转运策略对系统EBO作用效果的显著性主要由转运策略的可行作用空间大小决定，而作用空间的可行变化范围主要由备件需求由本地满足的概率、库存配置方案以及需求率和维修速率决定。

Spares transshipment strategy analysis based on a three-site inventory system

In this paper,the effect of variant transshipment strategies on expected backorders (EBO) of a three-site inventory system is researched.Based on the predefined assumptions and inventory control strategy,as well as the consumption and replenishment process of the spares,the state equations of spares on hand,spares due in from repair and resupply,and backorders are presented with the consideration of the supply priority among sites.By defining the ratio between EBO and the number of spares due in,the original nonlinear equations can be transformed into linear equations.Since the coefficient matrix of the linear equations is invertible,it can be said that the linear equations has only one solution.As indicated above,a Cauchy sequence of the number of spares due in is constructed to approach the sole solution.Finally,the numerical values of the EBO under two transshipment strategies (fixed probability transshipment and priority preferred transshipment) are compared.The results show that the strategy of priority preferred transshipment can not only increase the utilization rate of spares but also reduce EBO of the system in most cases.In addition,it can be found that the effect of different transshipment strategies on the EBO mainly depends on the feasible space of transshipment strategies,which is mainly determined by the rate of demands filled by local site,the inventory allocation scheme,and the repairing and demanding rate of each site.