Abstract: To minimize the inventory cost of Assemble to Order (ATO) system,the first step was to obtain the distribution law of its inventory position.Due to the complexity of its structure,the distribution law of inventory position under the (r,nQ) policy of a multi-component and multi-product ATO system was much more complex than that of make-to-stock system.The different distribution laws of inventory position of ATO systems were mainly studied.The stationary distribution of inventory position was proved to be uniform distribution over the total space or some subspace,and the forms of stationary distribution depended on the number of the solutions of a set of linear congruence equations.The influence of different distribution laws on order fill rates and total inventory cost per unit time was indicated through numerical experiments.

Key words: assemble-to-order, inventory position, stationary distribution, common components, linear congruence equations, order fill rate, irreducible Markov process

摘要： 为了对按订单装配系统进行库存优化,获得其库存位值的分布规律是第一步。对于一个多零部件—多产品的按订单装配系统,由于系统结构的复杂性,使得其在(r,nQ)策略下的库存位置分布规律比按库存生产系统要复杂得多。针对以上问题,研究了按订单装配系统库存位置分布规律的不同形式,证明了库存位置的平稳分布是全空间或某个子空间上的均匀分布,而不同平稳分布的形式取决于一组与物料清单及补货批量有关的线性同余方程组的解的个数。最后,通过算例初步揭示了按订单装配系统库存位置的不同分布规律对于订单满足率和单位时间库存总成本这两个关键系统性能指标的影响。

关键词: 按订单装配, 库存位值, 平稳分布, 通用零部件, 线性同余方程组, 订单满足率, 不可约马尔可夫过程