﻿ 三站点备件供应保障关系建模与分析<sup>*</sup>
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1. 北京航空航天大学 可靠性与系统工程学院, 北京 100083;
2. 中国航天标准化与产品保证研究院, 北京 100071

Modeling and analysis of spares supply support relations among three stations
ZHANG Ying1, WANG Yun2, XUE Pei1
1. School of Reliability and Systems Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
2. China Academy of Aerospace Standardization and Product, Beijing 100071, China
Received: 2016-09-05; Accepted: 2016-10-14; Published online: 2016-11-14 09:05
Corresponding author. WANG Yun, E-mail:ywang8_09@163.com
Abstract: For modeling, the existing spares-related researches have insufficient consideration of lateral transshipments. In this paper, the authors select a three-site inventory system as the research object, and by introducing spares supply support relationship between sites, longitudinal and lateral transshipments are considered at the same time. The quantitative probability values are used to represent the spares demand relationship between sites, and based on inventory balance theory, a relationship is established between the number of spares due in, the initial inventory, the number of spares on hand and the number of backorders. Based on the single-site inventory balance equations and the demand supply relations between sites, the three-site spare parts backorder equations are given. Then coefficients-matrix of the equations is found reversible and so the equations have only one unique solution. Then according to the principle of contractive mapping theory, an iterative method is used for solving the equations. Finally, an example is calculated to verify the fitness of the model and the validity of the solving method.
Key words: spares     supply support     station     repair turnaround     iteration algorithm

1 分析及建模 1.1 问题描述及假设

 图 1 备件和故障件在三站点库存系统中的流动模型 Fig. 1 Transportation model of spares and failure items in inventory systems of three stations
1.2 模型的建立

 (1)

 (2)

 (3)

 (4)

 (5)

 (6)

 (7)

 (8)

 (9)
2 模型解唯一性判定

，则由a1a2a3的定义可知：

 (10)

 (11)

3 模型的求解与算例分析 3.1 模型的求解

 (12)

 图 2 系统延期交货量迭代方法计算流程 Fig. 2 Calculation process of EBO with iteration method
3.2 算例分析

 图 3 三站点总的EBO随p11变化曲线 Fig. 3 Curve of total EBO within three stations versus p11

4 结论

1) 本文虽然通过弱化保障组织内站点间的层级关系建立了较为通用的备件供应保障关系模型，但是文中结论也是在众多的假设和限定的基础上得来的，因而所得模型也会与实际情况存在一定的出入。

2) 在很多考虑横向保障或横向转运的相关研究中，横向保障往往是在备件缺货时才被考虑。这也就意味着站点的备件需求概率与站点的备件满足率相关，而本文中模型并未考虑这种情况。作者认为，针对这种较为复杂的情况，只要在本文所给模型的基础上，另构造一个备件需求概率或备件满足率的柯西数列，基于本文给出的计算流程建立一个两层迭代算法即可。

3) 尽管本文提出的模型存在一定的应用局限性(在现实中备件供应保障站点的数目往往会远大于3个)，但是文中的研究方法具有很好的扩展性，可以为后续复杂对象的研究提供一定的理论参考。

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文章信息

ZHANG Ying, WANG Yun, XUE Pei

Modeling and analysis of spares supply support relations among three stations

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(8): 1625-1631
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0709