-
摘要:
就建模层面而言备件相关的现有研究在考虑横向保障时存在一定的不足。本文选取三站点组成的备件供应保障系统作为研究对象，通过引入站点间的备件供应保障关系实现了将站点间备件纵向保障和横向保障的综合考虑。运用定量化的概率值表征站点间的备件需求关系，基于库存平衡理论建立了应得备件数量、初始库存量、可用库存量和备件短缺数之间的关系表达式。在建立单站点库存平衡方程的基础上，又依据三站点间的供应保障关系联立得到了三站点备件延期交货量方程组。对方程组解的情况进行了分析，在确定其解唯一性的基础上基于压缩映射原理给出了方程组的迭代求解方法。对于简单示例进行了计算，验证了模型的正确性和求解方法的有效性。
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
-
图 1 备件和故障件在三站点库存系统中的流动模型
Figure 1. Transportation model of spares and failure items in inventory systems of three stations
-
[1] SHERBROOKE C C.METRIC:A multi-echelon technique for recoverable item control[J].Operations Research, 1968, 16(1):122-141. doi: 10.1287/opre.16.1.122 [2] MUCKSTADT J A.A model for a multi-item, multi-echelon, multi-indenture inventory system[J].Management Science, 1973, 20(4):472-481. doi: 10.1287/mnsc.20.4.472 [3] SHERBROOKE C C.VARI-METRIC:Improved approximations for multi-indenture, multi-echelon availability models[J].Operations Research, 1986, 34(8):311-319. http://citeseerx.ist.psu.edu/showciting?cid=258697 [4] 王乃超, 康锐.基于备件保障概率的多级库存优化模型[J].航空学报, 2009, 30(6):1043-1047. http://www.cnki.com.cn/Article/CJFDTOTAL-HKXB200906015.htmWANG N C, KANG R.Optimization of multi-echelon repairable item inventory systems with fill rate as objective[J].Acta Aeronautica et Astronautica Sinica, 2009, 30(6):1043-1047(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-HKXB200906015.htm [5] 刘任洋, 李庆民, 李华.基于横向转运策略的可修件三级库存优化模型[J].航空学报, 2014, 35(12):3341-3349. http://www.cnki.com.cn/Article/CJFDTOTAL-HKXB201412017.htmLIU R Y, LI Q M, LI H.Optimal model of three-echelon inventory for repairable spare parts with lateral transshipments strategy[J].Acta Aeronautica et Astronautica Sinica, 2014, 35(12):3341-3349(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-HKXB201412017.htm [6] 阮曼智, 彭英武, 李庆民, 等.基于体系保障度的装备备件三级库存方案优化[J].系统工程理论与实践, 2012, 32(7):1623-1630. doi: 10.12011/1000-6788(2012)7-1623RUAN M Z, PENG Y W, LI Q M, et al.Optimization of three-echelon inventory project for equipment spare parts based on system support degree[J].Systems Engineering-Theory & Practice, 2012, 32(7):1623-1630(in Chinese). doi: 10.12011/1000-6788(2012)7-1623 [7] LEE Y H, JUNG J W, JEON Y S.An effective lateral transshipment policy to improve service level in the supply chain[J].International Journal of Production Economics, 2007, 106(1):115-126. doi: 10.1016/j.ijpe.2006.05.007 [8] LEE H L.A multi-echelon inventory model for repairable items with emergency lateral transshipments[J].Management Science, 1987, 33(10):1302-1316. doi: 10.1287/mnsc.33.10.1302 [9] TAGARAS G.Pooling in multi-location periodic inventory distribution systems[J].Omega, 1999, 27(1):39-59. doi: 10.1016/S0305-0483(98)00030-9 [10] GROSS D.Centralized inventory control in multi-location supply systems[M].Stanford:Stanford University Press, 1963:47-84. [11] KUKREJA A, SCHMIDT C P, MILLER D M.Stocking decisions for low-usage items in a multi-location inventory system[J].Management Science, 2001, 47(10):1371-1383. doi: 10.1287/mnsc.47.10.1371.10263 [12] AXSÄTER S.Evaluation of unidirectional lateral transshipments and substitutions in inventory systems[J].European Journal of Operational Research, 2003, 149(2):438-447. doi: 10.1016/S0377-2217(02)00447-2 [13] KUKREJA A, SCHMIDT C P.A model for lumpy demand parts in a multi-location inventory system with transshipments[J].Computers & Operations Research, 2005, 32(8):2059-2075. http://linkinghub.elsevier.com/retrieve/pii/S0305054804000085 [14] WONG H, VAN H G J, CATTRYSSE D, et al.Multi-item spare parts systems with lateral transshipments and waiting time constraints[J].European Journal of Operational Research, 2006, 171(3):1071-1093. doi: 10.1016/j.ejor.2005.01.018 [15] SHERBROOKE C C.Multi-echelon inventory systems with lateral supply[J].Naval Research Logistics, 1992, 39:29-40. doi: 10.1002/(ISSN)1520-6750 [16] TAGARAS G, COHEN M A.Pooling in two-location inventory systems with non-negligible replenishment lead-times[J].Management Science, 1992, 38(8):1067-1083. doi: 10.1287/mnsc.38.8.1067 [17] GRAHOVAC J, CHAKRAVARTY A.Sharing and lateral transshipment of inventory in a supply chain with expensive low demand items[J].Management Science, 2001, 47(4):579-594. doi: 10.1287/mnsc.47.4.579.9826 [18] AXSÄTER S.Modeling emergency lateral transshipments in inventory systems[J].Management Science, 1990, 36(11):1329-1338. doi: 10.1287/mnsc.36.11.1329 [19] TAGARAS G, VLACHOS D.Effectiveness of stock transshipment under various demand distributions and no negligence transshipment times[J].Production and Operational Management, 2002, 11(2):183-198. doi: 10.1007%2F0-387-24977-X_3 [20] OLSSON F.An inventory model with unidirectional lateral transshipments[J].European Journal of Operational Research, 2010, 200(3):725-732. doi: 10.1016/j.ejor.2009.01.024 -
下载:
点击查看大图
计量
- 文章访问数: 722
- HTML全文浏览量: 84
- PDF下载量: 413
- 被引次数: 0
