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1. 海军航空工程学院 研究生管理大队, 烟台 264000;
2. 海军航空工程学院 战略导弹工程系, 烟台 264000;
3. 海军航空工程学院 训练部, 烟台 264000

Optimization of carrier-based aircraft repairable spares inventory systems under limited maintenance ability
ZHANG Shuai1, LI Junliang1, LYU Weimin2, TENG Kenan3
1. Graduate Students Brigade, Naval Aeronautical and Astronautical University, Yantai 264000, China;
2. Department of Strategic Missile Engineering, Naval Aeronautical and Astronautical University, Yantai 264000, China;
3. Training Department, Naval Aeronautical and Astronautical University, Yantai 264000, China
Abstract:The repair capability of carrier-based aircraft is constrained by finite repair channels. To make Palm's theorem and Metric theory applicable to the optimal allocation of carrier-base aircraft repairable spares, the modified accommodative models of repair and supply channels under conditions of dedicated channels, general channels and hybrid channels were researched and proposed by making the sum of actual repair time and waiting time under finite repair channels equal to the repair time under infinite repair channels based on the queuing theory. According to the modified accommodative models, the mean and variance models of two indenture spares in repair and supply channels were found. Combined with the application instance, the impact of spares demand rate and the amount of repair channels on the repair time were analyzed. The application effect of the stockpiles programs under the finite repair channels model and infinite repair channels model were compared and analyzed. The applicable conditions of each model were given. And the results show that the modified accommodative models are effective.
Key words: repairable spares     optimal allocation     demand rate     repair channel     carrier-based aircraft

 图 1 备件需求和故障件送修过程Fig. 1 Spare requirement and spares maintenance process
1.2 优化思路

Palm定理假设“无限渠道排队”,舰载机维修是“有限渠道排队”.前者是M/G/∞模型,维修时间相互独立同分布,后者是M/M/c模型,维修时间相互影响.为利用Palm定理,舰载机维修必须符合M/G/∞模型.对比分析两个模型,已知后者中的负指数分布M是前者中一般分布G的特殊形式,问题的关键是将后者中的有限渠道c转换等效于前者中的无限渠道∞.已知M/M/c模型中,在服务强度小于1的情况下,M/M/c模型具有稳定的服务时间,各个故障件逗留时间服从同一均值概率分布,将此逗留时间看作故障件在系统中的平均维修服务时间,相当于具有无限维修渠道,则M/M/c模型可近似于M/G/∞模型.基于排队论,对舰载机有限维修渠道,求取其系统平均排队等待时间Wi,将其与系统平均维修时间Ti加和,得到备件在维修系统中的平均逗留时间Ti,可将Ti等效为备件在舰载机维修渠道中的平均服务时间,从而将M/M/c模型等效为M/G/∞模型.即舰载机维修系统转换为:维修时间服从一般分布,维修渠道无限,平均服务时间为Ti,从而适用Palm定理. 1.3 模型假设

 图 2 专用维修渠道Fig. 2 Special repair channel

M/M/c模型可得专用维修渠道的状态概率:

2.2 通用维修渠道时间修正

 图 3 通用维修渠道Fig. 3 General repair channel

Mj/(Kjμj)<1时,维修渠道服务强度为

2.3 混合维修渠道时间修正

 图 4 混合维修渠道1Fig. 4 Combined repair channel one

mij作为备件项i第2阶段维修渠道的到达率,第2阶段k项备件总的到达率 Mj=mij. 假设第2阶段有Kj个相互独立的维修渠道,每个维修渠道对备件项i的平均服务时间为Tij,服务率μij=1/Tij,对所有备件项的平均服务时间和平均服务率分别为

Mj/(Kjμj)<1时,依据通用维修渠道修正方法,即可得到混合维修渠道的修正结果.

 图 5 混合维修渠道2Fig. 5 Combined repair channel two

SRU供应渠道修正后的均值和方差为

 备件项 需求率/(件·天-1) 基层级平均维修时间/天 隔离率q 维修率r 平均送修时间/天 基地需求率/(件·天-1) 基地平均维修时间/天 单价/万元 安装数/件 站点1 站点2 站点1 站点2 LRU1 1.500 1.500 0.6 0.8 0.60 0.3 100 2 LRU2 1.200 1.300 0.5 0.7 0.75 0.2 120 1 SRU11 0.600 0.600 3.0 0.5 0.6 15 10 0.78 1.0 50 1 SRU12 0.600 0.600 4.0 0.5 0.5 0.90 2.0 50 2 SRU21 0.504 0.546 4.0 0.6 0.5 0.975 2.0 50 1 SRU22 0.336 0.364 4.0 0.4 0.5 0.65 2.0 70 1
4.1 维修时间分析

 站点 方案 LRU1 LRU2 SRU11 SRU12 SRU21 SRU22 基层站点 无限渠道维修时间/天 0.6 0.5 3.0 4.0 4.0 4.0 方案1维修渠道数 2 2 2 3 2 2 站点1时间/天 0.689 3 0.523 1 4.234 9 4.313 7 5.362 0 4.509 1 站点2时间/天 0.689 3 0.527 3 4.234 9 4.313 7 5.698 9 4.610 9 方案2维修渠道数 2 1 2 2 2 2 站点1时间/天 0.689 3 0.862 1 4.234 9 6.250 0 5.362 0 4.509 1 站点2时间/天 0.689 3 0.917 4 4.234 9 6.250 0 5.698 9 4.610 9 方案3维修渠道数 3 2 3 4 3 3 站点1时间/天 0.610 5 0.523 1 3.171 4 4.052 9 4.186 2 4.057 1 站点2时间/天 0.610 5 0.527 3 3.171 4 4.052 9 4.236 1 4.071 9 后方基地 无限渠道维修时间/天 0.3 0.2 1.0 2.0 2.0 2.0 维修渠道数 2 2 3 5 5 4 修正时间/天 0.302 4 0.201 1 1.022 0 2.025 3 2.035 7 2.035 4

 需求率/(件·天-1) 维修渠道数/个 1 2 3 4 5 6 7 0.9 0.729 9 0.512 7 0.500 8 0.500 0 0.500 0 0.50 0.50 1.2 0.862 1 0.523 1 0.501 8 0.500 1 0.500 0 0.50 0.50 1.5 1.052 6 0.537 0 0.503 5 0.500 3 0.500 0 0.50 0.50 2.0 1.666 7 0.569 8 0.508 0 0.500 9 0.500 1 0.50 0.50

 图 6 不同维修渠道数和需求率下的平均维修时间Fig. 6 Comparisons of average repair time with different repair channels and demand rates

 图 7 不同需求率下的平均维修时间Fig. 7 Average repair time in different average demand rates

 方案 LRU1 SRU11 SRU12 LRU2 SRU21 SRU22 可用度/% 费用/万元 基地 站点1 站点2 基地 站点1 站点2 基地 站点1 站点2 基地 站点1 站点2 基地 站点1 站点2 基地 站点1 站点2 0 0 6 4 0 5 4 0 7 5 0 5 4 0 6 5 0 3 3 80.73 4 100 1 0 6 4 0 6 5 0 7 5 0 5 4 0 6 6 0 3 3 80.19 4 250 2 0 6 4 0 6 5 0 8 6 0 5 4 0 6 6 0 4 3 80.35 4 420 3 0 6 4 0 5 4 0 7 5 0 5 4 0 6 5 0 3 3 80.27 4 100

 度量标准 无限维修渠道 方案1 方案2 方案3 期望短缺数/件 8.172 9 9.421 0 10.550 0 8.380 2 可用度/% 80.73 78.02 75.61 80.27

 方案 LRU1 SRU11 SRU12 LRU2 SRU21 SRU22 可用度/% 费用/万元 基地 站点1 站点2 基地 站点1 站点2 基地 站点1 站点2 基地 站点1 站点2 基地 站点1 站点2 基地 站点1 站点2 0 0 7 5 0 6 5 0 7 6 0 7 6 0 6 5 0 4 3 91.02 5 000 1 0 7 5 0 6 5 0 7 6 0 7 5 0 7 6 0 4 3 89.16 4 980 2 0 7 5 0 6 5 0 8 7 0 6 5 0 7 6 0 4 3 87.08 4 960 3 0 7 5 0 6 5 0 7 6 0 7 6 0 6 5 0 4 3 90.73 5 000

 度量标准 无限维修渠道 方案1 方案2 方案3 期望短缺数/件 3.693 3 4.457 2 5.356 7 3.818 9 可用度/% 0.910 2 0.892 2 0.875 0 0.907 3
5 结 论

1) 有限维修条件下,维修能力较低,运用“无限渠道”多级备件配置模型,效果较差,通过对有限维修渠道模型进行适用性修正,提高了备件配置效果,满足任务需求.

2) 随着维修能力的增加,故障件维修时间趋于“无限渠道”维修时间,在维修能力较高时,可以近似运用“无限渠道”多级备件配置模型.

3) 备件需求率和维修渠道数是影响维修能力的两个重要因素,各备件项维修渠道数保持结构相对稳定和备件购置费用充足时,运用无限渠道模型配置库存能取得较好效果.

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#### 文章信息

ZHANG Shuai, LI Junliang, LYU Weimin, TENG Kenan

Optimization of carrier-based aircraft repairable spares inventory systems under limited maintenance ability

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(6): 1034-1041.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0393