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1. 海军工程大学 舰船动力工程军队重点实验室, 武汉 430033;2. 海军工程大学 动力工程学院, 武汉 430033

Warship spare parts allotment optimization method under mixed-constraints
CAI Zhiming1,2 , JIN Jiashan1,2 , CHEN Yanqiao1,2
1. Military Key Laboratory for Naval Ship Power Engineering, Naval University of Engineering, Wuhan 430033, China;
2. College of Power Engineering, Naval University of Engineering, Wuhan 430033, China
Abstract: The quantitative or qualitative constraints of the warship spare parts allotment optimization problems are mainly focused on by the group of international and domestic academics, the mixed problems which include all of them are relatively less in the previous papers. Firstly, the warship carrying spare parts at the mission preparation before sailing was taken as a research background, the warship support cost, warehouse space, carrying ability and maintainability were adopted as mixed-constraints conditions, an optimized model of the warship spare support probability was built, the method of scoring by experts, normalization and marginal algorithm were applied to build the warship spare parts allotment optimization model and process optimization. Secondly, the model algorithms and system resource constrained factors were being confirmed and dynamically updated. Finally, in the given example, the calculated result was analyzed, and the feasibility of the proposed method was verified.
Key words: mixed-constraints     spare parts     spares support probability     allotment optimization     comparison matrix     marginal effect method

1 单舰海上备件保障模式分析

 图 1 海上执行任务期间单舰备件保障模式 Fig. 1 Spares support mode for single warship on sea during mission
2 模型建立过程

2.1 目标函数

2.2 约束条件

2.3 模型建立

3 模型求解及算法优化 3.1 模型求解

3.2 算法优化 3.2.1 系统资源约束因子的确定及动态调整

wi为例进行说明.

 等级 不重要 一般 重要 关键 评分 (0,4) [4,6) ［6,8) ［8,10)

 备件名称 LRU1 LRU2 … LRUm SRU1 SRU2 … SRUn 分值 w1 w2 … wm w(m+1) w(m+2) … w(m+n)

 因子 λm λv λc λw 权重 wλm wλv wλc wλw

 备件名称 LRU1 LRU2 … LRUm SRU1 SRU2 … SRUn LRU1 w1/w1 w1/w2 … w1/wm w1/w(m+1) w1/w(m+2) … w1/w(m+n) LRU2 w2/w1 w2/w2 … w2/wm w2/w(m+1) w2/w(m+2) … w2/w(m+n)    …    …  LRUm wm/w1 wm/w2 … wm/wm wm/w(m+1) wm/w(m+2) … wm/w(m+n) SRU1 w(m+1)/w1 w(m+1)/w2 … w(m+1)/wm w(m+1)/w(m+1) w(m+1)/w(m+2) … w(m+1)/w(m+n) SRU2 w(m+2)/w1 w(m+2)/w2 … w(m+2)/wm w(m+2)/w(m+1) w(m+2)/w(m+2) … w(m+2)/w(m+n)    …    …  SRUn w(m+n)/w1 w(m+n)/w2 … w(m+n)/wm w(m+n)/w(m+1) w(m+n)/w(m+2) … w(m+n)/w(m+n)

A称为约束条件判断矩阵,显然wii=1,wij=1/wji.

 阶数 1 2 3 4 5 6 7 8 RI 0 0 0.58 0.9 1.12 1.24 1.32 1.41 阶数 9 10 11 12 13 14 15 RI 1.45 1.49 1.52 1.54 1.56 1.58 1.59

3.2.2 算法优化步骤

wi为例进行说明.

 专家 E1 E2 … Ex 权重系数 wE1 wE2 … wEx

4 案例分析

 备件名称 单机数量 备件属性 MTBF/a T0/a ti/a Ci/万元 Mi/kg Vi/m3 Wi/h LRU1 1 0.0513 0.4452 0.0836 1.4 19.6 0.49 4.7 LRU2 1 0.0795 0.5019 0.1073 2.1 27.3 0.82 4.3 LRU3 1 0.0878 0.3936 0.0994 1.5 21.4 0.64 3.8 LRU4 2 0.0613 0.4871 0.0552 1.8 23.8 0.75 4.5 SRU11 2 0.1374 0.3982 0.0976 0.5 1.47 0.14 2.6 SRU12 1 0.0927 0.4175 0.0665 0.4 2.31 0.22 1.9 SRU21 2 0.1219 0.4328 0.0811 0.9 1.88 0.38 2.4 SRU31 1 0.1573 0.3264 0.0817 0.4 1.59 0.17 0.9 SRU32 1 0.1781 0.2994 0.0907 0.6 2.37 0.15 0.7 SRU33 2 0.1292 0.3144 0.0786 0.3 2.61 0.11 1.1

 专家编号 专家打分 LRU1 LRU2 LRU3 LRU4 SRU11 SRU12 SRU21 SRU31 SRU32 SRU33 权重 1 4.7 4.3 3.8 4.5 2.6 1.9 2.4 0.9 0.7 1.1 0.3 2 4.8 4.5 3.6 4.7 2.6 2.0 2.1 0.7 0.7 0.9 0.25 3 4.8 4.4 3.9 4.7 2.7 2.1 2.2 0.8 0.6 1.2 0.25 4 4.9 4.4 3.7 4.8 2.5 1.8 2.0 0.8 0.8 1.1 0.1 5 4.6 4.2 3.8 4.3 2.7 1.9 2.5 0.9 0.8 1.0 0.1

 备件名称 相对值 C′ M′ V′ W′ Z′ LRU1 0.1414 0.1879 0.1266 0.1768 0.1582 LRU2 0.2121 0.2617 0.2119 0.1626 0.2121 LRU3 0.1515 0.2051 0.1654 0.1398 0.1655 LRU4 0.1818 0.2281 0.1938 0.1713 0.1938 SRU11 0.0505 0.0141 0.0362 0.0975 0.0496 SRU12 0.0404 0.0221 0.0568 0.0730 0.0481 SRU21 0.0909 0.0180 0.0982 0.0834 0.0726 SRU31 0.0404 0.0152 0.0439 0.0303 0.0325 SRU32 0.0606 0.0227 0.0388 0.0258 0.0370 SRU33 0.0303 0.0250 0.0284 0.0395 0.0308 注:C′,M′,V′,W′,Z′—备件费用、备件质量、备件体积、维修工时及系统资源约束因子的相对值.

 备件名称 备件携带量 方案1 方案2 方案3 方案4 方案5 LRU1 2 1 2 2 1 LRU2 1 1 1 1 1 LRU3 1 1 1 1 1 LRU4 3 3 3 3 3 SRU11 3 4 4 3 3 SRU12 2 2 1 1 1 SRU21 2 4 2 3 3 SRU31 1 1 1 1 1 SRU32 1 1 1 1 1 SRU33 3 3 3 3 3

 备件方案 备案方案结果 C/万元 M/kg V/m3 W/h 是否可行？(N/Y) 保障概率/% 方案1 17.8 183.88 6.96 52.3 N 93.08 方案2 18.7 169.51 7.37 55.0 N 88.39 方案3 17.9 183.04 6.88 53.0 N 93.05 方案4 18.3 183.45 7.12 52.8 N 93.77 方案5 16.9 163.85 6.63 48.1 Y 91.97 注:C,M,V,W—备件费用、备件质量、备件体积及维修工时的实际值.

1) 只考虑单个约束条件而不考虑其余约束条件的方案1~方案4都不满足要求,这从另一个方面验证了研究混合约束下编队备件配件优化的重要性、必要性.

2) 依据系统资源约束因子运用边际效应法求得备件最优配置方案,各项约束条件都满足给定指标要求且系统备件保障概率不是最小,从另外一个角度证明了本文方法的可行性.

 图 2 费用约束下的最优保障概率曲线 Fig. 2 Optimal curve of support probability under cost constraints

 图 3 质量约束下的最优保障概率曲线 Fig. 3 Optimal curve of support probability under mass constraints

 图 4 体积约束下的最优保障概率曲线 Fig. 4 Optimal curve of support probability under volume constraints

 图 5 维修能力每小时约束下的最优保障概率曲线 Fig. 5 Optimal curve of support probability under maintenance per hour constraints

 图 6 混合约束下的最优保障概率曲线 Fig. 6 Optimal curve of support probability under mix-constraints

1) 随船备件配置方案不仅受备件种类和数量的影响,同时受其各种指标条件约束.依据不同约束条件,运用边际效应法计算得到不同优化曲线.

2) 依据备件保障概率变化曲线,能够为决策者制定决策及设定各个指标范围提供依据.例如,以图 2为例,当编队备件保障概率达到87.01%时,备件总费用为14.2万元,因此,设定的费用约束必须满足C≥14.2万元,若给定的费用小于14.2万元时,必须相应降低备件保障概率指标ps来满足费用约束要求.

3) 备件保障概率关系曲线上的各个离散点是既定约束条件下的最优备件保障概率,且等同于该保障概率条件下最低指标值.

5 结 论

1) 算法可以为解决多个定量约束和多个定性约束的混合问题提供借鉴.

2) 算法可以在满足所有约束条件的前提下,使目标函数最优.

3) 算法不仅适用于海军随船备件配置优化问题,而且对于空军装备、航空航天装备及陆军集群装备等领域同样具有一定的参考价值.

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#### 文章信息

CAI Zhiming, JIN Jiashan, CHEN Yanqiao

Warship spare parts allotment optimization method under mixed-constraints

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(12): 2340-2347.
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0011