k-out-of-n系统机会维护与库存控制多层级优化策略

doi:10.16183/j.cnki.jsjtu.2022.030

摘要/Abstract

摘要：

面向服务型制造的复杂系统维护外包决策需求,针对k-out-of-n:G系统中冗余设备干涉、停机惩罚高昂和备件库存限制的挑战,提出了机会维护与库存控制多层级优化策略(OMICP).在设备层,构建各独立设备衰退模型,通过最小化维护成本率,贯序输出各设备预防维护周期;在系统层,以各设备维护时点为契机,综合考虑库存水平、关停数量和冗余干涉,制定动态组合机会维护策略;在联合层,基于机会维护决策反馈,建模分析备件订购利润结余,制定实时更新库存控制策略.通过服务商承担外包维护下的多层级交互决策,整合复杂系统维护与库存控制耦合关系,优化维护外包服务总成本.算例分析证明,所提OMICP具有复杂决策可行性和成本优化有效性.

关键词: 维护外包, k-out-of-n:G系统, 机会维护, 库存控制, 多层级优化

Abstract:

For the maintenance outsourcing requirements of complex systems in service-oriented manufacturing, a multi-level optimization policy of opportunistic maintenance and inventory control (OMICP) is proposed by considering the challenges of redundant machine interference, high shutdown penalty, and spare parts inventory limit of k-out-of-n: G system. At the machine layer, the degeneration model of each machine is built. Then, preventive maintenance cycles of each machine are outputted in sequence by minimizing the maintenance cost rate. At the system level, these maintenance time points are taken as opportunities. In addition, a dynamic combination opportunistic maintenance policy is established by comprehensively considering inventory level, shutdown quantity, and redundancy interference. At the joint level, based on the opportunistic maintenance decision feedback, the inventory control policy is updated in real time by modeling and analyzing the profit balance of spare parts ordering. Through this multi-level interactive decision-making under outsourcing maintenance, the coupling relationship between complex system maintenance and inventory control is integrated to optimize the total cost of maintenance outsourcing services. The case study has shown that OMICP has the feasibility of complex decision-making and the effectiveness of cost optimization.

Key words: maintenance outsourcing, k-out-of-n: G system, opportunistic maintenance, inventory control, multi-level optimization

中图分类号:

TH17

曹蕾, 安向昕, 夏唐斌, 郑美妹, 奚立峰. k-out-of-n系统机会维护与库存控制多层级优化策略[J]. 上海交通大学学报, 2023, 57(3): 285-296.

CAO Lei, AN Xiangxin, XIA Tangbin, ZHENG Meimei, XI Lifeng. Multi-Level Optimization Policy of Opportunistic Maintenance and Inventory Control of k-out-of-n System[J]. Journal of Shanghai Jiao Tong University, 2023, 57(3): 285-296.

图/表 12

图1

图2

表1

各台设备的可靠性与维护外包参数

j	β_j	η_j	ε_j	$T P i j$ /h	$T R i j$ /h	$C P i j$ /美元	$C R i j$ /美元	$V S j$ /美元	$V E j$ /美元	δ_j	$C D i j$ /美元	c_d/美元
1	3.1	7 000	1.035	20	66	6 500	18 000	700 000	630 000	0.11	2 400	3 000
2	2.8	6 800	1.042	25	74	7 000	20 000	760 000	660 000	0.15	2 800	3 000
3	3.1	7 200	1.054	20	58	6 400	18 800	700 000	650 000	0.12	2 200	3 000
4	2.9	7 500	1.041	18	68	6 000	16 800	730 000	650 000	0.16	2 800	3 000
5	2.8	6 600	1.036	15	55	6 800	22 900	750 000	670 000	0.12	2 500	3 000

表1

表2

表3

第8个系统层维护周期机会维护决策结果

j	t_ij/h	t₈/h	$T i j *$ /h	T'_ij/h	MPA_j₈/美元	MPR_j₈/美元	MPS_j₈/美元	Ω(j, t₈)
1	14 051	13 662	4 675	4 286	5 923.41	1 168.55	3 724.15	1
2	13 662	13 662	4 471	4 471	—	—	—	1
3	13 860	13 662	4 669	4 471	3 610.42	554.35	3 056.07	1
4	17 429	13 662	4 997	1 230	6 488.41	35 697.68	-29 209.28	0
5	16 304	13 662	3 872	1 230	6 945.97	26 402.82	-19 456.84	0

表3

表4

第8维护周期的优化后机会维护决策结果

j	Ω(j, t₈)	P_j₈/美元	MPS'_j₈/美元	Ω(j, t₈)'	$T 8 P$ /h
1	1	60 000.00	-56 275.85	1	25
2	1	—	—	1	25
3	1	60 000.00	-56 943.93	0	25
4	0	—	—	0	25
5	0	—	—	0	25

表4

表5

第4个联合层周期的库存控制计划

y_s4/件	IP $R y s 4 F$ /美元	IP $R y s 4 H$ /美元	IP $S y s 4$ /美元
0	0	0	0
1	4 000	510	-4 510
2	4 000	1 020	-5 020
3	4 000	1 530	-5 530

表5

表6

表7

图3

图4

图5

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u	t_u/h	v_s_u/件	Ω(j,t_u)					y_w/件
u	t_u/h	v_s_u/件	j=1	j=2	j=3	j=4	j=5	y_w/件
1	4 230	2	0	0	0	1	PM	4
2	4 604	4	0	PM	1	0	0	0
3	4 779	2	PM	0	0	0	0	6
4	8 425	4	0	0	0	1	PM	0
5	9 166	2	0	PM	1	0	0	0
6	9 356	2	PM	0	0	0	0	6
7	12 414	6	0	0	0	1	PM	0
8	13 662	4	1	PM	0	0	0	0
9	13 860	2	0	0	PM	0	0	0
10	16 304	1	0	0	0	0	PM	1
11	17 429	1	0	0	0	PM	0	3
12	18 093	3	0	PM	1	0	0	0
13	18 310	1	PM	0	0	0	0	1
14	20 143	1	0	0	0	0	PM	1
15	22 375	1	0	0	0	PM	0	6
16	22 460	6	0	PM	0	0	0	0
17	22 632	4	1	0	PM	0	0	—

成本/美元	SMP+(S, s) S=3 s=2	OM		IC		Joint Opt		OMICP
成本/美元	SMP+(S, s) S=3 s=2	OM+(S,s) S=2 s=1	OM+(S,s) S=3 s=2	IPM+IC	SMP+IC	2014 RESS 文献[16]	2021 EJOR 文献[15]	OMICP
C_D	80 365	56 920	51 420	79 130	73 430	78 555	79 421	56 480
C_P	163 500	176 700	172 780	159 540	130 800	163 500	163 500	172 780
C_R	128 865	116 220	90 340	132 740	176 050	116 315	123 591	85 780
C_B	63 000	15 000	12 000	5 400	147 000	35 400	37 350	12 000
C_F	100 000	62 400	60 000	38 400	20 400	96 000	10 280	38 400
C_U	166 500	171 000	169 000	170 000	151 500	149 350	157 800	156 000
C_H	157 501	170 932	236 470	214 069	86 292	80 500	149 125	132 673
C_E	21 000	42 000	22 400	17 500	24 500	41 090	6 860	23 800
维护相关成本	355 365	364 840	326 540	376 810	527 280	393 770	403 862	327 040
库存相关成本	445 001	446 332	487 870	439 969	282 692	366 940	324 065	350 873
总成本	880 731	811 172	814 410	816 779	809 972	760 710	727 927	677 913