面向多中心租赁制造网络的成组维护与团队协同调度策略

doi:10.16183/j.cnki.jsjtu.2022.074

摘要/Abstract

摘要：

随着广域服务型制造模式的广泛应用,承租制造企业规模连续扩大,进而带动维护外包服务的全球多区域化发展.针对出租方提供“产品+服务”中存在的多中心租赁制造服务网络的广域运维调度问题,提出系统层、网络层动态交互的多中心协同维护调度策略.在系统层综合考虑设备维护停机、累积失效损失以及系统组合选取对维护决策的影响,对同一制造租赁系统内的设备进行维护成组优化,得出总维护成本最小的成组维护方案和维护时间窗;在网络层进一步考虑服务路由优化、团队派遣选取和维护响应速度对调度决策的影响,输出最小化总调度成本所对应的各团队最优服务路线.通过算例分析,验证多中心协同维护调度策略在广域运维调度领域的可行性与有效性.

关键词: 预防性维护, 多中心租赁网络, 协同调度, 维护团队路由

Abstract:

With the wide application of the service-oriented manufacturing mode, the scale of leasing manufacturing enterprises continues to expand, which leads to the global multi-regional development of maintenance outsourcing services. To address the multi-location maintenance scheduling problem of multi-center leasehold networks in the provision of “products+services”, this paper proposes a multi-center collaboration maintenance scheduling (MCMS) strategy with the dynamic interaction between the system level and the network level. At the system level, it considers the impact of the maintenance downtime, cumulative failure, and system combination selection on maintenance decisions, then optimizes the maintenance grouping of machines in the same manufacturing system. Based on the proposed optimization model, the group maintenance set and the corresponding maintenance start time can be obtained by minimizing the total maintenance cost. At the network level, it further considers the impact of service routing optimization, team dispatch selection, and maintenance response speed on scheduling decision, and then outputs the optimal service route for each team by minimizing the total scheduling cost. It also verifies the feasibility and cost-effectiveness of the MCMS strategy in the field of multi-location maintenance scheduling problems by analyzing the case study.

Key words: group maintenance, multi-center leasehold network, collaboration sharing, maintenance team routing

中图分类号:

TH17

司国锦, 林泽宇, 郑宇, 夏唐斌, 奚立峰. 面向多中心租赁制造网络的成组维护与团队协同调度策略[J]. 上海交通大学学报, 2023, 57(3): 273-284.

SI Guojin, LIN Zeyu, ZHENG Yu, XIA Tangbin, XI Lifeng. Joint Group Maintenance Scheduling and Team Collaboration Sharing Strategy for Multi-Center Leasehold Manufacturing Network[J]. Journal of Shanghai Jiao Tong University, 2023, 57(3): 273-284.

图/表 14

图1

表1

成组维护决策优化模型的符号及含义

符号类别	符号	含义
集合与索引	M_i	租赁系统i中的设备集合(索引k∈M_i= $1, ? 2, ? …, M i$ )
	N_l	租赁系统集合(索引i, j∈N_l= $1, ? 2, ? …, ? I$ )
	G	成组维护集合(索引g∈G= $1, ? 2, ? …, ? G$ )
模型参数	λ_hk(t)	设备k在第h个维护周期的故障率函数
	c_hk(T_hk)	设备k在第h个维护周期内的成本率函数
	$T P h k$	设备k在第h个维护周期的预知维护作业时长
	P_i	租赁系统i单位时间的维护停机损失
	R	设备运维成本的系数项
	LP_i	租赁系统i的租赁服务期时长
	F_g	各成组维护集合的固定成本
	w_g	维护时间窗的窗宽
	$t E h g, t L h g$	各成组维护集合对应的维护时间窗
	n_hg	各成组维护集合中所需维护的设备数目
	$T h g m a x$	执行各成组维护集合所需的维护时长
决策变量	α_ik_,_g	租赁系统i的设备k在成组维护集g中时为1,否则为0
	τ_ik	租赁系统i的设备k的预知维护作业开始时间
	γ_g	成组维护集g中有待维护的设备时为1,否则为0

表1

表2

团队协同调度优化模型的符号及含义

符号类别	符号	含义
模型参数	C^rv	维护团队v∈V_r的单位时间路由成本
	t_ij	租赁系统i到租赁系统j的路由时间
	D^rv	维护团队v∈V_r的固定派遣成本
	W^rv	维护团队v∈V_r的单位时间的等待成本
	L_i	维护团队v∈V_r的单位时间的延时惩罚成本
	q^rv	维护团队v∈V_r一次派遣的最大可维护的设备数目
决策变量	$x i j r v$	维护团队v∈V_r由租赁系统i前往租赁系统j时为1,否则为0
	$y g r v$	维护团队v∈V_r被派遣以执行成组维护集合g时为1,否则为0
	z_i_,_g	成组维护集合g由系统i中的设备组成时为1,否则为0
	$? g r v$	维护团队v∈V_r执行成组维护集合g的实际开始时点

表2

图2

图3

表3

各租赁设备的可靠性和维护参数

k	i	β_k	η_k	b_hk	a_hk	$C P h k$ /美元	$C C h k$ /美元	$T P h k$ /h	$T C h k$ /h
1	1	3.15	5 600	1.05	0.025	6 500	18 000	20	66
2		1.70	4 900	1.036	0.016	9 000	30 000	25	74
3		2.51	5 500	1.02	0.018	6 000	17 000	14	48
4	2	1.94	4 200	1.015	0.023	3 900	8 800	10	38
5		1.85	6 400	1.03	0.038	4 600	21 000	12	68
6		2.95	5 300	1.025	0.048	3 200	6 800	8	18
7	3	2.57	6 100	1.03	0.038	6 700	28 000	12	68
8		1.83	6 000	1.04	0.036	4 600	22 000	10	22
9		2.97	4 300	1.025	0.048	3 900	7 000	8	19
10	4	1.84	4 200	1.015	0.023	4 300	8 200	10	39
11		1.72	5 500	1.03	0.038	7 600	26 000	12	68
12		1.83	3 800	1.04	0.036	9 800	16 000	10	22
13	5	1.74	4 300	1.036	0.016	9 000	20 000	25	72
14		2.51	5 500	1.02	0.018	6 000	17 000	14	48
15		3.13	4 600	1.018	0.036	7 000	13 000	16	40
16	6	2.93	4 700	1.025	0.048	4 000	6 800	8	18
17		1.83	3 500	1.04	0.036	9 800	16 000	10	22
18		1.84	4 500	1.04	0.018	8 200	21 000	25	74
19	7	2.62	5 000	1.05	0.025	6 000	15 000	20	66
20		2.34	5 300	1.027	0.046	7 000	22 000	22	60
21		2.89	4 200	1.04	0.036	9 800	16 000	10	24
22	8	2.25	5 500	1.03	0.038	9 600	28 000	12	68
23		1.78	3 600	1.04	0.036	9 800	16 000	10	22
24		1.76	5 600	1.036	0.016	8 000	30 000	25	74
25	9	3.29	4 400	1.018	0.036	7 000	13 000	16	40
26		2.51	5 200	1.02	0.018	6 000	17 000	14	48
27		1.84	4 200	1.015	0.023	3 600	8 800	10	38

表3

表4

表5

表6

第1个周期的系统层成组维护决策

序号	i	成组维护集合	n_hg	$T h g m a x$ /h	[ $t E h g$ , $t L h g$ ]
1	1	{1, 3}	2	20	[2 898, 2 922]
2	1	{2}	1	25	[3 167, 3 191]
3	2	{4, 6}	2	10	[3 069, 3 093]
4	2	{5}	1	12	[2 845, 2 869]
5	3	{7}	1	12	[3 261, 3 285]
6	3	{8, 9}	2	10	[2 865, 2 889]
7	4	{10}	1	10	[2 799, 2 823]
8	4	{11, 12}	2	12	[3 253, 3 277]
9	5	{13, 14, 15}	3	25	[3 170, 3 194]
10	6	{16, 17, 18}	3	25	[3 011, 3 035]
11	7	{19, 20, 21}	3	22	[2 912, 2 936]
12	8	{22}	1	12	[2 833, 2 857]
13	8	{23, 24}	2	25	[3 113, 3 137]
14	9	{25}	1	16	[3 069, 3 093]
15	9	{26, 27}	2	14	[2 864, 2 888]
总维护成本 TMC₁=155 017元

表6

表7

图4

表8

图5

图6

参考文献 15

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系统层模型参数设置		网络层模型参数设置
参数	取值	参数	取值
P_i/(元·h^-1)	300	C^rv/(元·h^-1)	200
R/元	6 000	D^rv/元	20 000
F_g/元	4 000	W^rv/(元·h^-1)	200
w_g/h	24	L_i/(元·h^-1)	300
LP_i/h	17 520	q^rv/台	7
		∑V_r(r∈N_c)/个	6

团队序号	出发点	出发时点	组合服务顺序	租赁系统服务路线
1	维护中心r₁	3 011	(3, 14, 10)	r₁→2→9→6→r₁
2	维护中心r₁	3 113	(13, 2, 9)	r₁→8→1→5→r₁
3	维护中心r₂	2 865	(6, 11)	r₂→3→7→r₂
4	维护中心r₂	3 253	(8, 5)	r₂→4→3→r₂
5	维护中心r₃	2 799	(7, 12, 15, 1, 4)	r₃→4→8→9→1→2→r₃
总调度成本TSC₁=237 200 元

h	成组维护集合G	最优服务路线	对应的团队出发点
1	{1, 3}{2}{4, 6}{5}{7}{8, 9}{10}{11, 12}{13, 14, 15} {16, 17, 18}{19, 20, 21}{22}{23, 24}{25}{26, 27}	(2→9→6, 8→1→5, 3→7, 4→3, 4→8→9→1→2)	(1, 2, 3, 2, 1)
2	{1, 3}{2}{4, 6}{5}{7}{8, 9}{10}{11, 12}{13, 14, 15} {16, 17, 18}{19, 20, 21}{22}{23, 24}{25}{26, 27}	(8→3→9, 3→4, 8→9, 6→2, 1→5, 4→1→7→2)	(3, 1, 3, 1, 2, 1)
3	{1, 3}{2}{4, 6}{5}{7}{8, 9}{10}{11, 12}{13, 14}{15} {16, 17}{18}{19, 20, 21}{22}{23}{24}{25}{26}{27}	(3→4→5, 6→2→7, 8→9→4, 1→3→9, 6→1, 9→8→2→8→5)	(2, 1, 2, 1, 1, 2)
4	{1, 3}{2}{4}{5}{6}{7}{8}{9}{10}{11}{12}{13, 14}{15} {16, 17}{18}{19}{20, 21}{22}{23}{24}{25}{26}{27}	(5→4, 3→6→1→3→7, 9→5→9, 2→9→8→3→6, 8→4, 7→1→2)	(2, 3, 3, 1, 2, 3)
5	{1, 3}{2}{4}{5}{6}{7}{8}{9}{10}{11}{12}{13}{14}{15} {16, 17}{18}{19}{20}{21}{22}{23}{24}{25}{26}{27}	(9→6→8, 7→8→2→4→6, 4→5, 8→3→5→3→2→7→1, 9, 1→3→2→9→7)	(3, 1, 2, 1, 3, 3)