考虑随机生产等待的串行生产系统机会维护建模

doi:10.16183/j.cnki.jsjtu.2020.320

摘要/Abstract

摘要：

为了充分利用由外部因素如原材料不足或需求不足等导致的随机生产等待带来的维护机会,针对多设备串行生产系统,引入质心与引力窗概念,提出一种时间窗与引力窗相结合的机会维护决策优化模型,同时考虑设备强制预防维护引发的内部维护机会和生产等待带来的外部维护机会,以最小化规划期内系统的维护总成本率为目标,获取最优维护策略.算例分析表明,时间窗与引力窗相结合的建模方法在降低维护总成本方面有明显优势,可有效解决生产等待的到达及持续时间的不确定性问题.

关键词: 多设备串行系统, 生产等待, 机会维护, 维护时间窗, 维护引力窗

Abstract:

In order to make full use of the maintenance opportunities brought by stochastic production waits caused by external factors such as shortage of raw materials and insufficient demands, the notions of mass center and gravity windows are introduced and an opportunity maintenance decision-making model combining the time window and the gravity window is proposed for multi-unit serial production systems. Considering both internal maintenance opportunities caused by equipment mandatory maintenance and external maintenance opportunities caused by production waits, the optimal maintenance strategy is obtained by minimizing the total maintenance cost rate of the system in the planning period. The example analysis shows that the combination of the time window and the gravity window has prominent advantages in reducing the total maintenance cost, and can effectively solve the uncertainty of the arrival and duration of production waits.

Key words: multi-unit serial system, production waits, opportunistic maintenance, maintenance time window, maintenance gravity window

中图分类号:

TP16

宁小涵, 周晓军. 考虑随机生产等待的串行生产系统机会维护建模[J]. 上海交通大学学报, 2021, 55(10): 1281-1290.

NING Xiaohan, ZHOU Xiaojun. Opportunistic Maintenance Modeling for Serial Production Systems with Stochastic Production Waits[J]. Journal of Shanghai Jiao Tong University, 2021, 55(10): 1281-1290.

图/表 12

图1

图2

图3

图4

表1

设备参数

i	$C i M$ /元	$C i CM$ /元	$c i pen$ /(元·h^-1)	$c i d$ /(元·h^-1)	$τ i M$ /h	α_i	β_i	θ_i
1	513	628.0	52.3	1748	3.42	3.10	67.00	0.97
2	507	711.0	44.8	1802	3.31	2.90	84.24	0.95
3	535	998.0	37.2	2378	3.00	3.03	107.78	0.98
4	629	1131.2	53.4	2752	3.20	2.88	103.36	0.95
5	908	876.0	51.4	1822	2.89	3.12	78.59	0.98
6	545	884.0	37.2	1804	3.14	3.70	98.26	0.97

表1

表2

图5

图6

表3

不同停机成本的仿真结果

κ	$T wi n *$ /h	F^*/kN	c $' 0 sys$ /(元·h^-1)	c $' 1 sys$ /(元·h^-1)	c $' 2 sys$ /(元·h^-1)	ϕ/%
0.10	60	2.9	318.71527	281.8392	274.4371	16.72
0.20	80	4.0	411.60728	361.1766	346.2340	22.86
0.40	90	3.7	506.00181	437.2519	412.4909	26.48
0.50	100	3.9	562.58874	490.8783	462.2401	28.54
0.80	90	4.2	656.73353	586.2013	524.3467	46.72
1.00	80	4.9	727.86663	668.7855	583.4952	59.08
1.25	140	4.5	783.24224	723.1189	624.9857	62.01
2.00	180	4.0	985.13845	913.2768	741.1534	70.55
2.50	210	7.2	1057.89010	989.7344	813.1143	72.16
5.00	240	5.9	1572.10250	1509.0660	1159.1510	84.74
10.00	340	5.4	2433.61210	2400.6480	2192.5110	86.33
25.00	470	6.2	4006.10830	3993.2380	3897.1900	88.18
50.00	560	13.0	6785.66750	6780.4334	6667.2504	95.58

表3

图7

图8

表4

不同生产等待到达频率的仿真结果

λ/(次·h^-1)	T^win*/h	F^*/kN	c $' 0 sys$ /(元·h^-1)	c $' 1 sys$ /(元·h^-1)	c $' 2 sys$ /(元·h^-1)	ϕ/%
1/40	80	1.6	838.8713	726.1197	656.9259	38.03
1/30	70	1.4	779.4774	689.2100	607.4620	47.52
1/25	60	1.9	755.5036	681.5043	585.6525	56.43
1/20	80	4.9	727.8666	668.7855	583.4952	59.08
1/15	180	5.1	703.8952	642.5038	536.2920	63.37
1/10	220	5.3	646.6898	612.3003	520.2427	72.80
1/5	180	1.0	609.5262	600.1814	482.0396	92.67

表4

参考文献 16

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i	系统维护活动次数
i	r=1	r=2	r=3	r=4	r=5	r=6	r=7	r=8	r=9
1	1	0	1	0	1	1	0	1	1
2	0	1	0	1	0	1	0	1	1
3	0	1	0	1	0	1	0	1	0
4	0	1	0	1	0	1	0	1	1
5	1	0	1	0	1	1	0	1	1
6	1	0	1	0	1	0	1	1	1
t/h	145.62	160.80	271.41	335.27	426.45	525.55	565.02	718.55	862.85
i	系统维护活动次数
i	r=10	r=11	r=12	r=13	r=14	r=15	r=16	r=17	r=18
1	0	1	0	1	0	1	1	1	0
2	0	1	0	0	1	1	1	0	0
3	1	0	0	1	0	1	0	1	1
4	0	0	1	0	0	1	0	1	0
5	0	1	0	0	1	1	1	1	0
6	0	1	0	0	1	1	1	1	0
t/h	903.84	985.06	1033.36	1065.04	1112.00	1240.07	1346.28	1478.07	1553.55