考虑材料外置时间窗约束的航空复材制造热压成型批调度研究

doi:10.16381/j.cnki.issn1003-207x.2023.1831

Abstract

Abstract:

The scheduling problem is investigated in the autoclave operations of aerospace composite material production. The problem stems from the wide application of composites in military and civilian aircraft， which has led to a prominent contradiction between supply and demand. As a bottleneck process in composites production delays occur frequently in autoclave operations. In this study， the production planning and scheduling of autoclave operations is taken as a research perspective， aiming to provide a timely and efficient scheduling program. The current production and processing characteristics of the autoclave operations are first analyzed， describing in detail the limitations on production and processing imposed by the out-time of the prepreg and the two-dimensional spatial characteristics of the workpiece preforms. It is assumed that the out-time of all job prepregs is known. Based on the above analysis and assumptions， the problem is for mulated under consideration as a two-dimensional single-machine batch scheduling with a release time window， with the objective of minimizing the total jobs delay time of the scheduling scheme. A mixed integer programming （MILP） model is developed and effective inequalities are proposed based on the jobs release time window. For small-scale instances of the considered problem， the MILP model can be solved by commercial solvers such as Gurobi to obtain an exact solution. For solving large-scale instances， a genetic algorithm embedded with a maximum delay jobs neighborhood search strategy is developed based on the concept of maximum time-compatible jobs set. In numerical experiments， the results show that the proposed MILP model outperforms the classical integer programming model in terms of solution efficiency， and the added effective inequalities can improve the solution efficiency of the model by 15% on average. The designed genetic algorithm can solve the large-scale arithmetic and the solving quality is significantly better than the classical genetic algorithm. The results of the case study based on the M plant show that the weekly plan scheduling scheme generated by the MILP model can improve the delay situation by up to 74% over the original scheduling scheme. The total delay time of the algorithm's resultant jobs exhibits an incremental trend with the increase in the percentage of short-release time-window jobs in the jobs.

Key words: aerospace composite manufacturing, hot compression molding process, 2D batch machine scheduling, release time window

CLC Number:

Jingqi Ding, Naiming Xie, Shaoxiang Zheng. Research of Hot Compression Molding Batch Scheduling for Aerospace Composite Manufacturing with Material External Time Window Constraints[J]. Chinese Journal of Management Science, 2024, 32(12): 130-139.

Figures/Tables 15

符号	定义
$N$	工件集合， $N = 1,2, …, N$ ， $n$ 表示工件数量
$B$	批次集合， $B = 1,2, …, B$ ， $b$ 表示批次数量
$w i, h i$	工件 $i$ 的宽度和高度， $i ∈ N$
$p i, d i$	工件 $i$ 的加工时间和预期交付时间， $i ∈ N$
$t i$	工件 $i$ 的释放时间窗， $t i = e s t i, l s t i, i ∈ N$ ， $e s t i$ 和 $l s t i$ 表示工件的最早可开始加工时间和最晚可开始加工时间
决策变量
$u i' i$	0-1变量，若工件 $i$ 和工件 $i'$ 分配到同一个批次则为1，否则为0
$e i i'$	0-1变量，若工件 $i$ 和 $i'$ 都是关键工件，且 $i$ 在 $i'$ 之前进行加工则为1，否则为0
$o i$	0-1变量，如果第 $i$ 个工件旋转90°放置则为1，否则为0
$a i i'$	0-1变量，若第 $i$ 个工件在第 $i'$ 工件的左侧则为1，否则为0
$b i i'$	0-1变量，若第 $i$ 个工件在第 $i'$ 工件的底部则为1，否则为0
$x i$	整数变量，工件 $i$ 左下角横坐标
$y i$	整数变量，工件 $i$ 左下角纵坐标
$f i$	整数变量，工件 $i$ 的实际完工时间

策略	工件尺寸（ $w j$ 和 $h j$ ）	工件释放时间窗时长
1	30%类型1，70%类型2	80%类型A，20%类型B
2	30%类型1，70%类型2	20%类型A，80%类型B
3	70%类型1，30%类型2	80%类型A，20%类型B
4	70%类型1，30%类型2	20%类型A，80%类型B
5	全部满足类型1条件	80%类型A，20%类型B
6	全部满足类型1条件	20%类型A，80%类型B

工件生成策略		MILP1			MILP2			MILP			$R T R T 1$	$R T R T 2$
工件生成策略		Obj	Gap	RT	Obj	Gap	RT	Obj	Gap	RT	$R T R T 1$	$R T R T 2$
20	1	10	0	0.5	10	0	0.06	10	0	0.06	0.12	1.00
	2	10	0	1.29	10	0	0.09	10	0	0.07	0.05	0.78
	3	10	0	0.69	10	0	0.06	10	0	0.05	0.07	0.83
	4	10	0	2.68	10	0	0.89	10	0	1.89	0.71	2.12
	5	10	0	0.97	10	0	0.34	10	0	0.33	0.34	0.97
	6	10	0	7.08	10	0	1.84	10	0	1.53	0.22	0.83
40	1	10	0	8.54	10	0	0.34	10	0	0.25	0.03	0.74
	2	10	0	92.79	10	0	3.28	10	0	1.72	0.02	0.52
	3	10	0	29.68	10	0	11.3	10	0	2.84	0.10	0.25
	4	9	2.61	511.03	8	15.91	340.7	9	6.36	366.72	0.72	1.08
	5	9	0.49	207.49	9	0.37	191.61	9	0.37	189.36	0.91	0.99
	6	10	0	242.63	5	40.3	1191.93	4	35.31	1262.6	5.20	1.06
60	1	10	0	84.19	10	0	1.08	10	0	1.01	0.01	0.94
	2	7	19.66	716.6	10	0	7.89	10	0	5.92	0.01	0.75
	3	8	1.67	501.84	8	1.52	398.19	8	1.11	396.19	0.79	0.99
	4	4	35.33	1395.03	4	37.28	1184.15	5	31.5	1117.44	0.80	0.94
	5	10	0	368.87	10	0	176.46	10	0	80.89	0.22	0.46
	6	3	72.37	1627.99	1	74.7	1725.96	0	68.37	1800.35	1.11	1.04
80	1	9	3.16	537.5	10	0	10.46	10	0	7.45	0.01	0.71
	2	1	63.92	1791.55	9	0.67	417.62	8	2.95	413.12	0.23	0.99
	3	9	0.93	726.02	8	0.31	505.19	8	0.31	398.5	0.55	0.79
	4	0	98.73	1800.62	0	74.43	1800.25	0	69.91	1800.26	1.00	1.00
	5	6	2.93	1434.74	6	11.72	921.54	6	5.57	835.95	0.58	0.91
	6	0	null	1800.25	0	80.05	1800.54	0	71.25	1800.19	1.00	1.00

工件规模	MILP		GA-MTC		$N S G A - M T C$		$g a p G A$	$g a p N S G A$
工件规模	obj	RT	obj	RT	obj	RT	$g a p G A$	$g a p N S G A$
80	114	5400	182.82	272.90	134.33	860.77	0.60	0.18
80	71	5400	104.00	397.70	85.67	945.66	0.46	0.21
80	152	5400	169.18	414.50	137.5	810.42	0.11	-0.10
80	96	5400	122.18	522.11	110.25	845.01	0.27	0.15
80	74	5400	158.82	517.88	98.52	793.97	1.15	0.33
80	80	5400	97.55	211.11	76.25	764.82	0.22	-0.05
80	102	5400	175.09	366.74	131.67	826.55	0.72	0.29
80	90	5400	123.90	423.91	105.25	738.81	0.38	0.17
80	145	5400	135.55	439.46	130	795.12	-0.07	-0.10
80	48	5400	88.64	299.47	63.25	939.26	0.85	0.32
100	149	5400	141.01	396.26	130.21	1674.25	-0.05	-0.13
100	179	5400	152.45	865.89	129.75	1866.68	-0.15	-0.28
100	164	5400	202.55	935.82	151.01	1742.47	0.24	-0.08
100	173	5400	179.00	742.53	151.75	1812.21	0.03	-0.12
100	142	5400	151.00	766.62	112.31	1960.77	0.06	-0.21
120	284	5400	261.91	868.08	242.5	1983.45	-0.08	-0.15
120	215	5400	198.64	987.26	178.75	1886.31	-0.08	-0.17
120	122	5400	142.50	880.35	105.37	1846.79	0.17	-0.14
120	null	5400	144.50	958.11	121.37	2038.80	null	null
120	146	5400	148.55	928.76	124.15	1983.45	0.02	-0.15

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预浸料卷尺寸类型	时间窗长度（小时）
尺寸1：预浸料卷长度:30米	[2, 6]
尺寸2：预浸料卷长度:10米	[16, 24]

Research of Hot Compression Molding Batch Scheduling for Aerospace Composite Manufacturing with Material External Time Window Constraints

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Figures/Tables 15

References 24

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序号	种群规模	交叉概率	变异概率	结果
1	50	0.7	0.05	153
2	50	0.8	0.1	156
3	50	0.9	0.15	150
4	100	0.7	0.1	145
5	100	0.8	0.15	141
6	100	0.9	0.05	142
7	150	0.7	0.15	140
8	150	0.8	0.05	142
9	150	0.9	0.1	138