Multi-Objective Spare Parts Scheduling Method in Wartime Considering Lateral Transshipment and Emergency Distribution

doi:10.12382/bgxb.2021.0809

Abstract

Abstract:

To deal with the fact that the existing wartime spare parts scheduling model is not flexible enough, ignores the priority sequencing of demand points, only handles a single type of spare parts, and has a low algorithm operation efficiency, a multi-objective spare parts scheduling method in wartime considering lateral transshipment and emergency distribution is proposed. On the basis of the traditional forward scheduling model, lateral transshipment and emergency distribution strategies are added, and a wartime spare parts scheduling model that simultaneously handles multiple types of spare parts is established with the objectives of the smallest number of missing parts and the shortest transportation time. A priority sequencing method for demand points based on the technique for order of preference by similarity to ideal solution (TOPSIS) is formulated, and the multi-objective evolutionary algorithm based on decomposition considering priority sequencing (MOEA/D-PS) is designed to solve the model using the framework of the multi-objective evolutionary algorithm based on decomposition (MOEA/D). The results show that: the scheduling model considering lateral transshipment and emergency distribution has the best support effect; the MOEA/D-PS algorithm can satisfy both the solution quality and the computational efficiency, and the average CPU running time is 62.86% shorter than the non-dominated sorting genetic algorithm II (NSGA-II); in addition, the priority sequencing and the required time limit significantly affect the effectiveness of spare parts supply support.

Key words: wartime spare parts scheduling, lateral transshipment, emergency distribution, priority sequencing, multi-type spare parts, multi-objective optimization

LI Jingfeng, CHEN Yunxiang, XIANG Huachun, GAO Yangjun, ZHAO Jing. Multi-Objective Spare Parts Scheduling Method in Wartime Considering Lateral Transshipment and Emergency Distribution[J]. Acta Armamentarii, 2023, 44(3): 816-830.

Figures/Tables 18

References 20

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参数符号		含义
	I	野战仓库数量，索引为i
	J	场站仓库数量，索引为j
	M	备件类型数量，索引为m
	D_j^m	作战单位j关于备件m的需求量
	S_j^m	野战仓库i关于备件m的库存量
	S_j^m	作战单位j关于备件m的库存量
	$ T_{0 i} $	后方仓库到野战仓库i的运输时间
	$ T_{i j} $	野战仓库i到场站仓库j的运输时间
	$ T_{j^{\prime} j} $	场站仓库j’到场站仓库j的横向转运时间
	$ T_{0 j} $	后方仓库到场站仓库j的紧急配送时间
	$ \delta_{j}^{m} $	场站仓库j关于备件m的要求时限
变量符号		含义
	$ x_{0 i}^{m} $	后方仓库向野战仓库i调度备件m的数量
	$ x_{i j}^{m} $	野战仓库i向场站仓库j调度备件m的数量
	$ x_{j^{\prime} j}^{m} $	场站仓库j’向场站仓库j横向转运备件m的数量
	$ x_{0 j}^{m} $	后方仓库向场站仓库j紧急配送备件m的数量
	$ \alpha_{j^{\prime} j}^{m} $	二元决策变量，场站仓库j’和j之间关于备件m存在横向转运等于1，不存在等于0
	$ \beta_{0 j}^{m} $	二元决策变量，后方仓库和场站仓库j之间关于备件m存在紧急配送等于1，不存在等于0
	LN	调度方案总缺件数
	T	调度方案总运输时间

参数符号		含义
	I	野战仓库数量，索引为i
	J	场站仓库数量，索引为j
	M	备件类型数量，索引为m
	D_j^m	作战单位j关于备件m的需求量
	S_j^m	野战仓库i关于备件m的库存量
	S_j^m	作战单位j关于备件m的库存量
	$ T_{0 i} $	后方仓库到野战仓库i的运输时间
	$ T_{i j} $	野战仓库i到场站仓库j的运输时间
	$ T_{j^{\prime} j} $	场站仓库j’到场站仓库j的横向转运时间
	$ T_{0 j} $	后方仓库到场站仓库j的紧急配送时间
	$ \delta_{j}^{m} $	场站仓库j关于备件m的要求时限
变量符号		含义
	$ x_{0 i}^{m} $	后方仓库向野战仓库i调度备件m的数量
	$ x_{i j}^{m} $	野战仓库i向场站仓库j调度备件m的数量
	$ x_{j^{\prime} j}^{m} $	场站仓库j’向场站仓库j横向转运备件m的数量
	$ x_{0 j}^{m} $	后方仓库向场站仓库j紧急配送备件m的数量
	$ \alpha_{j^{\prime} j}^{m} $	二元决策变量，场站仓库j’和j之间关于备件m存在横向转运等于1，不存在等于0
	$ \beta_{0 j}^{m} $	二元决策变量，后方仓库和场站仓库j之间关于备件m存在紧急配送等于1，不存在等于0
	LN	调度方案总缺件数
	T	调度方案总运输时间

仓库	LRU1	LRU2	LRU3	LRU4	LRU5	LRU6	LRU7	LRU8	LRU9	LRU10
场站1	12/0	8/0	30/4	13/0	8/2	21/8	14/3	38/10	32/21	2/0
场站2	13/0	6/1	42/7	3/1	2/0	8/7	56/13	57/15	10/5	11/10
场站3	15/0	3/3	21/6	14/2	5/1	27/4	21/3	47/6	36/16	2/9
场站4	10/0	7/1	33/10	0/4	4/2	9/8	11/2	23/15	16/11	25/8
场站5	8/0	0/4	12/8	5/0	7/3	18/5	15/3	53/18	39/13	0/10
场站6	5/0	2/0	21/5	0/0	7/0	25/3	37/6	78/5	42/10	20/1
场站7	20/0	1/1	44/4	2/1	8/3	32/10	28/4	94/3	45/22	21/2
场站8	11/0	10/0	30/6	17/3	3/1	34/9	21/6	13/7	27/12	22/3
场站9	17/0	10/0	1/5	14/4	7/3	19/6	50/14	57/8	5/11	2/7
场站10	13/0	5/5	39/0	6/3	7/1	4/6	35/2	47/11	13/5	10/1
场站11	19/0	8/3	42/3	19/2	1/0	5/6	33/7	34/13	55/11	6/7
场站12	5/0	1/3	31/1	0/3	1/0	9/2	55/14	16/2	9/14	20/1
场站13	3/0	4/0	34/2	9/1	5/2	30/3	17/1	18/6	50/15	11/7
场站14	2/0	10/5	34/3	8/4	10/3	9/5	46/15	80/20	32/9	23/5
场站15	11/0	8/3	18/5	16/1	3/2	29/2	45/4	31/0	60/8	4/8
野战1	0/30	0/16	0/64	0/26	0/15	0/78	0/102	0/150	0/69	0/54
野战2	0/50	0/14	0/141	0/44	0/15	0/62	0/86	0/100	0/101	0/33
野战3	0/40	0/20	0/95	0/56	0/22	0/40	0/112	0/200	0/130	0/41
后方	0/∞	0/∞	0/∞	0/∞	0/∞	0/∞	0/∞	0/∞	0/∞	0/∞

仓库	LRU1	LRU2	LRU3	LRU4	LRU5	LRU6	LRU7	LRU8	LRU9	LRU10
场站1	12/0	8/0	30/4	13/0	8/2	21/8	14/3	38/10	32/21	2/0
场站2	13/0	6/1	42/7	3/1	2/0	8/7	56/13	57/15	10/5	11/10
场站3	15/0	3/3	21/6	14/2	5/1	27/4	21/3	47/6	36/16	2/9
场站4	10/0	7/1	33/10	0/4	4/2	9/8	11/2	23/15	16/11	25/8
场站5	8/0	0/4	12/8	5/0	7/3	18/5	15/3	53/18	39/13	0/10
场站6	5/0	2/0	21/5	0/0	7/0	25/3	37/6	78/5	42/10	20/1
场站7	20/0	1/1	44/4	2/1	8/3	32/10	28/4	94/3	45/22	21/2
场站8	11/0	10/0	30/6	17/3	3/1	34/9	21/6	13/7	27/12	22/3
场站9	17/0	10/0	1/5	14/4	7/3	19/6	50/14	57/8	5/11	2/7
场站10	13/0	5/5	39/0	6/3	7/1	4/6	35/2	47/11	13/5	10/1
场站11	19/0	8/3	42/3	19/2	1/0	5/6	33/7	34/13	55/11	6/7
场站12	5/0	1/3	31/1	0/3	1/0	9/2	55/14	16/2	9/14	20/1
场站13	3/0	4/0	34/2	9/1	5/2	30/3	17/1	18/6	50/15	11/7
场站14	2/0	10/5	34/3	8/4	10/3	9/5	46/15	80/20	32/9	23/5
场站15	11/0	8/3	18/5	16/1	3/2	29/2	45/4	31/0	60/8	4/8
野战1	0/30	0/16	0/64	0/26	0/15	0/78	0/102	0/150	0/69	0/54
野战2	0/50	0/14	0/141	0/44	0/15	0/62	0/86	0/100	0/101	0/33
野战3	0/40	0/20	0/95	0/56	0/22	0/40	0/112	0/200	0/130	0/41
后方	0/∞	0/∞	0/∞	0/∞	0/∞	0/∞	0/∞	0/∞	0/∞	0/∞

节点		后方		野战1	野战2		野战3	场站1	场站2	场站3	场站4	场站5	场站6	场站7	场站8	场站9	场站10	场站11	场站12	场站13	场站14	场站15
后方				35	28		30	21	35	47	50	25	12	39	47	46	23	38	18	11	40	30
野战1		35						5	1	5.5	6	4	5	3	6	4	4.5	6	5	4	0.5	1.5
野战2		28						3	3	4.5	6	1.5	4	4.5	5	0.5	5.5	3	0.5	1	3	4.5
野战3		30						7	1	3.5	4	5	0.5	1	2.5	3	2	4	3.5	5.5	6	6.5
场站1		21		5	3		7		2	3	4.5	3	2.5	0.5	1	3	2.5	4	4	2.5	1	3
场站2		35		1	3		1	2		1.5	3	1.5	2	2	3	2	1	2.5	0.5	2	0.5	1.5
节点	后方		野战1			野战2	野战3	场站1	场站2	场站3	场站4	场站5	场站6	场站7	场站8	场站9	场站10	场站11	场站12	场站13	场站14	场站15
场站3	47		5.5			4.5	3.5	3	1.5		1	2.5	3.5	0.5	0.5	3	2	1	3	0.5	1	1
场站4	50		6			6	4	4.5	3	1		3.5	4.5	4	4	1	2	2	3	4	4	1
场站5	25		4			1.5	5	3	1.5	2.5	3.5		0.5	3.5	3	1	1.5	2	4	1	2	1
场站6	12		5			4	0.5	2.5	2	3.5	4.5	0.5		3	5	1	4.5	2	3	2	0.5	4
场站7	39		3			4.5	1	0.5	2	0.5	4	3.5	3		1	4	1.5	3	2	1	0.5	1
场站8	47		6			5	2.5	1	3	0.5	4	3	5	1		3.5	2	2	4	4.5	1	2
场站9	46		4			0.5	3	3	2	3	1	1	1	4	3.5		3	1	2	2	5.5	3
场站10	23		4.5			5.5	2	2.5	1	2	2	1.5	4.5	1.5	2	3		6	2.5	1	2	4
场站11	38		6			3	4	4	2.5	1	2	2	2	3	2	1	6		3	3	4	2
场站12	18		5			0.5	3.5	4	0.5	3	3	4	3	2	4	2	2.5	3		2.5	3	1
场站13	11		4			1	5.5	2.5	2	0.5	4	1	2	1	4.5	2	1	3	2.5		5	2
场站14	40		0.5			3	6	1	0.5	1	4	2	0.5	0.5	1	5.5	2	4	3	5		2
场站15	30		1.5			4.5	6.5	3	1.5	1	1	1	4	1	2	3	4	2	1	2	2