考虑横向转运和紧急配送的战时多目标备件调度方法

doi:10.12382/bgxb.2021.0809

摘要/Abstract

摘要：

针对现有战时备件调度模型灵活性不足，忽略需求点优先度排序，处理备件类型单一，以及算法运行效率不高等问题，提出一种考虑横向转运和紧急配送的战时多目标备件调度方法。在传统正向调度模型基础上加入横向转运和紧急配送策略，以缺件数最少和运输时间最短为目标构建同时处理多类型备件的战时备件调度模型。制定基于逼近理想解排序法的需求点优先度排序方法，利用基于分解的多目标进化算法(MOEA/D)框架设计考虑优先度排序的MOEA/D(MOEA/D-PS)求解模型。案例结果表明：考虑横向转运和紧急配送的调度模型保障效果最优；MOEA/D-PS能够兼顾求解质量和运算效率，CPU运行时间均值比改进的非支配排序遗传算法缩短62.86%；优先度排序和要求时限长短显著影响备件供应保障效果。

关键词: 战时备件调度, 横向转运, 紧急配送, 优先度排序, 多类型备件, 多目标优化

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

李京峰, 陈云翔, 项华春, 高杨军, 赵静. 考虑横向转运和紧急配送的战时多目标备件调度方法[J]. 兵工学报, 2023, 44(3): 816-830.

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.

图/表 18

参考文献 20

[1]	SHERBROOKE C C. Metric:a multi-echelon technique for recoverable item control[J]. Operations Research, 1968, 16(1):122-141. doi: 10.1287/opre.16.1.122 URL
[2]	MUCKSTADT J A. A model for a multi-item, multi-echelon, multi-indenture inventory system[J]. Management Science, 1973, 20(4):472-481. doi: 10.1287/mnsc.20.4.472 URL
[3]	GRAVES S C. A multi-echelon inventory model for a repairable item with one-for-one replenishment[J]. Management Science, 1985, 31(10):1247-1256. doi: 10.1287/mnsc.31.10.1247 URL
[4]	魏国强, 杨永清. 供应不足条件下战时连续消耗资源调度模型[J]. 系统工程与电子技术, 2012, 34(1): 102-106.
	WEI G Q, YANG Y Q. Dispatching model of continuous consumption resources in wartime under insufficient supply[J]. Systems Engineering and Electronics, 2012 34(1): 102-106. (in Chinese)
[5]	王亚东, 石全, 陈材, 等. 考虑中断风险的备件供应选址-分配优化模型[J]. 兵工学报, 2019, 40(8):1708-1715. doi: 10.3969/j.issn.1000-1093.2019.08.021
	WANG Y D, SHI Q, CHEN C, et al. Location-allocation joint optimization model of spare parts supply under supply disruption risk[J]. Acta Armamentarii, 2019, 40(8): 1708-1715. (in Chinese) doi: 10.3969/j.issn.1000-1093.2019.08.021
[6]	王亚东, 石全, 张芳, 等. 基于动态进化算法的多阶段备件供应优化决策[J]. 系统工程与电子技术, 2019, 41(11): 2514-2523.
	WANG Y D, SHI Q, ZHANG F, et al. Multi-stage spare parts supply optimization based on dynamic evolutionary algorithm[J]. Systems Engineering and Electronics, 2019, 41(11): 2514-2523. (in Chinese)
[7]	王亚东, 石全, 尤志锋, 等. 基于交叉效率排序多目标进化算法的备件供应优化[J]. 兵工学报, 2020, 41(11): 2338-2346. doi: 10.3969/j.issn.1000-1093.2020.11.022
	WANG Y D, SHI Q, YOU Z F, et al. Spare parts supply optimization and decision-making based on cross-efficiency multi-objective sorting evolutionary algorithm[J]. Acta Armamentarii, 2020, 41(11):2338-2346. (in Chinese) doi: 10.3969/j.issn.1000-1093.2020.11.022
[8]	FANCELLO G, MANCINI S, PANI C, et al. An emergency vehicles allocation model for major industrial disasters[J]. Transportation Research Procedia, 2017, 25: 1164-1179. doi: 10.1016/j.trpro.2017.05.134 URL
[9]	HU H, HE J, HE X F, et al. Emergency material scheduling optimization model and algorithms: a review[J]. Journal of Traffic and Transportation Engineering-English Edition, 2019, 6(5): 441-454.
[10]	ZHANG J H, LIU H Y, YU G D, et al. A three-stage and multi-objective stochastic programming model to improve the sustainable rescue ability by considering secondary disasters in emergency logistics[J]. Computers & Industrial Engineering, 2019, 135: 1145-1154. doi: 10.1016/j.cie.2019.02.003 URL
[11]	WANG Y S, DONG Z S, HU S L. A stochastic prepositioning model for distribution of disaster supplies considering lateral transshipment[J]. Socio-Economic Planning Sciences, 2021, 74: 100930. doi: 10.1016/j.seps.2020.100930 URL
[12]	TIACCI L, SAETTA S. Reducing the mean supply delay of spare parts using lateral transshipments policies[J]. International Journal of Production Economics, 2011, 133(1):182-191. doi: 10.1016/j.ijpe.2010.03.020 URL
[13]	阮旻智, 刘任洋. 随机需求下多层级备件的横向转运配置优化模型[J]. 系统工程理论与实践, 2016, 36(10):2689-2698. doi: 10.12011/1000-6788(2016)10-2689-10
	RUAN M Z, LIU R Y. Configuration and optimization model for multi-indenture spares with lateral transshipments under stochastic demand[J]. Systems Engineering-Theory & Practice, 2016 36(10): 2689-2698. (in Chinese)
[14]	张颖, 王蕴, 薛佩. 三站点备件供应保障关系建模与分析[J]. 北京航空航天大学学报, 2017, 43(8): 1625-1631.
	ZHANG Y, WANG Y, XUE P. Modeling and analysis of spares supply support relations among three stations[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(8): 1625-1631. (in Chinese)
[15]	王亚东, 石全, 夏伟, 等. 基于超启发式算法的备件供应网络结构优化[J]. 系统工程与电子技术, 2020, 42(3): 620-629.
	WANG Y D, SHI Q, XIA W, et al. Structure optimization of spare parts supply network based on hyper heuristic algorithm[J]. Systems Engineering and Electronics, 2020, 42(3): 620-629. (in Chinese)
[16]	ZHANG Q F, LI H. MOEA/D:a multiobjective evolutionary algorithm based on decomposition[J]. IEEE Transactions on Evolutionary Computation, 2007, 11(6): 712-731. doi: 10.1109/TEVC.2007.892759 URL
[17]	DEB K, KUMAR A. Real-coded genetic algorithms with simulated binary crossover:studies on multimodal and multiobjective problems[J]. Complex Systems, 1995, 9(6): 431-454.
[18]	HWANG C L, YOON K. Multiple attribute decision making[M]. Berlin, Germany:Springer-Verlag, 1981.
[19]	SHIH H S, SHYUR H J, LEE E S. An extension of TOPSIS for group decision making[J]. Mathematical & Computer Modelling, 2007, 45(7/8): 801-813.
[20]	SAATY T L. How to make a decision: the analytic hierarchy process[J]. European Journal of Operational Research, 1990, 48(1): 9-26. doi: 10.1016/0377-2217(90)90057-I URL

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