考虑自动引导车运输的分布式柔性作业车间与配送集成调度问题

doi:10.16381/j.cnki.issn1003-207x.2024.0888

中国管理科学 ›› 2026, Vol. 34 ›› Issue (8): 171-181.doi: 10.16381/j.cnki.issn1003-207x.2024.0888cstr: 32146.14.j.cnki.issn1003-207x.2024.0888

考虑自动引导车运输的分布式柔性作业车间与配送集成调度问题

张正佩¹^,³, 董红宇¹(), 付亚平¹^,³, 黄敏²

^1.北京工商大学计算机与人工智能学院，北京 100048
^2.东北大学信息科学与工程学院，辽宁沈阳 110819
^3.青岛大学商学院，山东青岛 266071

收稿日期:2024-06-04 修回日期:2025-02-10 出版日期:2026-08-25 发布日期:2026-07-14
通讯作者: 董红宇 E-mail:hongyu.dong@btbu.edu.cn
基金资助:
国家重点研发计划项目(2021YFB3300900);国家自然科学基金重大项目(92267206);国家自然科学基金重点项目(62032013);北京工商大学数字商科与首都发展创新中心项目(SZSK202208);北京市社会科学基金一般项目(23GLB014);北京工商大学高层次人才队伍建设项目(19008023207);北京工商大学高层次人才队伍建设项目(19008024076);北京工商大学高层次人才队伍建设项目(19008025034)

Integrated Scheduling Problems of Distributed Flexible Job Shops and Distribution Considering Automated Guided Vehicle Transportation

Zhengpei Zhang¹^,³, Hongyu Dong¹(), Yaping Fu¹^,³, Min Huang²

^1.School of Computer and Artificial Intelligence，Beijing Technology and Business University，Beijing 100048，China
^2.School of Information Science and Engineering，Northeastern University，Shenyang 110819，China
^3.School of Business，Qingdao University，Qingdao 266071，China

Received:2024-06-04 Revised:2025-02-10 Online:2026-08-25 Published:2026-07-14
Contact: Hongyu Dong E-mail:hongyu.dong@btbu.edu.cn

摘要/Abstract

摘要：

近年来，分布式生产调度问题受到了学者和实践者的广泛讨论。然而，针对这类问题的现有研究通常忽略了作业在机器间的转移过程以及作业被交付给客户的配送过程。因此，本研究提出了一个考虑自动引导车运输的分布式柔性作业车间与配送集成调度问题。首先，建立了一个混合整数规划模型来最小化最大完工时间和总延迟时间。其次，提出了一种结合问题特点的基于学习驱动的多目标人工蜂群算法来处理该模型。最后，在一组基准算例上，将该算法与现有文献中两种著名的元启发式方法进行了比较。实验结果证实了所开发的模型和算法在解决所研究问题方面具有优越的性能。

关键词: 分布式柔性作业车间调度, 生产与配送集成调度, 自动引导车运输, 人工蜂群算法, Q学习方法

Abstract:

In recent years， distributed production scheduling has received significant attention from both researchers and practitioners. However， existing studies often neglect two crucial aspects：（1） job transfer processes among machines within distributed systems and （2） the distribution of finished jobs to customers. To address these gaps， an integrated scheduling framework is proposed that combines distributed flexible job shops with logistics distribution， explicitly incorporating automated guided vehicle （AGV） transportation operations. First， a mixed-integer programming （MIP） model is formulated to minimize two objectives： the makespan and total tardiness. Second， a learning-driven multi-objective artificial bee colony （ABC） algorithm is developed to efficiently solve the proposed model， leveraging problem-specific heuristics to enhance the search performance. Finally， the effectiveness of the proposed approach is validated through extensive experiments on benchmark instances and compared against two state-of-the-art metaheuristics. The results demonstrate that the proposed model and algorithm achieve superior performance in both solution quality and computational efficiency.

Key words: distributed flexible job shop scheduling, integrated scheduling of production and distribution, automated guided vehicle transportation, artificial bee colony algorithm, Q-learning method

中图分类号:

TH165

张正佩,董红宇,付亚平, 等. 考虑自动引导车运输的分布式柔性作业车间与配送集成调度问题[J]. 中国管理科学, 2026, 34(8): 171-181.

Zhengpei Zhang,Hongyu Dong,Yaping Fu, et al. Integrated Scheduling Problems of Distributed Flexible Job Shops and Distribution Considering Automated Guided Vehicle Transportation[J]. Chinese Journal of Management Science, 2026, 34(8): 171-181.

图/表 8

图1

图2

图3

图4

表1

LMABC和CPLEX的比较结果"

$n$	权重	CPLEX		LMABC
$n$	权重	值	时间（秒）	值	时间（秒）
5	(1.0, 0.0)	329^*	6780.165	335	22.542
	(0.5, 0.5)	384^*	703.702	392	22.395
	(0.0, 1.0)	437^*	20.581	437^*	22.746
7	(1.0, 0.0)	402	10800.000	383	31.843
	(0.5, 0.5)	516	10800.000	505	31.727
	(0.0, 1.0)	620^*	101.824	620^*	31.835
10	(1.0, 0.0)	—	10800.000	453	45.631
	(0.5, 0.5)	—	10800.000	668	45.396
	(0.0, 1.0)	836^*	10500.013	836^*	45.428

表1

表2

表3

三种算法关于IGD指标的比较结果"

算例	LMABC			NSGA-II				MOEA/D
算例	均值	最优值	$R$	均值	最优值	$t$	$R$	均值	最优值	$t$	$R$
ISPD01	0.3635	0.0000	1	0.6592	0.1552	+	2	1.3424	1.1906	+	3
ISPD02	0.2568	0.0000	1	0.6453	0.1409	+	2	1.3603	1.2068	+	3
ISPD03	0.3072	0.0000	1	0.6809	0.3039	+	2	1.3480	1.0275	+	3
ISPD04	0.4251	0.0847	1	0.6246	0.0000	+	2	1.3532	1.2168	+	3
ISPD05	0.3720	0.0000	1	0.5921	0.2677	+	2	1.3389	1.2037	+	3
ISPD06	0.1728	0.0272	1	0.4491	0.0935	+	2	1.2274	0.9416	+	3
ISPD07	0.3573	0.0266	1	0.5541	0.0583	+	2	1.3327	1.2034	+	3
ISPD08	0.3496	0.0000	1	0.5095	0.1722	+	2	1.3541	1.2522	+	3
ISPD09	0.3617	0.0000	1	0.6366	0.1352	+	2	1.3627	1.2211	+	3
ISPD10	0.3324	0.0000	1	0.5308	0.1452	+	2	1.3004	1.1403	+	3
ISPD11	0.1654	0.0196	1	0.4917	0.0149	+	2	1.2826	1.1430	+	3
ISPD12	0.2239	0.0504	1	0.3983	0.0183	+	2	1.2857	0.9705	+	3
ISPD13	0.3733	0.1887	1	0.4926	0.0470	+	2	1.3251	1.2303	+	3
ISPD14	0.4012	0.0569	1	0.5165	0.0000	+	2	1.3719	1.3114	+	3
ISPD15	0.2490	0.0077	1	0.4623	0.1480	+	2	1.3123	1.1547	+	3
ISPD16	0.2937	0.0000	1	0.4528	0.1198	+	2	1.3449	1.2245	+	3
ISPD17	0.1971	0.0699	1	0.4117	0.0970	+	2	1.2259	0.9844	+	3
ISPD18	0.2270	0.0000	1	0.5330	0.1031	+	2	1.2937	1.0384	+	3
ISPD19	0.4443	0.2403	2	0.3923	0.0415	~	1	1.2932	1.1206	+	3
ISPD20	0.2941	0.0824	1	0.3689	0.0653	~	2	1.2679	1.1738	+	3
ISPD21	0.3437	0.1468	2	0.3386	0.0053	~	1	1.2891	1.1762	+	3
ISPD22	0.3420	0.0573	1	0.4650	0.0273	~	2	1.2922	1.1957	+	3
ISPD23	0.2892	0.0177	1	0.3822	0.0760	~	2	1.2678	1.1030	+	3
ISPD24	0.2855	0.0622	1	0.5803	0.0748	+	2	1.2651	1.0497	+	3
ISPD25	0.3033	0.0223	1	0.4970	0.2331	+	2	1.2892	0.9260	+	3
ISPD26	0.3705	0.0000	1	0.4302	0.1429	~	2	1.3504	1.1907	+	3
ISPD27	0.3835	0.1638	2	0.3418	0.0081	~	1	1.2354	1.0948	+	3
ISPD28	0.3910	0.1991	1	0.4929	0.0000	~	2	1.3501	1.2466	+	3
ISPD29	0.3393	0.1369	1	0.3424	0.0432	~	2	1.2414	1.1211	+	3
ISPD30	0.3671	0.2175	1	0.5562	0.0000	+	2	1.3025	1.2084	+	3
平均值	0.3194	0.0626	1.10	0.4943	0.0913		1.90	1.3069	1.1423		3.00

表3

图5

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算例	LMABC		MABC		算例	LMABC		MABC
算例	均值	最优值	均值	最优值	算例	均值	最优值	均值	最优值
ISPD02	0.6836	0.0000	1.2029	0.9173	ISPD18	0.7756	0.0000	1.0591	0.5721
ISPD04	0.9497	0.0000	1.0359	0.2179	ISPD20	0.8545	0.0000	1.1708	0.3810
ISPD06	0.6501	0.1964	0.9534	0.1804	ISPD22	0.9067	0.0000	1.0951	0.3788
ISPD08	0.9523	0.0000	1.0565	0.1831	ISPD24	0.7701	0.0375	1.0051	0.3711
ISPD10	1.0144	0.0000	1.0022	0.5310	ISPD26	0.9545	0.0000	1.2189	0.7984
ISPD12	0.8518	0.1061	0.7402	0.2246	ISPD28	0.7334	0.0000	1.2624	0.7914
ISPD14	0.9467	0.4110	0.8629	0.2610	ISPD30	0.7625	0.0000	1.2033	0.6694
ISPD16	0.9108	0.1515	0.9896	0.0000	平均值	0.8478	0.0602	1.0572	0.4318

考虑自动引导车运输的分布式柔性作业车间与配送集成调度问题

Integrated Scheduling Problems of Distributed Flexible Job Shops and Distribution Considering Automated Guided Vehicle Transportation

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