当日达服务下无人车动态补货车辆路径优化研究

doi:10.16381/j.cnki.issn1003-207x.2024.2034

中国管理科学 ›› 2026, Vol. 34 ›› Issue (9): 184-196.doi: 10.16381/j.cnki.issn1003-207x.2024.2034

当日达服务下无人车动态补货车辆路径优化研究

肖建华¹^,⁴(), 陈亮¹, 康柳江², 娄旭江¹

^1.南开大学现代物流研究中心，天津 300071
^2.北京交通大学交通运输学院，北京 100044
^3.南开大学经济行为与政策模拟实验室，天津 300071
^4.南开大学前沿交叉学科研究院，天津 300071

收稿日期:2024-11-07 修回日期:2025-03-28 出版日期:2026-09-25 发布日期:2026-09-01
通讯作者: 肖建华 E-mail:jhxiao@nankai.edu.cn
基金资助:
国家自然科学基金项目(62573245);国家自然科学基金项目(72542015);国家自然科学基金项目(72288101);教育部哲学社会科学实验室专项基金项目(H0125795);教育部哲学社会科学实验室专项基金项目(H0124709)

Autonomous Vehicle Assisted Delivery Problem with Dynamic Resupply in Same-Day Delivery

Jianhua Xiao¹^,⁴(), Liang Chen¹, Liujiang Kang², Xujiang Lou¹

^1.Research Center of Logistics，Nankai University，Tianjin 300071，China
^2.School of traffic and transportation，Beijing Jiaotong University，Beijing 100044，China
^3.The Laboratory for Economic Behaviors and Policy Simulation，Nankai University，Tianjin 300071，China
^4.Academy for Advanced Interdisciplinary Studies，Nankai University，Tianjin 300071，China

Received:2024-11-07 Revised:2025-03-28 Online:2026-09-25 Published:2026-09-01
Contact: Jianhua Xiao E-mail:jhxiao@nankai.edu.cn

摘要/Abstract

摘要：

本文针对当日达服务下高动态、强时效的随机需求，引入无人车动态补货策略，以完成配送时间最短为目标，构建当日达服务下无人车动态补货车辆路径优化模型。针对模型NP难特性，本文提出了基于周期内优化和动态补货的两阶段算法。在算法中，利用自适应大邻域搜索算法求解周期内优化，利用短视周期补货策略和自适应周期补货策略求解动态补货优化。最后，通过不同规模算例和案例分析，验证了本文模型和算法的可行性及高效性，为高时效性的当日达配送企业提供决策参考。

关键词: 当日达配送, 无人车动态补货, 车辆路径优化, 两阶段算法

Abstract:

The demand for same-day delivery （SDD） has increased rapidly over the past few years and has become a popular delivery option for customers. In this paper， the Autonomous Vehicle Assisted Delivery Problem with Dynamic Resupply （AVADDR） is proposed to address the challenge of high-frequency， time-sensitive stochastic requests in same-day delivery. Throughout the day， customers place requests for same-day delivery （SDD） services without prior knowledge of the exact timing or delivery locations. The dispatcher then dynamically allocates the courier with autonomous vehicle resupply to fulfill these requests. It is assumed that the autonomous vehicle performs multiple trips from the warehouse to replenish the courier at any required time while the courier delivers the orders. The AVADDR is decomposed into two stages： routing optimization and dynamic resupply. A mathematical programming model is developed for AVADDR to minimize the delivery time. An adaptive large neighborhood search algorithm （ALNS） is designed to solve the routing optimization problem， and myopic and adaptive resupply strategies are proposed to address the dynamic resupply issue. Comprehensive testing and analysis demonstrate the superior effectiveness of our approach compared to benchmarks. The approach can provide effective decision-making support for same-day delivery companies with high time-sensitivity requirements. In the end， several managerial implications are obtained through sensitivity analysis experiments. （i） It is advisable to select the distribution center within the service area in SDD. （ii）The sorting time is an important factor influencing the total time required to complete same-day deliveries. If enterprises can conduct sorting in advance before dispatching for delivery， it can effectively reduce the total delivery completion time.

Key words: same-day delivery, dynamic replenishment with autonomous vehicles, vehicle routing optimization, two-stage algorithm

中图分类号:

U492.22

肖建华,陈亮,康柳江, 等. 当日达服务下无人车动态补货车辆路径优化研究[J]. 中国管理科学, 2026, 34(9): 184-196.

Jianhua Xiao,Liang Chen,Liujiang Kang, et al. Autonomous Vehicle Assisted Delivery Problem with Dynamic Resupply in Same-Day Delivery[J]. Chinese Journal of Management Science, 2026, 34(9): 184-196.

图/表 13

图1

图2

图3

表1

算例相关参数设置"

参数	含义	取值
$N 1$	初始客户订单数量	16
$Q$	无人车容量限制	16
$q$	配送员容量限制	3
$f$	理货时间	2
$p$	停车时间	4
$t s$	顾客服务时间	0.6
$t l o a d$	装载时间	2
$d$	无人车行驶速度	1.6
$w$	配送员步行速度	0.4
$f ̂$	批量理货单位时间	0.5

表1

表2

表3

表4

不同模式下的算例求解结果(Dis =0 km)"

算例	AVADDR_A		AVADDR_M		DAVADP		TAVADP		CDPP		Improvement
算例	Best	Avg	Best	Avg	Best	Avg	Best	Avg	Best	Avg	Dec1	Dec2	Dec3	Dec4
$λ 1 . 1$	327	333	330	335	374	374	413	417	905	909	1.0	12.5	20.8	63.8
$λ 1 . 2$	358	362	364	366	404	404	445	447	967	970	1.6	11.2	19.5	62.9
$λ 1 . 3$	344	350	345	352	397	397	440	443	965	969	0.2	13.4	21.8	64.4
$λ 1 . 4$	366	375	368	372	438	438	482	485	1053	1056	0.6	16.4	24.1	65.2
$λ 2 . 1$	423	425	419	425	510	510	562	565	1223	1228	-0.9	17.2	24.8	65.4
$λ 2 . 2$	403	405	404	408	480	481	535	539	1175	1178	0.4	16.1	24.7	65.7
$λ 2 . 3$	393	399	399	401	474	474	525	527	1154	1156	1.3	17.0	25.0	65.9
$λ 2 . 4$	410	416	419	423	518	518	566	570	1234	1237	2.2	20.8	27.5	66.8
$λ 3 . 1$	446	452	454	456	562	563	618	624	1354	1360	1.9	20.7	27.9	67.1
$λ 3 . 2$	453	456	454	459	562	562	626	631	1376	1378	0.2	19.4	27.7	67.1
$λ 3 . 3$	463	468	465	470	563	564	635	639	1398	1402	0.5	17.8	27.1	66.9
$λ 3 . 4$	463	472	473	478	587	587	654	659	1436	1440	2.1	21.1	29.2	67.7

表4

图4

图5

图6

图7

图8

表5

参考文献 29

[1]	Klapp M A， Erera A L， Toriello A. Request acceptance in same-day delivery［J］. Transportation Research Part E： Logistics and Transportation Review， 2020， 143： 102083.
[2]	Côté J F， Alves de Queiroz T， Gallesi F， et al. A branch-and-regret algorithm for the same-day delivery problem［J］. Transportation Research Part E： Logistics and Transportation Review， 2023， 177： 103226.
[3]	Ulmer M W， Streng S. Same-Day delivery with pickup stations and autonomous vehicles［J］. Computers & Operations Research， 2019， 108： 1-19.
[4]	Chen X， Ulmer M W， Thomas B W. Deep Q-learning for same-day delivery with vehicles and drones［J］. European Journal of Operational Research， 2022， 298（3）： 939-952.
[5]	Li M， Zhao P， Zhu Y， et al. A learning and searching integration approach for same-day delivery problem with heterogeneous fleets considering uncertainty［J/OL］. Transportmetrica A： Transport Science， 2024..
[6]	Chen X， Wang T， Thomas B W， et al. Same-day delivery with fair customer service［J］. European Journal of Operational Research， 2023， 308（2）： 738-751.
[7]	Dienstknecht M， Boysen N， Briskorn D. The traveling salesman problem with drone resupply［J］. OR Spectrum， 2022， 44（4）： 1045-1086.
[8]	Dayarian I， Savelsbergh M， Clarke J P. Same-day delivery with drone resupply［J］. Transportation Science， 2020， 54（1）： 229-249.
[9]	Xiao J， Chen L， Niu Y， et al. Request prompt response in same-day delivery problem with drone resupply［J］. International Journal of Production Research， 2025， 63（13）： 4845-4863.
[10]	Pina-Pardo J C， Silva D F， Smith A E， et al. Dynamic vehicle routing problem with drone resupply for same-day delivery［J］. Transportation Research Part C： Emerging Technologies， 2024， 162： 104611.
[11]	Liu W， Liu L， Qi X. Drone resupply with multiple trucks and drones for on-time delivery along given truck routes［J］. European Journal of Operational Research， 2024， 318（2）： 457-468.
[12]	Banerjee D， Erera A L， Toriello A. Pricing and demand management for integrated same-day and next-day delivery systems［J］. Transportation Science， 2024， 59（2）： 279-300.
[13]	Klein V， Steinhardt C. Dynamic demand management and online tour planning for same-day delivery［J］. European Journal of Operational Research， 2023， 307（2）： 860-886.
[14]	Banerjee D， Erera A L， Toriello A. Fleet sizing and service region partitioning for same-day delivery systems［J］. Transportation Science， 2022， 56（5）： 1327-1347.
[15]	Wu H， Herszterg I， Savelsbergh M， et al. Service network design for same-day delivery with hub capacity constraints［J］. Transportation Science， 2023， 57（1）： 273-287.
[16]	高佳静，镇璐. 多卡车多机器人联合配送系统路径问题研究［J］. 中国管理科学， 2023， 31（3）： 48-57.
	Gao J J， Zhen L. Research on routing problem for joint delivery system based on multiple trucks and robots［J］. Chinese Journal of Management Science， 2023， 31（3）： 48-57.
[17]	肖建华，陈萍，刘秉镰. 基于城市道路拥堵的物流配送车辆停车收费定价研究［J］. 商业经济与管理， 2018（2）： 16-23.
	Xiao J H， Chen P， Liu B L. Research on parking pricing of logistics distribution vehicle under urban traffic congestion［J］. Journal of Business Economics， 2018（2）： 16-23.
[18]	Allen J， Piecyk M， Piotrowska M， et al. Understanding the impact of e-commerce on last-mile light goods vehicle activity in urban areas： The case of London［J］. Transportation Research Part D： Transport and Environment， 2018， 61： 325-338.
[19]	京东. 第六代无人车技术发布！京东物流将规模化布局搭载大模型的智能配送车［EB/OL］.（2024-09-24）［2024-10-21］..
	JD.com.The sixth-generation autonomous delivery vehicle technology has been released！ JD logistics will deploy large-scale intelligent delivery vehicles powered by large language models［EB/OL］.（2024-09-24）［2024-10-21］..
[20]	Reed S， Campbell A M， Thomas B W. The value of autonomous vehicles for last-mile deliveries in urban environments［J］. Management Science， 2022， 68（1）： 280-299.
[21]	Reed S， Campbell A M， Thomas B W. Impact of autonomous vehicle assisted last-mile delivery in urban to rural settings［J］. Transportation Science， 2022， 56（6）： 1530-1548.
[22]	Zhang R. Branch-and-price for the capacitated autonomous vehicle assisted delivery problem［J］. INFORMS Journal on Computing， 2024， 37（5）： 1328-1349.
[23]	Senna F， Coelho L C， Morabito R， et al. An exact method for a last-mile delivery routing problem with multiple deliverymen［J］. European Journal of Operational Research， 2024， 317（2）： 550-562.
[24]	Ropke S， Pisinger D. An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows［J］. Transportation Science， 2006， 40（4）： 455-472.
[25]	Shaw P. Using constraint programming and local search methods to solve vehicle routing problems［C］//Proceedings of the 4th International Conference on Principles and Practice of Constraint Programming， Pisa， Italy， October 26-30 ，Springer Berlin Heidelberg，1998： 417-431.
[26]	郭放，黄志红，黄卫来. 考虑前置仓选址与服务策略的同时取送货车辆路径问题研究［J］. 系统工程理论与实践， 2021， 41（4）： 962-978.
	Guo F， Huang Z H， Huang W L. Integrated sustainable planning of fast-pick area network and vehicle routing with simultaneous delivery and pick-up［J］. Systems Engineering —Theory & Practice， 2021， 41（4）： 962-978.
[27]	刘志硕，左兴权，吴建军. 面向小容销比客户的库存路径问题模型与算法［J］. 系统工程理论与实践， 2024， 44（6）： 2018-2032.
	Liu Z S， Zuo X Q， Wu J J. Model and algorithm of the inventory routing problem for customers with small capacity sales ratio［J］. Systems Engineering —Theory & Practice， 2024， 44（6）： 2018-2032.
[28]	王征，李婷玉，岳彩凡. 同城即时配送问题基于多预测场景的在线调度［J］. 系统工程理论与实践， 2018， 38（12）： 3197-3211.
	Wang Z， Li T Y， Yue C F. Online scheduling for the instant delivery problem in a city based on multiple prediction scenarios［J］. Systems Engineering —Theory & Practice， 2018， 38（12）： 3197-3211.
[29]	Wang L， Zhou G， Xu Y， et al. A hybrid artificial bee colony algorithm for the fuzzy flexible job-shop scheduling problem［J］. International Journal of Production Research， 2013， 51（12）： 3593-3608.

算例	CPLEX		ALNS
算例	求解结果	求解时间(s)	最优值	平均值	平均求解时间(s)	Best Dev.％	Avg Dev.％
6.1	23.06	8.97	23.06	23.06	0.11	0	0
6.2	19.22	15.42	19.22	19.22	0.20	0	0
6.3	22.17	8.86	22.17	22.17	0.08	0	0
6.4	21.74	9.15	21.74	21.74	0.07	0	0
8.1	29.15	42.49	29.15	29.15	0.09	0	0
8.2	24.91	68.39	24.91	24.91	0.09	0	0
8.3	27.94	40.04	27.94	27.94	0.09	0	0
8.4	27.14	40.70	27.14	27.14	0.08	0	0
10.1	33.89	138.51	33.89	33.89	0.09	0	0
10.2	29.19	232.54	29.19	29.19	0.09	0	0
10.3	32.39	199.45	32.39	32.39	0.09	0	0
10.4	31.56	154.63	31.56	31.56	0.08	0	0
12.1	38.78	407.71	38.78	38.78	0.10	0	0
12.2	34.09	466.34	34.09	34.09	0.09	0	0
12.3	37.34	412.06	37.34	37.34	0.09	0	0
12.4	36.05	454.67	36.05	36.05	0.09	0	0

算例	ALNS
算例	最优值	平均值	最差值	标准差	平均求解时间(s)
60.1	138.60	139.66	140.72	0.65	1.06
60.2	138.80	139.25	140.23	0.45	0.98
60.3	138.57	139.44	140.46	0.70	0.91
60.4	140.96	141.54	142.19	0.46	1.06
80.1	177.33	178.30	179.01	0.64	2.25
80.2	173.30	175.66	178.10	1.44	2.26
80.3	181.46	182.63	183.76	0.89	2.03
80.4	178.72	180.31	181.37	0.85	2.24
100.1	217.13	218.73	219.96	1.05	4.23
100.2	215.96	217.42	218.61	0.90	4.52
100.3	218.56	220.24	222.86	1.40	4.32
100.4	216.38	218.01	220.33	1.36	4.66

顾客服务顺序		补货点	会面点
第一轮服务：	｛0｝-｛27｝-｛2｝-｛10｝-｛9｝-｛20-23-28｝-｛14｝-｛17-16｝-｛11-21-4-1｝	11	1
第二轮服务：	｛8｝-｛43-29-5-6｝-｛19｝-｛24-35｝-｛3｝-｛42-7｝-｛40｝-｛45｝-｛34-44｝-｛37｝-｛39-31｝-｛41｝-｛30-26｝-｛15-36｝-｛12｝-｛33-18-32-22｝	33	22
第三轮服务：	｛98｝-｛68｝｛97-96-64｝-｛48-72-99-46｝-｛78｝-｛75-104-51｝-｛88-85-77-69｝-｛87-52-54｝-｛102-82-60｝-｛71-74-105-38｝	71	38
第四轮服务：	｛123-135｝-｛86｝-｛129｝-｛143｝-｛93-101｝-｛67-111｝-｛115-108-13-94｝	115	94
第五轮服务：	｛125-136-65｝-｛126-63-133｝-｛142-50-70-84｝-｛76｝-｛100-89-90-106｝-｛95-134-58｝-｛137-139-138｝-｛62-59-83-55｝-｛47-57-110｝	47	110
第六轮服务：	｛128｝-｛73｝-｛49-56｝-｛107｝-｛79-119-130｝-｛118-66-112-61｝-｛109-114-81-103｝-｛80-91｝-｛122｝-｛13-120-124-92｝-｛121｝-｛117-141-116-140｝	117	140
第七轮服务：	｛132｝-｛127｝-｛25｝-｛131-53｝｝	—	—

当日达服务下无人车动态补货车辆路径优化研究

Autonomous Vehicle Assisted Delivery Problem with Dynamic Resupply in Same-Day Delivery

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

图/表 13

参考文献 29

相关文章 2

Metrics

本文评价

推荐阅读 0

[1]	徐哲, 有维宝, 赵松, 郭松清, 苏艺璇. 考虑转移时间的分布式资源受限多项目鲁棒调度优化[J]. 中国管理科学, 2026, 34(2): 89-102.
[2]	王晓博, 李一军. 电子商务下基于改进两阶段算法的有时间窗车辆调度优化[J]. 中国管理科学, 2007, 15(6): 52-59.