考虑心理成本的应急物流选址路径问题

doi:10.16381/j.cnki.issn1003-207x.2023.0577

摘要/Abstract

摘要：

将卡车－无人机协同配送模型应用于人道主义物流，以配送时间、系统经济成本和受影响人群心理成本最小化为目标，建立了需求可拆分的卡车无人机协同选址－路径模型。提出带局部搜索算子的改进非支配排序遗传算法，通过一组数值实验验证算法性能。以上海市抗原试剂配送为例，将卡车无人机协同选址－路径模型与仅卡车配模型进行比较，发现该模型物资配送效率方面具有优势。在此基础上，对不同无人机参数对卡车－无人机协同配送效率的影响进行了敏感性分析，阐述了所提出的模型和算法在实际中的应用。

关键词: 应急物流, 车辆-无人机, 选址路径问题, 心理成本

Abstract:

With the increasing risks of geological disasters， large-scale infectious diseases， and climate change， humanitarian rescue efforts have risen significantly. To reduce disaster losses， scientific emergency facility location and material distribution system optimization are crucial. Additionally， attention must be given to the psychological and mental impact on affected populations post-disaster. In emergency logistics management， unmanned aerial vehicles （UAVs） have become a focus due to their efficiency， flexibility， low energy consumption， and minimal road occupancy advantages. Integrating trucks and UAVs for joint delivery can effectively address traditional distribution challenges and “last-mile” risks. This new logistics operation model poses significant theoretical and practical challenges to vehicle routing problems， gaining more scholarly attention.The Location-Routing Problem with Drone （LRPD） is a novel optimization problem that requires solving warehouse location， UAV and vehicle path decisions， as well as addressing synchronization issues in UAV and vehicle separation and convergence operations. A demand-splitting truck-UAV collaborative location-routing model is established， including：（i） developing a location-routing model allowing demand splitting and truck-UAV joint delivery to minimize delivery time， system economic costs， and affected population's psychological costs；（ii） proposing an improved Non-Dominated Sorting Genetic Algorithm （NSGA-II） with a local search operator and verifying its performance through a set of numerical experiments.Through constructing the m-SDLRPD test set， the computational performance and speed of the ENSGA-II algorithm are tested. The experimental results demonstrate that the hybrid multi-objective evolutionary algorithm with dedicated local search operators possesses good solution quality and algorithmic performance. Comparing m-SDLRPD with the truck-only mode， it is found that UAV application significantly enhances material delivery efficiency. Sensitivity analysis of UAV parameters reveals that batch delivery is more effective in reducing travel time compared to increasing UAV payload capacity. An application example of Shanghai's material distribution illustrates the practical use of the proposed model and algorithm.

Key words: emergency logistics, truck-drone, location-routing problem, psychological cost

中图分类号:

C931

彭丽芳,赵楠楠. 考虑心理成本的应急物流选址路径问题[J]. 中国管理科学, 2026, 34(1): 234-243.

Lifang Peng,Nannan Zhao. Location-routing Problem Considering Psychological Cost in Emergency Logistics[J]. Chinese Journal of Management Science, 2026, 34(1): 234-243.

图/表 13

图1

表1

变量符号及其含义"

符号	说明	符号	说明
π	卡车可以到达的节点( $N ⋃ V t$ )	$Q 1$	卡车最大载重量
K	每个卡车及其对应的无人机的集合，k ∈ K	$Q 2$	无人机最大载重量
$q i$	需求点i的需求量	$T t$	无人机最大飞行时间
$p i$	需求点i的受灾人数	$C h$	一辆卡车(含无人机)的固定成本
$d i j k t$	卡车k在弧（i, j）行驶距离	$C t$	卡车行驶单位距离的成本
$d i j k d$	无人机k在弧（i, j）行驶距离	$C d$	无人机行驶单位距离的成本
$v t$	卡车平均行驶速度	$F n$	应急设施点的固定建设费用
$v d$	无人机平均行驶速度	$w i$	需求点i的等待时间
$Q n$	仓库n的容量	P(t)	单位心理成本
$a n$ :选择n处为应急设施点为1，否则为0
$b n k$ :车辆k分配给设施点n为1，否则为0
$z i n$ :设施点n为需求点i提供物资为1，否则为0
$x i j k$ :若卡车k从i到j为1，否则为0
$y i j l k$ :当无人机k从节点i出发访问j回到l为1，否则为0
$u i k$ :卡车k访问节点i的顺序
$s i j$ :i点与j点访问的前后顺序，i点在前则为1
$r i j k$ :为卡车k携带的无人机从i点出发访问j点携带重量占j点顾客需求量的比重
$X k$ :是否使用车辆k

表1

图2

表2

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表5

图3

图4

图5

表7

图6

图7

参考文献 22

[1]	Kundu T， Sheu J B， Kuo H T. Emergency logistics management—Review and propositions for future research［J］. Transportation Research Part E： Logistics and Transportation Review， 2022， 164： 102789.
[2]	Statista. Number of natural disasters worldwide 2021［EB/OL］. （2022-2-2）［2022-8-5］. .
[3]	Wang H， Du L， Ma S. Multi-objective open location-routing model with split delivery for optimized relief distribution in post-earthquake［J］. Transportation Research Part E： Logistics and Transportation Review， 2014， 69： 160-179.
[4]	Salhi S， Rand G K. The effect of ignoring routes when locating depots［J］. European Journal of Operational Research， 1989， 39（2）： 150-156.
[5]	Wang S， Tao F， Shi Y. Optimization of location–routing problem for cold chain logistics considering carbon footprint［J］. International Journal of Environmental Research and Public Health， 2018， 15（1）： 86-103.
[6]	王海军，杜丽敬，马士华. 震后应急物流系统中双目标开放式选址：路径问题模型与算法研究［J］. 管理工程学报， 2016， 30（2）： 108-115.
	Wang H J， Du L J， Ma S H. Model and algorithms for integrated open location and routing problem in emergency logistics under earthquake［J］. Journal of Industrial Engineering and Engineering Management， 2016， 30（2）： 108-115.
[7]	Peng Z， Wang C， Xu W， et al. Research on location-routing problem of maritime emergency materials distribution based on bi-level programming［J］. Mathematics， 2022， 10（8）： 1-23.
[8]	Kinston W， Rosser R. Disaster： Effects on mental and physical state［J］. Journal of Psychosomatic Research， 1974， 18（6）： 437-456.
[9]	Sheu J B， Pan C. A method for designing centralized emergency supply network to respond to large-scale natural disasters［J］. Transportation Research Part B： Methodological， 2014， 67： 284-305.
[10]	Hu Z H， Sheu J B， Yin Y Q， et al. Post-disaster relief operations considering psychological costs of waiting for evacuation and relief resources［J］. Transportmetrica A： Transport Science， 2017， 13（2）： 108-138.
[11]	顺丰科技.顺丰无人机助力抗疫第一线，累计运送物资超 11吨［EB/OL］.（2020-3-6）［2022-8-5］. .
	SF Technology. SF drone helps the first line of anti-epidemic， the cumulative delivery of materials exceeds 11 tons.［EB/OL］.（2020-3-6）［2022-8-5］..
[12]	中国网.无人机为重庆山火救援出力空中科技已成应急救援重要帮手［EB/OL］. （2022-9-1）［2022-9-15］. .
	Net China. Aerial technology has become an important aid for emergency rescue in Chongqing［EB/OL］. （2022-9-1）［2022-9-15］. .
[13]	Murray C C， Chu A G. The flying sidekick traveling salesman problem： Optimization of drone-assisted parcel delivery［J］. Transportation Research Part C： Emerging Technologies， 2015， 54： 86-109.
[14]	Agatz N， Bouman P， Schmidt M. Optimization approaches for the traveling salesman problem with drone［J］.Transportation Science，2018，52（4）： 965-981.
[15]	颜瑞，陈立双，朱晓宁，等. 考虑区域限制的卡车搭载无人机车辆路径问题研究［J］. 中国管理科学， 2022， 30（5）： 144-155.
	Yan R， Chen L S， Zhu X N， et al. Research on vehicle routing problem of truck carrying UAV considering area restriction［J］. Chinese Journal of Management Science， 2022， 30（5）： 144-155.
[16]	曹英英，陈淮莉. 基于集群的卡车与无人机联合配送调度研究［J］. 计算机工程与应用， 2022， 58（11）： 287-294.
	Cao Y Y， Chen H L. Research on truck and drone joint distribution scheduling based on cluster［J］. Computer Engineering and Applications， 2022， 58（11）： 287-294.
[17]	Lu Y， Yang C， Yang J. A multi-objective humanitarian pickup and delivery vehicle routing problem with drones［J］. Annals of Operations Research， 2022， 319（1）： 291-353.
[18]	Kuo R J， Lu S H， Lai P Y， et al. Vehicle routing problem with drones considering time windows［J］. Expert Systems with Applications， 2022， 191： 116264.
[19]	Kyriakakis N A， Stamadianos T， Marinaki M， et al. The electric vehicle routing problem with drones： An energy minimization approach for aerial deliveries［J］. Cleaner Logistics and Supply Chain， 2022， 4： 100041.
[20]	Deb K， Pratap A， Agarwal S， et al. A fast and elitist multiobjective genetic algorithm： NSGA-II［J］. IEEE Transactions on Evolutionary Computation， 2002， 6（2）： 182-197.
[21]	Zhang Q， Li H. MOEA/D： A multiobjective evolutionary algorithm based on decomposition［J］. IEEE Transactions on Evolutionary Computation， 2007， 11（6）： 712-731.
[22]	Zitzler E， Thiele L. Multiobjective evolutionary algorithms： A comparative case study and the strength Pareto approach［J］. IEEE Transactions on Evolutionary Computation， 1999， 3（4）： 257-271.

类型	算例	需求点数量	候选仓库	节点数量	区域
S	S1-S5	10	2	12	10×10
M	M1-M5	50	6	56	50×50
L	L1-L5	120	12	132	100×100

算例	ENSGA-II						NSGA-II
算例	目标1	目标2	目标3	IGD	HV	RT	目标1	目标2	目标3	IGD	HV	RT
S1	0.49	28310.99	2335.06	0.39	0.93	76.22	0.49	28314.00	2517.57	0.44	0.93	72.65
S2	0.77	24014.76	3760.73	0.53	0.44	66.25	0.78	24014.93	3760.73	0.59	0.35	65.5
S3	0.30	25130.99	2512.90	0.35	0.75	89.08	0.34	25134.47	2514.83	0.32	0.65	89.08
S4	0.53	23937.13	2681.90	0.40	0.86	74.01	0.53	23938.24	2681.74	0.34	0.82	66.78
S5	0.83	21344.17	3567.91	0.48	0.40	73.89	0.84	21344.17	3637.51	0.56	0.38	71.57
M1	2.41	25485.30	62386.73	0.28	0.78	101.69	2.66	26769.96	72685.87	0.30	0.63	90.41
M2	2.69	49974.95	67315.76	0.34	0.77	114.65	2.73	49920.89	70633.06	0.37	0.63	105.18
M3	2.34	27241.96	65420.06	0.27	0.83	98.65	2.58	28112.59	74683.02	0.33	0.84	91.66
M4	2.50	26607.13	60975.33	0.27	0.85	101.57	2.49	26664.67	66951.70	0.26	0.77	93.39
M5	2.36	28829.30	67952.22	0.31	0.83	98.94	2.84	29258.68	72437.38	0.25	0.78	88.49
L1	8.66	83985.67	438618.54	0.37	0.83	177.08	9.04	84281.34	513641.03	0.27	0.76	162.55
L2	7.28	71900.16	412912.97	0.36	0.71	173.6	7.67	80357.30	455425.31	0.38	0.71	160.64
L3	7.57	81969.99	401440.47	0.29	0.74	177.29	8.22	89749.63	472506.05	0.36	0.84	162.97
L4	8.01	87282.02	404709.85	0.30	0.69	194.64	8.30	89607.98	445726.60	0.28	0.68	181.78
L5	8.06	97707.57	420210.44	0.34	0.91	196.42	9.42	97371.74	498813.67	0.28	0.86	188.31

应急设施	费用（千元）	容量（件）
1	21	5600
2	24	5800
3	23	4200
5	24	5800
5	22	5200
6	29	4100

配送模型	目标一		目标二		目标三		IGD	HV
配送模型	min	mean	min	mean	min	mean	IGD	HV
truck_drone	2.34	2.55	45642.25	46687.36	2819808.80	3393923.88	0.32	0.92
only_truck	9.00	9.50	47005.38	50264.83	14332289.58	17143453.94	0.33	0.72
Gap	6.66	6.94	1363.12	3577.46	11512480.78	13749530.06	0.01	-0.19