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

Abstract

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

CLC Number:

C931

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

Figures/Tables 13

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

References 22

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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

Location-routing Problem Considering Psychological Cost in Emergency Logistics

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需求点	需求量	服务类型
1	275	卡车
2	133	卡车
3	227	卡车
4	407	卡车
5	36	卡车
6	49	卡车
7	266	卡车
…	…	…
81	108	无人机
82	129	无人机
83	78	无人机
84	45	无人机
85	26	无人机
86	132	无人机

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