冷链物流配送的绿色车辆路径模型及其求解算法

doi:10.16381/j.cnki.issn1003-207x.2022.0461

Abstract

Abstract:

In recent years， fresh food e-commerce in China has developed rapidly， with a significantly growing demand for cold-chain logistics distribution. In order to promote energy conservation and emission reduction in cold-chain logistics， the Green Vehicle Routing Problem in Cold-chain Logistics Distribution （GVRPCLD） has attracted increasing attention from both academia and industry. The GVRPCLD discussed in this paper involves set constraints， including （1） distribution center locations，（2） capacity-constrained homogeneous refrigerated vehicles，（3） customers’ number， locations， demands， time windows， service times， and （4） a low temperature kept in the cabin during distribution. The optimal vehicle routing plan is expected to realize the dual goals of total cost minimization and customer satisfaction maximization. Specifically， there are five types of costs that are included in the total cost， which are vehicle usage cost， deterioration cost， cooling cost， fuel consumption and carbon emission cost， and piecewise penalty costs for earliness and tardiness of deliveries. In the design， a freshness decay function is firstly applied to calculate the deterioration cost during distribution. Based on the comprehensive mode emission model （CMEM）， the measurement functions of fuel consumption and carbon emission are determined， with the consideration of the influence of vehicle load， speed， low temperature and other factors on fuel consumption and carbon emission rate. Then， a customer satisfaction function is established according to the relationship between delivery time and customer satisfaction. Finally， a dual-objective GVRPCLD optimization model is constructed. In order to solve the GVRPCLD model， a hybrid algorithm （VNSNSGA-II） is designed in this paper， which is based on the Non-dominated Sorting Genetic Algorithm II （NSGA-II） and the Variable Neighborhood Search （VNS）. The basic idea of the algorithm can be described as follows. Firstly， the VNS is used to optimize some chromosomes in the population to expand the solution space. Secondly， the NSGA-II is performed to obtain non-dominated sorting and crowding degree. Thirdly， based on the individual's rank and crowding distance， the top 50% of chromosomes are obtained and retained as new parent population. Finally， the Pareto-optimal set is obtained by iteration. The simulation results show the following. For one thing， the GVRPCLD model can achieve multi-objective optimization among logistics cost， deterioration cost， fuel consumption and carbon emissions， and customer satisfaction. Furthermore， it is found that logistics cost is negatively correlated with customer satisfaction， indicating that the delivery plan makers can choose different delivery options according to their preference. Last but not least， the proposed VNSNSGA-II is tested， and it is confirmed that the algorithm can contribute to a Pareto-optimal set.

Key words: cold-chain logistics distribution, green vehicle routing problem, NSGA-II, variable neighborhood search

CLC Number:

F252

Xian-cheng ZHOU,Tao-ying JIANG,Cai-hong HE,Li WANG,Yang LV. Green Vehicle Routing Model and Its Solution Algorithm in Cold-chain Logistics Distribution[J]. Chinese Journal of Management Science, 2023, 31(12): 203-214.

Figures/Tables 17

符号	含义
$A$	配送网络节点集合 $A = {0,1, 2, …, N}$ ，共N+1个节点，0表示配送中心
$A'$	顾客点集合 $A' = A \ {0}$ ，共N个顾客
$B$	配送车辆集合 $B = {1,2, …, K}$ ，共K辆冷藏车
$d i j$	从节点i到节点j的距离
$D$	所有车辆配送距离之和
$Q$	车辆最大容量
$w i j k$	车辆k行驶在道路 $(i, j)$ 上的载重
$q i$	顾客点i的需求量
$Z 1$	配送总成本
$Z 2$	顾客平均满意度
$M i$	顾客点i的满意度
$t s i$	顾客点i的服务时间
$t i j k$	车辆k在道路 $(i, j)$ 上的行驶时间
$v$	配送车辆的行驶速度
$τ 0$	车辆从配送中心出发的时刻
$t i k$	车辆k到达节点i的时刻
$[e 0, l 0]$	配送中心时间窗
$[e T i, l T i]$	顾客i期望的理想服务时间窗（硬时间窗）
$[E T i, L T i]$	顾客i可接受的服务时间窗（软时间窗）
$F i j k$	车辆k从节点i行驶到节点j产生的油耗量（单位：升）
$F i j k'$	车辆k从节点i到节点j因制冷产生的油耗量（单位：升）
$ψ$	燃油排放参数
$E i j k$	车辆k从节点i行驶到节点j产生的碳排放量（单位：千克）
$E i j k'$	车辆k从节点i到节点j因制冷产生的碳排放量（单位：千克）
$φ$	配送车辆的固定发车费用（单位：元/辆）
$μ$	车辆使用单位时间成本（单位：元/小时）
$ρ$	冷链产品单位重量的价格（单位：元/千克）
$θ$	车辆行驶过程中货物新鲜度衰减系数；
$σ 1$	车辆行驶过程中制冷系统的油耗率（单位：升/小时）
$σ 2$	车辆在配送服务期间制冷系统的油耗率（单位：升/小时）
$λ f$	单位油耗费用（单位：元/升）
$λ e$	单位碳排放费用（单位：元/千克）
$ω e$	早到顾客点服务的时间窗违背惩罚系数（单位：元/小时）
$ω l$	晚到顾客点服务的时间窗违背惩罚系数（单位：元/小时）
$x i j k$	0-1变量，当车辆k由节点i向节点j行驶时其值为1，否则为0
$y i k$	0-1变量，当顾客i由车辆k服务时其值为1，否则为0

模型参数	取值
$φ$	200元/辆
$ρ$	5元/千克
$v$	50千米/小时
$ω e$	6元/小时
$ω l$	9元/小时
$θ$	0.005
$σ 1$	3升/小时
$σ 2$	6升/小时
$μ$	60元/小时
$β 1$	1.004×10^-3
$β 2$	1.265×10^-2
$β 3$	4.312×10^-4
$w 0$	1930千克
$Q$	3000千克
$ψ$	2.621千克/升
$λ f$	6.5元/升
$λ e$	0.07元/千克

算法参数	取值
$p c$	1
$p m$	0.3
$ξ 1$	50个
$ξ 2$	40%
genmax	800代
VNSgenmax	10代
H	10次

前沿点	优化目标							D	K
前沿点	Z₁	Z₂	C₁	C₂	C₃	C₄	C₅	D	K
1	6748.20	0.920	2990.30	1117.91	1960.96	55.35	623.68	825.25	5
2	6781.02	0.922	2999.41	1126.06	1973.33	55.70	626.52	832.84	5
3	6792.45	0.923	3001.96	1126.14	1974.54	55.73	634.07	834.97	5
4	6837.06	0.926	3018.14	1125.97	1993.16	56.26	643.54	848.45	5
5	6839.06	0.929	3028.17	1097.79	2007.95	56.68	648.47	856.81	5
6	6853.43	0.931	3038.55	1107.40	2021.71	57.07	628.70	865.46	5
7	6870.99	0.932	3045.78	1137.42	2034.28	57.42	596.10	871.48	5
8	6881.21	0.934	3053.00	1105.18	2040.49	57.60	624.95	877.50	5
9	6905.57	0.936	3054.74	1112.69	2043.50	57.68	636.96	878.95	5
10	6922.91	0.937	3057.86	1117.61	2048.24	57.81	641.39	881.55	5
11	6955.64	0.938	3072.57	1143.62	2064.86	58.28	616.30	893.81	5
12	7007.06	0.941	3113.77	1127.06	2121.59	59.88	584.75	928.15	5
13	7064.86	0.942	3119.87	1167.71	2135.21	60.27	581.80	933.23	5
14	7079.98	0.943	3121.24	1169.90	2136.99	60.32	591.54	934.37	5
15	7131.49	0.944	3146.46	1152.16	2167.38	61.18	604.31	955.39	5
16	7136.47	0.944	3157.24	1174.33	2159.67	60.96	584.28	964.36	5
17	7159.99	0.948	3194.84	1138.59	2231.85	63.00	531.72	995.70	5
18	7189.64	0.950	3169.95	1144.62	2197.16	62.02	615.89	974.96	5
19	7192.27	0.953	3176.11	1189.71	2193.64	61.92	570.90	980.09	5
20	7215.48	0.954	3183.59	1189.22	2203.70	62.20	576.77	986.33	5
21	7243.31	0.955	3194.09	1195.25	2219.76	62.66	571.56	995.08	5
22	7261.61	0.956	3199.41	1189.96	2224.38	62.79	585.07	999.51	5
23	7273.49	0.957	3204.25	1196.38	2230.70	62.96	579.20	1003.54	5
24	7284.97	0.959	3223.97	1179.87	2263.31	63.88	553.94	1019.98	5
25	7297.84	0.961	3213.13	1203.90	2253.61	63.61	563.59	1010.94	5
26	7342.02	0.963	3228.95	1205.35	2274.42	64.20	569.10	1024.13	5
27	7350.58	0.964	3237.90	1188.93	2284.04	64.47	575.25	1031.58	5
28	7387.23	0.964	3249.49	1203.08	2300.87	64.94	568.85	1041.24	5
29	7404.43	0.965	3268.26	1201.76	2324.95	65.62	543.84	1056.88	5
30	7462.23	0.969	3296.17	1218.69	2362.80	66.69	517.88	1080.14	5
31	7480.08	0.969	3306.96	1215.13	2376.49	67.08	514.41	1089.13	5
32	7499.79	0.971	3308.33	1218.50	2378.48	67.14	527.35	1090.28	5
33	7559.18	0.971	3335.27	1215.51	2412.16	68.09	528.15	1112.72	5
34	7583.55	0.972	3338.10	1259.96	2420.09	68.31	497.09	1115.08	5
35	7618.04	0.974	3350.26	1259.42	2435.70	68.75	503.91	1125.22	5
36	7755.90	0.977	3357.55	1321.94	2448.89	69.12	558.40	1131.29	5
37	7786.98	0.977	3372.00	1320.55	2467.81	69.66	556.96	1143.33	5
38	7802.03	0.978	3373.37	1322.68	2469.57	69.71	566.70	1144.48	5
39	7849.50	0.981	3407.70	1315.43	2518.75	71.09	536.53	1173.08	5
40	7891.09	0.982	3411.24	1334.76	2525.80	71.29	548.00	1176.03	5
41	7903.19	0.983	3421.18	1326.79	2537.98	71.64	545.61	1184.31	5
42	8052.04	0.984	3470.83	1346.36	2608.69	73.63	552.53	1225.69	5
平均值	7277.47	0.954	3202.67	1195.51	2239.27	63.21	576.82	1002.22	5

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优化目标	总成本最小	货损最小	碳排放最小
Z₁	6617.2	6812.6	6752.5
Z₂	0.897	0.912	0.910
C₁	3009.8	3086.9	2966.4
C₂	1032.2	1001.8	1117.8
C₃	1991.1	2071.3	1933.8
C₄	56.23	58.46	54.58
C₅	526.86	594.16	680.00
D	841.53	905.72	805.32
K	5	5	5

算例	PN	优化目标							D	K
算例	PN	Z₁	Z₂	C₁	C₂	C₃	C₄	C₅	D	K
R202	41	7680.0	0.853	2772.1	1167.6	1957.1	55.2	1727.8	810.1	4
R204	41	6949.7	0.973	2905.5	1254.7	2129.8	60.1	599.6	921.2	4
R206	42	7723.4	0.886	2986.9	1247.9	2236.2	63.1	1189.2	989.1	4
R208	41	6675.9	0.976	2901.5	1167.6	2115.6	59.7	431.5	917.9	4
RC202	40	8440.9	0.853	3269.3	1172.3	2319.7	65.5	1614.1	1024.1	5
RC204	42	7277.5	0.954	3202.6	1195.5	2239.2	63.2	576.8	1002.2	5
RC206	41	8729.1	0.841	3371.4	1291.0	2458.2	69.3	1539.2	1142.8	5
RC208	42	8293.4	0.906	3507.6	1396.5	2648.8	74.8	665.8	1277.4	5

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Green Vehicle Routing Model and Its Solution Algorithm in Cold-chain Logistics Distribution

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