考虑能量消耗的纯电动物流车柔性时间窗路径规划问题

doi:10.13229/j.cnki.jdxbgxb.20210822

摘要/Abstract

摘要：

为提高物流企业收益，从模型驱动下的实验分析角度，研究了柔性时间窗约束下的纯电动物流车路径规划问题（EVRP-FlexTW）。首先，提出了考虑启动-制动的纯电动物流车能量消耗模型，揭示纯电动物流车在行驶过程中的能量消耗规律；其次，考虑了能量消耗的影响，增加车辆载重、柔性时间窗和耗电量等约束，建立了总配送成本最低的纯电动物流车路径优化模型，并设计了蚁群算法求解模型。行驶速度、柔性时间窗对决策目标的敏感性分析表明：减小纯电动物流车的最大行驶速度，会得到更好的路径规划结果；满足柔性时间窗约束虽然付出了更大的行驶距离和耗电量，但能够达成降低总配送成本的目标；上述发现体现了模型和算法的有效性。

关键词: 运输规划, 柔性时间窗, 纯电动物流车, 路径规划问题, 能量消耗估计模型

Abstract:

Vehicle Routing Problem （VRP） with flexible time window is useful to increase the profits of logistics companies by loosening the time constraints with less penalty cost. In this paper， the electric logistics vehicle routing problem with flexible time window （EVRP-FlexTW） is studied as a model driven experimental approach. Firstly， an energy consumption model considering the start-brake process is proposed for electric logistics vehicles to reveal their characteristics of energy consumption. Then the influence of energy consumption is integrated into the EVRP-FlexTW model with minimum total distribution cost in consideration in additional constraints such as vehicle loading capacity， flexible time window and electrical energy. The improved Ant Colony Algorithm is also designed to solve the model. Sensitivity analysis on the trip speed and flexible time window impact to the proposed model shows that reducing the maximum driving speed is generally contributed to get the better routing solution. Satisfying the constraints of flexible time window cannot shorten the distribution distance or reduce the electricity consumption of electric vehicles but can achieve the lowest total distribution cost. As a whole， those founding can come to the proposed model validation.

Key words: transportation planning, flexible time window, electric delivery vehicles, vehicle routing problem, energy consumption estimation model

中图分类号:

N945.15

孙宝凤,刘娇娇,姚天姿,任欣欣. 考虑能量消耗的纯电动物流车柔性时间窗路径规划问题[J]. 吉林大学学报(工学版), 2023, 53(4): 1047-1059.

Bao-feng SUN,Jiao-jiao LIU,Tian-zi YAO,Xin-xin REN. Electric delivery vehicle routing problem with flexible time window integrated with energy consumption estimation[J]. Journal of Jilin University(Engineering and Technology Edition), 2023, 53(4): 1047-1059.

图/表 7

图1

表1

TC最低配送方案"

车辆编号	行驶路径顺序 $r o u t e$	总载重 $S u m l o a d$ /kg	总耗电量 $E$ /（kW·h）	总距离 $D$ /km	总时间 $t$ /min
合计		3696.16	248.57	623.59	1090.54
1	0→7→1→11→2→3→4→6→D→8→10→0	1289.28	88.05	221.36	411.16
2	0→13→5→9→16→15→I→14→20→24→17→0	1363.20	103.65	258.18	449.32
3	0→18→12→25→19→21→23→22→0	1043.68	56.87	144.05	230.06

表1

表2

不同vˉij下纯电动物流车的eˉij (kW·h)"

$v ˉ i j$		$d ˉ i j$ =50 m	$d ˉ i j$ =200 m	$d ˉ i j$ =350 m	$d ˉ i j$ =500 m	$d ˉ i j$ =650 m	$d ˉ i j$ =800 m	$d ˉ i j$ =900 m	$d ˉ i j$ =990 m
变速	48 km/h	0.074	0.188	0.228	0.267	0.306	0.346	0.372	0.309
	54 km/h	0.075	0.228	0.272	0.315	0.359	0.403	0.407	0.342
	60 km/h	0.076	0.292	0.340	0.389	0.442	0.510	0.492	0.428
匀速	48 km/h	0.013	0.053	0.092	0.131	0.171	0.210	0.236	0.260
	54 km/h	0.015	0.058	0.102	0.146	0.190	0.233	0.262	0.289
	60 km/h	0.016	0.065	0.113	0.162	0.210	0.259	0.291	0.320

表2

图2

图3

表3

不同vˉij条件下求解结果对比"

$v ˉ i j$ /（km·h^-1）	$n *$ /辆	$D$ /km	$W$	$E$ /（kW·h）	$T C$ /元
60	3	648.47	0.782	298.37	832.42
54	3	623.59	0.789	248.56	783.65
48	3	542.8	0.791	184.99	618.48
42	3	576.92	0.792	168.97	493.29
36	3	593.26	0.790	147.63	443.33
30	4	639.48	0.497	148.44	619.87

表3

表4

柔性时间窗系数组合求解结果对比"

客户数量N	时间窗系数组合	$n *$ /辆	$D$ /km	$W$	$E$ /（kW·h）	$T C$ /元
$15$	（1） $p i = 0.25, (C e, C d) = (0.5,1.0)$	2	422.42	0.703	166.47	536.86
	（2） $p i = 0.50, (C e, C d) = (0.5,1.0)$	2	407.33	0.706	160.90	502.02
	（3） $p i = 0.25, (C e, C d) = (2.0,4.0)$	2	429.27	0.697	168.82	599.21
	（4） $p i = 0.50, (C e, C d) = (2.0,4.0)$	2	425.21	0.705	167.15	562.89
	（5） $无 p i, (C e, C d) = (0.5,1.0)$	2	364.10	0.702	143.42	603.82
	（6） $无 p i, (C e, C d) = (2.0,4.0)$	2	430.64	0.706	169.43	851.50
$25$	（7） $p i = 0.25, (C e, C d) = (0.5,1.0)$	3	623.59	0.789	248.56	783.64
	（8） $p i = 0.50, (C e, C d) = (0.5,1.0)$	3	579.06	0.790	230.75	762.18
	（9） $p i = 0.25, (C e, C d) = (2.0,4.0)$	3	628.04	0.778	259.11	1255.07
	（10） $p i = 0.50, (C e, C d) = (2.0,4.0)$	3	604.93	0.790	240.7675	1052.62
	（11） $无 p i, (C e, C d) = (0.5,1.0)$	3	606.35	0.788	241.63	983.73
	（12） $无 p i, (C e, C d) = (2.0,4.0)$	3	688.39	0.789	274.5864	1418.52

表4

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