考虑骑手配送时效奖惩的外卖多目标路径优化研究

doi:10.16381/j.cnki.issn1003-207x.2024.2209

Abstract

Abstract:

Presently， the takeaway industry continues to demonstrate robust growth， with takeaway services becoming increasingly entrenched in people's daily lives. Nevertheless， given the differences in focal points of platforms， consumers， and riders， a pronounced discord of interests has emerged among the three parties， even hindering the development of the industry. Distribution timeliness， a pivotal factor， impacts not only customer satisfaction and platform profits but also directly influences the rewards and punishments for riders. To address these challenges， a multi-objective routing optimization problem is proposed for takeout delivery， considering the rewards and punishments for riders based on the perspective of distribution timeliness. The primary aim of this study is to further balance the interests of all parties dynamically. A soft time window concept is adopted to portray customer expectations and tolerance of delivery time， and a linear time satisfaction function is constructed to assess customer satisfaction. Concurrently， the rider's rewards and penalties are designated， encompassing the rider's overtime penalty cost based on on-time rate， the order overtime penalty cost in step-pricing style， and the performance reward based on satisfaction. The functions of rider revenue， driving cost， waiting cost， and platform revenue are then combined to establish a complex objective optimization model for maximizing customer satisfaction， rider revenue， and platform profit. Secondly， an enhanced NSGA-II algorithm based on KNN classification is proposed. The proposed algorithm first allocates orders based on geographic distance and time window， generates high-quality and diverse initial populations， and subsequently outputs a Pareto solution using the enhanced NSGA-II algorithm. To assess the efficacy of the proposed algorithm， two ordinary region examples and one commercial region example are utilized for testing purposes. It then compares this algorithm with the traditional NSGA-II and MOPSO algorithms for validation purposes. The convergence of the algorithm and the diversity of the solution set are further verified by analyzing the iterative convergence curves of each objective function as well as the indicators of spacing and maximum spread of the solution set. Finally， a comparative analysis of customer satisfaction， rider revenue， and platform profit under different reward and punishment rules is conducted. It is indicated that the platform's punishment measures can enhance delivery efficiency， foster customer satisfaction and augment platform revenue. Equitable sanctions have the potential to engender a mutually beneficial scenario for all three parties. While the incentive mechanism may temporarily reduce platform revenue， it can enhance delivery efficiency and rider revenue. Consequently， a theoretical foundation is offered for the coordination of interests among multiple parties in the future of takeaway services and the establishment of a platform's reward and punishment mechanism for riders.

Key words: takeout delivery, distribution timeliness, rewards and penalties of riders, multi-objective optimization, the improved NSGA-II algorithm

CLC Number:

C931

Hao Xiong,Xiaodie Chen,Huili Yan. Multi-Objective Routing Optimization of Takeout Delivery Considering Rider Rewards and Penalties of Distribution Timeliness[J]. Chinese Journal of Management Science, 2026, 34(9): 209-224.

Figures/Tables 18

符号	定义	符号	定义
R	订单集合	$c 1$	骑手单位行驶成本
$r$	订单编号	$c 2$	骑手单位等待成本
S	商家坐标集合，可以表示为 $S = 1,2, …, s$	$N$	节点坐标的合集，可表示为 $N = S ⋃ C ∪ {O}$
C	顾客集合，可以表示为 $C = s + 1, s + 2, …, s + c$	$y k r$	0-1变量，若为1表示订单r分配给骑手k,否则为0
O	配送中心	$θ$	平台佣金比例
$φ i$	骑手配送收入， $i ∈ {1,2, 3}$	$b$	平台保底佣金
$K$	骑手集合	$α$	顾客满意度奖励标准
$k$	骑手编号	$β$	允许超时订单数量
$S r$	订单r对应的商家	$c 3$	超时惩罚成本
$C r$	订单r对应的顾客	$O r$	订单r的餐饮金额
$m k$	骑手k配送订单的平均满意度	$n k$	骑手k超时订单数量, $k ∈ K$
$Q$	电瓶车最大可承载容量	$d k$	骑手k激励补贴额
$D$	电瓶车最长可行驶公里数	$t r 0$	订单r商家出餐时间
$x i j$	由节点i到节点j所需行驶的距离， $i, j ∈ N$	$E r$	订单r允许车辆到达的最早时间
$w i j k$	0-1变量，若为1表示骑手k选择从商家点i至顾客点j,否则为0	$z j i k$	0-1变量，若为1表示骑手k从顾客点j至商家点i，否则为0
$e r$	订单r满意的最早到达时间	$L r$	订单r允许车辆到达的最晚时间
$H r$	平台赚取的订单r收入	$l r$	订单r满意的最晚到达时间
$D r$	订单r配送收入, $r ∈ R$	$t i j$	骑手从节点i到节点j的行驶时间
$a$	骑手绩效奖励	$t i k$	骑手k到达节点i的时间
$t S r k$	骑手k配送订单r时到达商家节点的时间	$c 4 i$	骑手超时单位时间惩罚成本， $i ∈ {1,2}$

$c 1$	$c 2$	$c 3$	$φ 1$	$φ 2$	$φ 3$	$θ$	$a$	$b$	$α$	β	$c 41$	$c 42$	$λ$
0.3元/km	0.35元/min	2元/单	8元/单	10元/单	12元/单	21%	25元	12元	85%	1	0.1元/分钟	0.2元/分钟	0.1

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算例	测试次数	算法类型	顾客满意度(%)	骑手收益(元)	平台利润(元)	测试次数	算法类型	顾客满意度(%)	骑手收益(元)	平台利润(元)
算例1	1	KNN-NSGA-II	82.38	41.75	352.10	4	KNN-NSGA-II	81.28	37.01	350.27
		NSGA-II	69.35	28.50	338.14		NSGA-II	72.96	32.88	331.47
		MOPSO	72.30	27.5	327.50		MOPSO	68.51	20.87	337.01
	2	KNN-NSGA-II	83.33	39.28	354.05	5	KNN-NSGA-II	82.10	41.04	348.80
		NSGA-II	75.07	32.46	343.63		NSGA-II	75.32	32.81	332.61
		MOPSO	75.00	29.73	324.19		MOPSO	75.74	37.13	302.08
	3	KNN-NSGA-II	81.65	40.16	353.08	6	KNN-NSGA-II	83.25	40.89	356.90
		NSGA-II	73.67	34.63	344.15		NSGA-II	73.08	31.03	334.11
		MOPSO	69.89	21.72	334.60		MOPSO	65.18	21.34	333.68
算例2	1	KNN-NSGA-II	72.64	31.94	444.89	4	KNN-NSGA-II	72.10	31.95	439.45
		NSGA-II	64.23	20.42	422.13		NSGA-II	62.37	17.18	421.94
		MOPSO	65.00	22.56	423.25		MOPSO	65.48	19.84	428.84
	2	KNN-NSGA-II	72.63	31.97	458.64	5	KNN-NSGA-II	72.43	30.14	439.71
		NSGA-II	61.22	18.97	420.24		NSGA-II	62.37	17.82	409.61
		MOPSO	66.22	19.83	421.32		MOPSO	66.90	20.41	429.91
	3	KNN-NSGA-II	72.61	30.65	437.71	6	KNN-NSGA-II	71.53	31.03	436.70
		NSGA-II	62.85	19.51	403.11		NSGA-II	61.39	18.08	413.11
		MOPSO	62.87	19.10	419.12		MOPSO	67.55	22.32	429.61
算例3	1	KNN-NSGA-II	79.50	38.87	803.83	4	KNN-NSGA-II	78.37	37.95	802.00
		NSGA-II	61.25	30.97	786.90		NSGA-II	66.39	30.89	789.75
		MOPSO	64.67	34.93	787.34		MOPSO	66.53	30.92	790.35
	2	KNN-NSGA-II	81.15	40.81	806.75	5	KNN-NSGA-II	80.13	39.87	804.41
		NSGA-II	62.74	31.52	786.77		NSGA-II	63.14	28.83	784.19
		MOPSO	62.03	30.01	774.40		MOPSO	62.00	31.31	783.55
	3	KNN-NSGA-II	80.79	41.23	805.51	6	KNN-NSGA-II	82.28	42.74	809.71
		NSGA-II	64.34	28.48	785.22		NSGA-II	68.36	30.88	784.15
		MOPSO	63.28	28.43	783.75		MOPSO	69.55	33.79	780.25

算例	指标	测试1	测试2	测试3	测试4	测试5	测试6
算例1	MS	1.5781	1.3764	1.3377	1.5338	1.4379	1.3984
算例1	Spacing	0.5821	0.6022	0.5921	0.6234	0.6102	0.6491
算例2	MS	1.3518	1.3103	1.3061	1.3710	1.4881	1.4341
算例2	Spacing	0.6595	0.6009	0.6464	0.5868	0.5357	0.6250
算例3	MS	1.4344	1.4614	1.4194	1.4181	1.4118	1.3649
算例3	Spacing	0.6013	0.6146	0.5693	0.6115	0.6213	0.6129

Multi-Objective Routing Optimization of Takeout Delivery Considering Rider Rewards and Penalties of Distribution Timeliness

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