考虑配送截止时间的“货到人”订单拣选优化问题研究

doi:10.16381/j.cnki.issn1003-207x.2022.1049

摘要/Abstract

摘要：

电商企业每日产生数量庞大的订单，如何高效地实现订单拣选及配送成为电商企业面临的重要挑战。一方面，订单数量大、商品种类多等特点使传统“人到货”拣选模式效率大幅降低；另一方面，诸如当日达、次日达等考虑配送截止时间的配送策略对电商企业提出了更高的时效性要求。为此，本文以最小化订单总延迟时间为目标，构建考虑配送截止时间的“货到人”订单拣选优化整数规划模型。针对该模型的特点，首先，提出改进的知识引导果蝇优化算法确定订单分配和排序决策；然后，设计最短等待时间订单拣选规则，优化货架访问顺序；最后，通过数值实验验证了模型的可行性和算法的有效性。实验结果表明，在确保快速求解的前提下，相较于现实中常用的先到先服务策略，改进的知识引导果蝇优化算法及最短等待时间订单拣选规则能显著提高解的质量。本文提出的模型和算法可为电商企业提高运营效率、降低物流成本提供科学的决策依据。

关键词: “货到人”订单拣选, 配送截止时间, 知识引导, 果蝇优化算法, 启发式算法

Abstract:

With the rapid advancement and widespread adoption of E-commerce， online shopping has become an integral component of modern life. However， the unique characteristics of online orders pose significant challenges to warehouse operational efficiency. A primary concern is the heightened consumer demand for timely deliveries， particularly with the increasing prevalence of next-day and same-day delivery services， which substantially amplify delivery complexities. Additionally， the sheer volume of daily orders， each typically comprising multiple stock-keeping units （SKUs）， coupled with the overlap of SKUs across different orders， further complicates the process. Moreover， real-time orders often originate from diverse geographic regions， introducing additional logistical challenges. These factors collectively exert considerable pressure on the order picking and delivery systems of E-commerce enterprises. According to Statista， during 2020–2021， over 4.5% of Amazon orders experienced delays. In traditional picker-to-parts systems， pickers spend approximately 60% of their time traveling within the warehouse. To enhance efficiency and reduce operational costs， E-commerce platforms have increasingly adopted automated order picking systems， such as parts-to-picker systems or robotic mobile fulfillment systems （RMFS）， exemplified by Amazon’s Kiva system and JD.com’s Ground wolf system. Motivated by these operational challenges， this study focuses on optimizing decision-making processes in intelligent warehouses with delivery deadlines to minimize total order tardiness.

Key operational challenges include order assignment， order sequencing， and rack visit sequencing. （i） Order assignment： In warehouses with multiple parallel picking stations， balancing workloads and optimizing efficiency across stations is critical due to variations in order sizes， SKU compositions， and delivery due dates. （ii） Order sequencing： Orders arrive with varying due dates， necessitating prioritization of urgent orders to reduce the likelihood of tardiness. （iii） Rack visit sequencing： Adjacent orders at a picking station may share common SKUs， enabling simultaneous retrieval. However， since each rack carries only one type of SKU， determining the optimal sequence for retrieving SKUs—equivalent to sequencing rack visits—becomes a pivotal issue.

To address these challenges， this study formulates a mixed-integer programming model aimed at minimizing total order tardiness in parts-to-picker systems with delivery due dates. Leveraging the model’s characteristics， an improved knowledge-guided fruit fly optimization algorithm （IKGFOA） is proposed to determine optimal order allocation and sequencing schedules. The algorithm incorporates heuristic rules to accelerate solution convergence and introduces a knowledge-guided search mechanism to balance local and global search capabilities， thereby enhancing the rationality of order assignment and sequencing decisions. Additionally， a shortest waiting time （SWT） rule is designed to optimize order picking and rack visit sequences at each picking station.

The feasibility of the proposed model and the effectiveness of the algorithm are validated through numerical experiments. Small-scale experiments demonstrate that the IKGFOA-SWT algorithm achieves solutions comparable to those obtained by CPLEX under certain conditions. Large-scale experiments further confirm the algorithm’s superiority over the commonly used first-come-first-served （FCFS） strategy in real-world applications. The model and algorithms developed in this study provide E-commerce enterprises with scientifically robust decision-making tools， emphasizing the importance of incorporating delivery due dates into operational optimization strategies to minimize order tardiness in intelligent warehouses.

Key words: “parts-to-picker” order picking, delivery due dates, knowledge-guided, fruit fly optimization algorithm, heuristic algorithm

中图分类号:

F274

赵金龙, 蒋忠中, 万明重, 张春征. 考虑配送截止时间的“货到人”订单拣选优化问题研究[J]. 中国管理科学, 2025, 33(3): 239-255.

Jinlong Zhao, Zhongzhong Jiang, Mingzhong Wan, Chunzheng Zhang. Order Picking Optimization in "Parts-to-Picker" Systems Considering Delivery Due Dates[J]. Chinese Journal of Management Science, 2025, 33(3): 239-255.

图/表 20

图1

图2

图3

表1

图 4

表2

编码"

$x i j$	$(O 1, M 1)$	$(O 2, M 1)$	$(O 3, M 2)$	$(O 4, M 1)$	$(O 5, M 1)$	$(O 6, M 2)$	$(O 7, M 2)$	$(O 8, M 1)$
$x i p$	$(O 1, 7)$	$(O 2, 3)$	$(O 3, 4)$	$(O 4, 1)$	$(O 5, 2)$	$(O 6, 8)$	$(O 7, 6)$	$(O 8, 5)$

表2

表3

解码"

$M 1$	$O 4$	$O 5$	$O 2$	$O 8$	$O 1$
$M 2$	$O 3$	$O 7$	$O 6$	-	-

表3

图 5

图 6

表4

实验一结果"

$N$	(10,5)		(15,5)		(15,10)		(20,10)		(25,15)
$N$	$t a r$	$t i m e$	$t a r$	$t i m e$	$t a r$	$t i m e$	$t a r$	$t i m e$	$t a r$	$t i m e$
50	199.00	63.90	193.00	93.16	155.00	123.94	154.00	222.65	139.60	324.34
100	444.00	125.55	448.00	183.07	361.00	251.73	360.00	453.68	317.00	656.20
150	1404.00	197.50	1384.00	293.81	1199.00	390.93	1186.00	731.23	1173.00	1142.86

表4

图 7

表5

实验二结果（MTCR=0.6）"

$M$	$N$	CPLEX		FCFS		IKGFOA-SWT		改善幅度
$M$	$N$	$t a r$	$t i m e$	$t a r$	$t i m e$	$t a r$	$t i m e$	$\| G a p 1 \|$	$G a p 1 (%)$	$\| G a p 2 \|$	$G a p 2 (%)$
3	10	3.80	247.59	10.00	0.06	3.80	35.68	$-$ 6.20	$-$ 163.16	0.00	0.00
3	15	5.00	2896.780	14.00	0.04	5.00	58.52	$-$ 9.00	$-$ 180.00	0.00	0.00
3	20	25.20	3600.00	33.40	0.10	15.80	65.64	$-$ 8.20	$-$ 32.54	9.40	37.30

表5

表6

实验二结果（MTCR=0.7）"

$M$	$N$	CPLEX		FCFS		IKGFOA-SWT		改善幅度
$M$	$N$	$t a r$	$t i m e$	$t a r$	$t i m e$	$t a r$	$t i m e$	$\| G a p 1 \|$	$G a p 1 (%)$	$\| G a p 2 \|$	$G a p 2 (%)$
3	10	4.00	777.18	11.80	0.05	4.00	35.95	$-$ 7.80	$-$ 195.00	0.00	0.00
3	15	8.20	2979.40	23.80	0.03	8.20	48.30	$-$ 15.60	$-$ 190.24	0.00	0.00
3	20	15.00	3600.00	28.00	0.10	10.80	68.49	$-$ 13.00	$-$ 86.67	4.20	28.00

表6

表7

实验二结果（MTCR=0.8）"

$M$	$N$	CPLEX		FCFS		IKGFOA-SWT		改善幅度
$M$	$N$	$t a r$	$t i m e$	$t a r$	$t i m e$	$t a r$	$t i m e$	$\| G a p 1 \|$	$G a p 1 (%)$	$\| G a p 2 \|$	$G a p 2 (%)$
3	10	14.00	3600.00	23.40	0.03	14.00	36.88	$-$ 9.40	$-$ 67.14	0.00	0.00
3	15	12.00	3115.90	29.20	0.04	10.80	51.85	$-$ 17.20	$-$ 143.33	1.20	10.00
3	20	28.60	3600.00	49.80	0.03	14.80	61.15	$-$ 21.20	$-$ 74.13	13.80	48.25

表7

图 8

表8

实验三结果（MTCR=0.6）"

$M$	$N$	FCFS		IKGFOA		IKGFOA-SWT		改善幅度
$M$	$N$	$t a r$	$t i m e$	$t a r$	$t i m e$	$t a r$	$t i m e$	$\| G a p 3 \|$	$G a p 3 (%)$	$\| G a p 4 \|$	$G a p 4 (%)$
3	50	194.40	0.04	104.20	127.62	97.20	127.77	90.20	46.40	97.20	50.00
3	100	731.60	0.05	496.40	254.02	465.40	253.88	235.20	32.15	266.20	36.39
3	150	1381.80	0.06	1020.40	386.58	941.60	387.04	361.40	26.15	440.20	31.86
5	50	86.80	0.03	41.40	125.99	39.20	125.67	45.40	52.30	47.60	54.84
5	100	318.60	0.05	212.60	254.51	197.60	252.04	106.00	33.27	121.00	37.98
5	150	496.00	0.07	376.60	383.74	357.20	383.68	119.40	24.07	138.80	27.98

表8

表9

实验二结果（MTCR=0.7）"

$M$	$N$	FCFS		IKGFOA		IKGFOA-SWT		改善幅度
$M$	$N$	$t a r$	$t i m e$	$t a r$	$t i m e$	$t a r$	$t i m e$	$\| G a p 3 \|$	$G a p 3 (%)$	$\| G a p 4 \|$	$G a p 4 (%)$
3	50	254.80	0.04	148.00	127.79	139.40	127.59	106.80	41.92	115.40	45.29
3	100	728.80	0.04	459.40	253.69	432.00	252.42	269.40	36.96	296.80	40.72
3	150	1920.40	0.07	1433.80	395.80	1374.80	395.02	486.60	25.34	545.60	28.41
5	50	128.20	0.03	66.00	124.43	62.20	124.50	62.20	48.52	66.00	51.48
5	100	294.00	0.05	178.80	249.17	166.60	249.06	115.20	39.18	127.40	43.33
5	150	739.80	0.06	538.00	387.73	507.40	387.86	201.80	27.28	232.40	31.41

表9

表10

实验二结果（MTCR=0.8）"

$M$	$N$	FCFS		IKGFOA		IKGFOA-SWT		改善幅度
$M$	$N$	$t a r$	$t i m e$	$t a r$	$t i m e$	$t a r$	$t i m e$	$\| G a p 3 \|$	$G a p 3 (%)$	$\| G a p 4 \|$	$G a p 4 (%)$
3	50	358.60	0.03	181.40	124.62	170.80	123.44	177.20	49.41	187.80	52.37
3	100	1296.80	0.05	853.60	247.83	789.60	247.41	443.20	34.18	507.20	39.11
3	150	2530.20	0.06	1902.80	382.32	1795.20	379.83	627.40	24.80	735.00	29.05
5	50	153.80	0.02	90.00	119.38	86.40	118.89	63.08	41.48	67.40	43.82
5	100	578.60	0.04	358.20	245.87	336.00	245.82	220.40	38.09	242.60	41.93
5	150	990.60	0.06	728.60	375.44	697.20	375.08	262.00	26.45	293.40	29.62

表10

图 9

图 10

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