设置货架缓存区的订单和货架排序问题研究

doi:10.16381/j.cnki.issn1003-207x.2024.0255

Abstract

Abstract:

With the rapid development of e-commerce enterprises and the wide application of robotic mobile fulfillment systems， the importance of order picking for warehousing operational efficiency is increasingly evident， and configuring rack buffer zones can enhance order picking efficiency. Therefore， it focuses on the research of the order and rack sequencing problem with rack buffer zones. In the scenario of limited capacity in the rack buffer zone， it aims to jointly optimize the order picking sequence， rack retrieval sequence， and buffering strategy. Taking into consideration factors such as the shared storage mode for products， the quantity of each product stored on individual racks， the ordered quantities in customer orders， and the limited capacity of the buffer zone， an integer programming model is established for the order and rack sequencing problem with rack buffer zones. The objective is to minimize the number of rack retrievals while considering these factors. Considering the characteristics of the problem， an interactive heuristic algorithm is designed to synchronously address the three sub-problems. Through case study experiments， the correctness and effectiveness of the proposed model and algorithm have been verified. The experimental results indicate that the average relative deviation between the feasible solutions obtained by the interactive heuristic algorithm and the exact solutions is approximately 5.4%， demonstrating that the proposed algorithm can achieve high-quality feasible solutions in a relatively short time. Furthermore， comparisons with the baseline algorithm and the heuristic algorithm without the rack buffer zone further validate the efficiency of the proposed algorithm. Specifically， the average improvement in the objective function achieved by the proposed algorithm is about 9.6% compared to the benchmark algorithm， and the implementation of the rack buffer zone significantly reduces the number of times racks are transported during the order fulfillment picking process by about 14.1%. The proposed model and algorithm in this paper provide decision-making foundations for enterprises to strategically set up rack buffer zones， reduce the number of rack retrievals， and enhance order-picking efficiency.

Key words: robotic mobile fulfillment system, order and rack sequencing, rack buffer zone, interactive heuristic algorithm, product quantity

CLC Number:

O211.4

Qianqian Han,Kang Wang,Zhenping Li. Study on the Order and Rack Sequencing Problem with Rack Buffer Zones[J]. Chinese Journal of Management Science, 2026, 34(4): 168-177.

Figures/Tables 10

符号	定义
$N$	订单数量， $n = 1, …, N$
$K$	货架数量， $k = 1, …, K$
$S$	商品数量， $s = 1, …, S$
$P$	时间槽数量， $p = 1, …, P$
$C$	拣选台容量
$H$	货架缓存区容量
$O$	订单集合， $o n ∈ O$
$R$	货架集合， $r k ∈ R$
$q k s$	货架 $r k$ 上存储商品 $s$ 的数量
$d n s$	订单 $o n$ 中订购商品 $s$ 的数量
	决策变量
$x n p$	0-1变量，若订单 $o n$ 在时间槽 $p$ 被拣选为1，否则为0
$y k p$	0-1变量，若在时间槽 $p$ 需要货架 $r k$ 为1，否则为0
$c k p$	0-1变量，若在时间槽 $p$ 将货架 $r k$ 存入缓存区为1，否则为0
$u k p$	0-1变量，若在时间槽 $p$ 出库货架 $r k$ 为1，否则为0
$z n k p s$	整数变量，在时间槽 $p$ 从货架 $r k$ 向订单 $o n$ 中拣选商品s的数量

参数名称	小规模参数取值	大规模参数取值
订单数量（ $N$ ）	4, 6	100, 150, 200
货架数量（ $K$ ）	8, 10	400, 500, 600
商品数量（ $S$ ）	10, 15	1000,1500,2000
拣选台容量（ $C$ ）	3	15
缓存区容量（ $H$ ）	3	10

算例参数	Gurobi		交互启发式算法		$N u m$	$G a p 1$ (%)
$N - K - S$	$z g$	$t g$	$z 1$	$t 1$	$N u m$	$G a p 1$ (%)
4-8-10	2.6	8.8	2.8	0.04	4	7.1
4-8-15	2.4	3.9	2.6	0.05	4	7.7
4-10-10	2.4	127	2.4	0.04	5	0
4-10-15	2.6	9.8	2.8	0.04	4	7.1
6-8-10	2.8	140.4	3.0	0.05	4	6.7
6-8-15	3.0	264.2	3.0	0.05	5	0
6-10-10	2.6	289.7	2.8	0.04	4	7.1
6-10-15	2.8	264.9	3.0	0.05	4	6.7
平均值	2.65	138.6	2.8	0.05	4.25	5.4

算例参数	交互启发式算法		基准算法		无缓存区算法		$G a p 2$ (%)	$G a p 3$ (%)
$N - K - S$	$z ¯ 1$	$t ¯ 1$	$z ¯ 2$	$t ¯ 2$	$z ¯ 3$	$t ¯ 3$	$G a p 2$ (%)	$G a p 3$ (%)
100-400-1000	113.0	0.2	121.6	0.2	130.4	0.2	7.1	13.3
100-400-1500	111.8	0.2	118.8	0.2	124.8	0.2	5.9	10.4
100-400-2000	114.0	0.3	121.0	0.3	123.6	0.3	5.8	7.8
100-500-1000	111.0	0.3	122.0	0.3	129.2	0.2	9.0	14.1
100-500-1500	125.6	0.3	136.8	0.3	146.4	0.3	8.2	14.2
100-500-2000	132.0	0.3	141.8	0.4	149.6	0.4	6.9	11.8
100-600-1000	124.0	0.3	132.6	0.4	143.4	0.4	6.5	13.5
100-600-1500	127.4	0.3	132.8	0.5	141.6	0.4	4.1	10.0
100-600-2000	133.0	0.3	140.6	0.4	148.6	0.3	5.4	10.5
150-400-1000	144.0	0.3	161.4	0.4	169.4	0.3	10.8	15.0
150-400-1500	148.4	0.3	162.4	0.4	171.0	0.4	8.6	13.2
150-400-2000	152.0	0.3	173.4	0.4	181.8	0.4	12.3	16.4
150-500-1000	151.2	0.4	167.8	0.5	181.0	0.4	9.9	16.5
150-500-1500	160.0	0.4	178.6	0.5	191.8	0.4	10.4	16.6
150-500-2000	162.8	0.4	180.6	0.4	189.6	0.4	9.9	14.1
150-600-1000	164.6	0.4	181.0	0.5	196.4	0.5	9.1	16.2
150-600-1500	171.2	0.5	194.8	0.6	200.2	0.5	12.1	14.5
150-600-2000	179.4	0.5	197.6	0.6	205.2	0.5	9.2	12.6
200-400-1000	181.2	0.5	204.2	0.5	214.6	0.4	11.3	15.6
200-400-1500	184.8	0.5	208.0	0.5	219.4	0.4	11.2	15.8
200-400-2000	184.8	0.4	211.8	0.5	217.2	0.4	12.7	14.9
200-500-1000	189.6	0.5	215.4	0.6	226.8	0.5	12.0	16.4
200-500-1500	203.0	0.5	229.0	0.6	238.8	0.5	11.4	15.0
200-500-2000	216.4	0.7	239.8	0.7	252.4	0.6	9.8	14.3
200-600-1000	201.2	0.6	226.2	0.7	237.6	0.5	11.1	15.3
200-600-1500	221.6	0.7	245.2	0.8	258.6	0.7	9.6	14.3
200-600-2000	226.0	0.7	248.6	0.8	258.0	0.7	9.1	12.4
平均值	160.5	0.4	177.5	0.5	186.9	0.4	9.6	14.1

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订单中商品种类数	订单出现概率
1	0.43
2	0.26
3	0.16
4	0.09
5	0.06

Study on the Order and Rack Sequencing Problem with Rack Buffer Zones

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