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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2023, Vol. 57 Issue (11): 2188-2199    DOI: 10.3785/j.issn.1008-973X.2023.11.006
    
Compound operation scheduling optimization in four-way shuttle warehouse system
Li-li XU1(),Yan ZHAN1,*(),Jian-sha LU1,Yi-ding LANG2
1. College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310032, China
2. Ningbo Fujia Industrial Co. Ltd, Ningbo 330200, China
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Abstract  

The compound operation scheduling optimization in four-way shuttle warehouse system was studied to improve the efficiency of storage system operations. A mathematical model was established with the goal of minimizing inbound and outbound operation times to optimize the scheduling problem of the system. This model was based on the combined operation of a four-way shuttle and an elevator, and the collaborative operation characteristics in both horizontal and vertical directions were considered. Furthermore, the model was analyzed under various operating modes by examining the connection between the start and end operation times of the four-way shuttle and the elevator, as well as the starting operation tiers. The method based on the task classification was proposed to initialize the population of the genetic algorithm. The crossover and the mutation of the population were completed to solve the model, and then the task allocation and sequence of the system were optimized. Some experiments were conducted to verify the effectiveness of the improved genetic algorithm. The influence of the number of four-way shuttles on the operation time and system cost was analyzed, and the operation efficiencies of single and double elevators in the system were compared. The effectiveness of the genetic algorithm based on the task classification was verified, and the results showed that the operation efficiency was improved by at least 10.3%, by using the proposed algorithm.

Key words： four-way shuttle warehouse system      scheduling optimization      compound operation      task classification      genetic algorithm     
Received: 09 December 2022      Published: 11 December 2023
CLC:  TP 391  
Fund:  浙江省尖兵研发攻关计划资助项目（2023C01063）；浙江省重点研发计划资助项目（2018C01003）
Corresponding Authors: Yan ZHAN     E-mail: 2111602062@zjut.edu.cn;yzhan@zjut.edu.cn
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Li-li XU
Yan ZHAN
Jian-sha LU
Yi-ding LANG
Cite this article:

Li-li XU,Yan ZHAN,Jian-sha LU,Yi-ding LANG. Compound operation scheduling optimization in four-way shuttle warehouse system. Journal of ZheJiang University (Engineering Science), 2023, 57(11): 2188-2199.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2023.11.006     OR     https://www.zjujournals.com/eng/Y2023/V57/I11/2188


四向穿梭车仓储系统复合作业调度优化

为了提高仓储系统作业效率，对四向穿梭车仓储系统复合作业开展调度优化研究. 在四向穿梭车和提升机采用复合作业完成任务的基础上，考虑设备在水平方向和垂直方向的协同作业特性. 通过四向穿梭车和提升机开始和结束作业时间以及开始作业层数之间的联系，在不同作业模式下进行讨论，从而构建以出入库作业时间最短为目标的数学模型. 提出基于任务分类的方法对遗传算法的种群进行初始化，随后在该方法的基础上完成种群的交叉和变异来求解模型，进而得出系统的最优任务分配及排序. 通过实例分析四向穿梭车数量及单双台提升机对系统作业效率和成本的影响，验证基于任务分类的遗传算法的有效性，结果表明该算法至少提高10.3%的作业效率.


关键词： 四向穿梭车仓储系统,  调度优化,  复合作业,  任务分类,  遗传算法 
Fig.1 Diagram of four-way shuttle warehouse system
Fig.2 Schematic diagram of compound operation path of four-way vehicle system
Fig.3 Diagram of idle load operation path completed by four-way shuttle under $ z(u) = z(v) $
Fig.4 Ptah diagram of two elevators
Fig.5 Flow chart of improved genetic algorithm
Fig.6 Chromosome Examples
Fig.7 Schematic diagram of chromosome crossing operation in first layer
序号 入库货位 序号 出库货位
1 （?10，4，3） 1 （7，19，2）
2 （?1，5，4） 2 （8，9，3）
3 （?8，7，2） 3 （8，3，3）
4 （?9，7，4） 4 （2，17，2）
5 （5，2，3） 5 （9，7，4）
6 （?7，7，1） 6 （6，10，4）
7 （10，7，4） 7 （?10，19，2）
8 （?4，12，3） 8 （2，7，2）
9 （4，8，5） 9 （?5，7，5）
10 （3，8，5） 10 （9，19，5）
11 （?9，17，4） 11 （?4，7，4）
12 （7，12，4） 12 （4，17，3）
13 （?7，3，5） 13 （10，8，1）
14 （2，7，1） 14 （?10，5，1）
15 （10，7，2） 15 （4，13，5）
16 （?5，15，5） 16 （?7，2，1）
17 （?1，7，3） 17 （6，7，4）
18 （?7，15，1） 18 （2，15，1）
19 （?7，7，3） 19 （4，14，1）
20 （2，7，4） 20 （8，4，2）
Tab.1 Inbound and outbound tasks list
编号 装载货位 编号 装载货位 编号 装载货位
1 (3, 3, 5) 9 (2, 6, 3) 17 (3, 17, 1)
2 (5, 7, 3) 10 (5, 6, 3) 18 (5, 2, 5)
3 (3, 16, 1) 11 (5, 2, 4) 19 (5, 3, 3)
4 (4, 2, 4) 12 (9, 9, 3) 20 (?10, 3, 4)
5 (1, 11, 3) 13 (?10, 2, 3) 21 (5, 2, 1)
6 (2, 14, 3) 14 (6, 17, 4) 22 (4, 7, 5)
7 (2, 13, 3) 15 (5, 2, 2) 23 (5, 5, 2)
8 (7, 7, 4) 16 (5, 3, 4) 24 (?4, 4, 4)
Tab.2 Loading position under initial status
m TZ/s TW/s TM/s TC/s
1 186.36 0 73.43 186.36
2 104.40 47.70 65.16 152.10
63.20 88.90
3 67.90 61.22 59.35 129.12
42.24 86.88
35.30 93.82
4 24.06 95.47 64.86 119.53
51.93 65.20
55.90 63.63
64.60 54.93
Tab.3 System operation time of IGA optimization under different number of four-way shuttle
Fig.8 Cost under different numbers of four-way shuttles
编号 作业顺序
1 3-6, 4-7,19-11,14-16,15-8,17-12
2 2-1,10-3,20-5,9-15,16-14,7-10
3 8-4,13-9,12-18,11-17,5-2,6-19,18-13
Tab.4 Sequence under number of four-way vehicles of three
no 算法 AVE/s δ/% VAR
20 IGA 188.12 11.9 4.60
GA 213.54 6.78
50 IGA 286.90 12.3 3.52
GA 327.31 4.38
70 IGA 416.67 16.3 5.57
GA 467.80 7.86
100 IGA 724.30 10.3 6.67
GA 787.20 9.65
200 IGA 2068.70 15.7 10.39
GA 2302.67 16.74
500 IGA 5643.20 17.0 14.60
GA 6096.10 19.30
Tab.5 Algorithm optimization results under different order sizes
Fig.9 Algorithm iteration diagram under order size of 500
Fig.10 System operation time optimized by algorithm under order size of 200
Fig.11 Completion time under kinds of elevators and order sizes
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