机械加工生产线平衡问题分类、研究现状及展望

胡俊逸; 张则强; 刘思璐; 何宗兴; 杨峰

doi:10.3969/j.issn.0258-2724.20260064

机械加工生产线平衡问题分类、研究现状及展望

doi: 10.3969/j.issn.0258-2724.20260064

胡俊逸^{1, 2,},
张则强^{1, 3, 4, ,},
刘思璐^{5, 6},
何宗兴¹,
杨峰¹

1.
西南交通大学轨道交通运维技术与装备四川省重点实验室，四川成都 610031
2.
浙江交通职业技术学院轨道交通学院，浙江杭州 311112
3.
西南交通大学桥梁智能与绿色建造全国重点实验室，四川成都 611756
4.
西南交通大学唐山研究院，河北唐山 063000
5.
西南交通大学创新创业学院，四川成都 611756
6.
西南交通大学经济管理学院，四川成都 610031

基金项目: 国家自然科学基金项目（52375268，52342505，72401239）；教育部人文社会科学研究规划基金项目（23YJA630139）；河北省自然科学基金项目（E2024105031）；四川省科技计划（2025ZNSFSC0425，2024NSFSC1048）

详细信息

作者简介:
胡俊逸（1986—），男，副教授，博士研究生，研究方向为制造系统建模与优化，E-mail：hujunyi_jt@zjviti.edu.com

通讯作者:
张则强（1978—），男，教授，博士，研究方向为制造系统与智能装备，E-mail： zhangzq@home.swjtu.edu.cn

中图分类号: TG95；TG5；TP18
计量
- 文章访问数: 115
- HTML全文浏览量: 54
- PDF下载量: 16
- 被引次数: 0
出版历程
- 收稿日期: 2026-01-31
- 修回日期: 2026-04-19
- 刊出日期: 2026-04-23

Classification, Status, and Prospects of Transfer Line Balancing Problems

HU Junyi^{1, 2
,},
ZHANG Zeqiang^{1, 3, 4
, ,},
LIU Silu^{5, 6},
HE Zongxing¹,
YANG Feng¹

1.
Technology and Equipment of Rail Transit Operation and Maintenance Key Laboratory of Sichuan Province, School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China
2.
School of Rail Transit, Zhejiang Institute of Communications, Hangzhou 311112, China
3.
State Key Laboratory of Bridge Intelligent and Green Construction, Southwest Jiaotong University, Chengdu 611756, China
4.
Tangshan Institute, Southwest Jiaotong University, Tangshan 063000, China
5.
School of Innovation and Entrepreneurship, Southwest Jiaotong University, Chengdu 611756, China
6.
School of Economics and Management, Southwest Jiaotong University, Chengdu 610031, China

摘要

摘要:
机加工线平衡问题（TLBP）广泛应用于大批量制造的产品结构件生产流程，通过将零件每个加工要素合理分配到各个工作站的机床中，实现机加工产线高效平衡生产. TLBP的研究对于提升产品加工效率、质量和产量，并降低综合成本具有重要意义，该问题已被研究27年，由于问题的特殊性和工艺复杂性导致机加工线平衡问题无法直接适用装配线和拆卸线平衡问题模型及求解方法，针对该问题的研究热度不足且现有文献较少. 尽管研究历史悠久，但国内至今尚无综述性研究系统梳理其过去、当前及未来的发展脉络. 本文采用层次-元组复合表示法对问题进行系统剖析，对组成问题框架的3个关键层次（问题结构类型层次、问题系统配置层次、问题决策支持层次）进行详尽分析和多维展示. 为该领域提供结构化的全景视图，明晰研究现状的同时重点提炼出研究盲点，并指明未来可能的研究方向.
- 机加工产线 /
- 机加工传输线 /
- 生产线平衡 /
- 生产线设计
Abstract:
The transfer line balancing problem (TLBP) is widely applied in the production process of structural components in high-volume manufacturing. By reasonably allocating each processing element of parts to the machine tools in each workstation, efficient and balanced production of machining production lines is achieved. The research on TLBP is of great significance for improving product processing efficiency, quality, and output, as well as reducing comprehensive costs. TLBP has been studied for 27 years. However, due to the particularity of the problem and the complexity of the process, the models and solution methods for assembly line and disassembly line balancing problems cannot be directly applied to solving TLBP. As a result, the research on this problem has not received sufficient attention, and the existing literature is limited. Despite its long research history, there is still no systematic review in China that sorts out its past, current, and future development context. Therefore, a hierarchical-tuple composite representation method was adopted to systematically analyze the problem. The in-depth analysis and multi-dimensional display were conducted on the three key levels composing the problem framework: the level of problem structure types, the level of problem system configuration, and the level of problem decision support. A structured panoramic view of the field was provided, and the current research status was clarified. The research blind spots were refined, and possible future research directions were pointed out.
- machining production line /
- machining transfer line /
- production line balancing /
- production line design

HTML全文

图 1 工位图

Figure 1. Machine tool workstation

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图 2 双主轴机床示意

Figure 2. Dual-spindle machine tool

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图 3 六主轴珩磨机示意

Figure 3. Six-spindle honing machine

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图 4 TLBP研究的英文关键词共现图

Figure 4. Co-occurrence map of English keywords in TLBP research

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图 5 TLBP研究合作者网络

Figure 5. Collaboration network map in TLBP research

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图 6 国内外TLBP问题年度发表论文数量趋势

Figure 6. Trends in annual publication volume of TLBP-related research papers in China and foreign countries

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图 7 TLBP问题的结构类型

Figure 7. Structural types of TLBP

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图 8 TLBP的问题规格定义

Figure 8. Specification definition for TLBP

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图 9 车铣复合机床的刀具转塔

Figure 9. Tool turret of turning-milling compound machine tool

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图 10 大型卧式加工中心的可旋转工作台

Figure 10. Rotary worktable of large horizontal machining center

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图 11 TLBP问题的优化目标分类与定义

Figure 11. Classification and definition of optimization objectives for TLBP

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图 12 TLBP问题求解方法

Figure 12. Solution methods for TLBP

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图 13 3种机加工线类型不同系统结构频数

Figure 13. Frequencies of different system structures for three machining line types

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图 14 β₁设备相关特性参数对比频率图

Figure 14. Frequency comparison of β₁ equipment-related characteristic parameters

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图 15 β₂时间相关特性参数对比频率图

Figure 15. Frequency comparison of β₂ time-related characteristic parameters

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图 16 β₃工艺相关特性参数对比频率图

Figure 16. Frequency comparison of β₃ process-related characteristic parameters

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图 17 战术层目标函数θ₁、θ₂出现频率对比

Figure 17. Comparison of occurrence frequencies of tactical-level objective functions （θ₁ and θ₂）

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图 18 战略层目标函数θ₃、θ₄、θ₅出现频率对比

Figure 18. Comparison of occurrence frequencies of strategic-level objective functions （θ₃, θ₄, and θ₅）

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表 1 文献分类详表

Table 1. Detailed literature classification

文献	类型	问题结构（α₁r + r） + α₂ + α₃	问题规格			目标函数 θ	决策层级	求解方法
文献	类型	问题结构（α₁r + r） + α₂ + α₃	β₁	β₂	β₃	目标函数 θ	决策层级	求解方法
文献[4]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	MP, G
文献[46]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	MP, D
文献[47]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	MP, G
文献[48]	DTL	（S1） + 0 + 1	Ts，MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	MP, B&B
文献[49]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	MP, H
文献[50]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	MP, H
文献[51]	FTL	（Sn） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	MP
文献[52]	DTL	（S1） + 0 + 1	MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	H
文献[53]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	H
文献[54]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	B&B
文献[55]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	H
文献[56]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	MP
文献[57]	RTL	（PS1 + 0） + 0 + 1	MCS	Tdst	Cprec	Cycti	TD	Sim
文献[58]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	MP, H
文献[59]	DTL	（S1） + 0 + 1	MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	MP, D
文献[60]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	MP, H
文献[22]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	G
文献[61]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	D
文献[62]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	RM
文献[63]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	GRASP
文献[64]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	G, MP，H
文献[65]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	G
文献[66]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	H
文献[67]	DTL	（S1） + 0 + 1	MCM，MCS	LUti，Tdst	Cprec，Cinc，Cexc	Lico	SD	H
文献[68]	DTL	（R1） + 0 + 1	MCM，MCS	LUti，Tdst	Cprec，Cinc，Cexc	Lico	SD	MP
文献[69]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	SP
文献[15]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	B&B
文献[70]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	B&B
文献[18]	RTL	（PS1 + 0） + 0 + 1	Wf，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	GRASP
文献[71]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	GA
文献[72]	DTL	（R1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	MP, G
文献[19]	RTL	（PS1 + 0） + 0 + 1	Wf，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	ACO
文献[73]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	RM
文献[74]	DTL	（S1） + 0 + 1	MCM，MCS	LUti，Tdst	Cprec，Cinc，Cexc	Lico	SD	GRASP，GA
文献[10]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	SP
文献[75]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	SP
文献[76]	RTL	（PS1 + 0） + 0 + 1	Wf，MCS	Tdst	Cprec，Cinc，Cexc	NM	TD	DP
文献[77]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	MP
文献[78]	RTL	（PS1 + 0） + 0 + 1	Wf，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	GRASP
文献[79]	RTL	（S0 + 1） + 0 + 1	MCS	LUti，Tdst	Cprec，Cinc，Cexc	Lico	SD	MP
文献[80]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	CA
文献[81]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	RM
文献[82]	RTL	（PS0 + n） + 0 + 1	MCS	Tdst	Cprec	NM	TD	GA
文献[83]	DTL	（R1） + 0 + 1	MCrt，MCM，MCS	Trti，Tcti，Tdst	Cprec，Cinc，Cexc	Lico	SD	MP, D
文献[84]	RTL	（PS1 + 0） + 0 + 1	Wf，MCS	Tdst	Cprec，Cinc，Cexc	NM	TD	GA
文献[25]	RTL	（PS1 + 0） + 0 + 1	Wf，MCS	Tdst	Cprec，Cinc，Cexc	NM	TD	CG, B&C, parallel B&C
文献[85]	RTL	（Snb） + 0 + 1	Tm，MCM，MCS	Tdst	Cprec	Lico	SD	MP, H
文献[86]	DTL	（S1） + 0 + 1	Ts，Tm，MCS	Tcti，LUti，Ttti，Tdst	Cprec，Cinc，Cexc	NonPti	TD	MP
文献[87]	RTL	（S0 + 1） + 0 + 1	MCM，MCS	LUti，Tdst	Cprec，Cinc，Cexc	Lico	SD	MP
文献[23]	DTL	（S1） + 0 + 1	Ts，Tm，MCS	Tcti，LUti，Ttti，Trti，Tdst	Cprec，Cinc，Cexc	NonPti	TD	MP，D，D + ACO，ACO
文献[88]	DTL	（S1） + 0 + 1	MCM，MCS	Trti，Tcti，Tdst	Cprec，Cinc，Cexc	Lico	SD	MP，G
文献[89]	DTL	（R1） + 0 + 1	MCM，MCS	LUti，Tdst	Cprec，Cinc，Cexc	Lico	SD	MP，G，H
文献[90]	DTL	（S1） + 0 + 1	MCS	Tdst	Cprec	SI	TD	SA-PSO
文献[91]	DTL	（PS1） + 0 + 1	MCS	Trti，Tcti，Tdst	Cprec	Lico，Cycti	SD, TD	PSO
文献[32]	DTL	（R1） + 0 + 1	MCS	Tcti，Trti，Tdst	Cprec，Cinc，Cexc	Lico，CE	SD, TD	MP, TS
文献[92]	DTL	（PS1） + 0 + 1	MCS	Trti，Tcti，Tdst	Cprec	Cycti，SI，NM	SD, TD	ACO
文献[93]	RTL	（PS1 + 0） + 0 + 1	Wf，MCS	Tdst	Cprec，Cinc，Cexc	Lico，PR	SD	MP, GRASP
文献[42]	RTL	（PS1 + 0） + 0 + 1	Wf，Tm，MCS	Tcti，Trti，Tdst	Cprec，Cinc，Cexc	NM，Cycti，LBR	SD, TD	MP, H
文献[94]	RTL	（PS0 + n） + 0 + 1	MCS	Tdst	Cprec	NM	TD	MP, GA
文献[95]	FTL	（Rn） + 0 + 1	MCrt，MCS	Tcti，Trti，Tdst	Cprec，Cinc，Cexc	Lico	SD	MP, H
文献[96]	FTL	（Rn） + 0 + 1	MCrt，MCM，MCS	Tcti，Trti，Tdst	Cprec，Cinc，Cexc	Lico	SD	MP
文献[97]	DTL	（S1） + 0 + 1	Bual，MCS，Wf	Tdst	Cprec	Lico，PR	SD	Sim, GA-PSO
文献[98]	RTL	（C1 + 0） + 0 + 1	MCS	Tdst	Cprec	Cycti	TD	MP, H
文献[99]	RTL	（PS0 + n） + 0 + 1	MCS	Tdst	Cprec	NM	TD	MP, GA
文献[37]	RTL	（PS1 + 0） + 0 + 1	Ts，Wf，Tm，MCS	Tcti，LUti，Trti，Tdst	Cprec，Cinc，Cexc	NonPti，Manco	SD, TD	MP, CS
文献[100]	RTL	（C1 + 0） + 0 + 1	MCS	Tdst	Cprec，Cinc，Cexc	Lico	SD	MP, B&B, DB&B
文献[101]	RTL	（C1 + 0） + 0 + 1	MCS	Tdst	Cprec	NM	TD	MP, D
文献[102]	RTL	（PS1 + 0） + 0 + 1	Wf，MCS	Tdst	Cprec，Cinc，Cexc	NM	TD	PA
文献[39]	RTL	（C1 + 0） + 0 + 1	MCS	Tdst	Cprec	Cycti，SI; Pro	SD, TD	HB&B, HABC
文献[103]	RTL	（PS1 + 0） + 0 + 1	Wf，MCS	Tdst	Cprec，Cinc，Cexc	NM	TD	GA
文献[41]	RTL	（PS1 + 0） + 0 + 1	Ts，Wf，Bual，MCS	Tdst	Cprec，Cinc，Cexc	Toco，PR	SD, TD	MP, MOPSO, NSGA-Ⅱ, Sim
文献[104]	RTL	（Snb） + 0 + 1	MCrt，MCM，MCS	Tcti，Ttti，Tdst	Cprec，Cinc，Cexc	Lico	SD	MP
文献[34]	RTL	（PS1 + 0） + 0 + 1	Wf，MCS	Tdst	Cprec，Cinc，Cexc	NM	TD	PA
文献[13]	RTL	（PS1 + 0） + 0 + 1	Wf，MCS	Tdst	Cprec	Manco，Recco	SD, TD	MP, GRASP
文献[45]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec	SR	SD	MP, H
文献[105]	RTL	（PS1 + 0） + 0 + 1	Wf，MCS	Tdst	Cprec，Cinc，Cexc	NM	TD	MH
文献[21]	DTL	（S1） + 1 + 12	Wf，Mp，MCS	Taoti，Tqeti，Tdst	Cprec，Cinc，Cch	Cycti，SI	TD	ACO
文献[106]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cexc	Cycti	TD	MP, B&B
文献[107]	RTL	（Rnb） + 0 + 1	MCrt，MCM，MCS	Tcti，Trti，Tdst	Cprec，Cinc，Cexc	Lico	SD	MP, H
文献[43]	RTL	（PS1 + 0） + 0 + 1	MCS	Tdst	Cprec	Scal	SD	CA
文献[44]	RTL	（PS1 + 0） + 0 + 1	MCS	Tdst	Cprec	Lico，Enco，Sele	SD, TD	MH
文献[108]	RTL	（PS1 + 0） + 0 + 1	MCS	Tdst	Cprec，Cinc，Cexc	NM	TD	GA
文献[12]	DTL	（S1） + 0 + 1	MCS，MCrt	Trti，Tcti，Tdst	Cprec，Cinc，Cexc	Lico	SD	MP，MH
文献[40]	RTL	（PS1 + 0） + 0 + 1	MCS	Tdst	Cprec，Cch	Enco	SD	MP，MH
文献[38]	DTL	（S1） + 0 + 1	MCM，MCS	Tdst	Cprec，Cexc	Cycti	TD	MP，B&B
文献[36]	DTL	（S1） + 0 + 1	MCS	Tcti，Trti，Tdst	Cprec，Cexc，Cacc，Cinc	Cycti，Enco	SD, TD	MP
文献[109]	DTL	（S1） + 0 + 1	MCS	Tcti，Trti Tdst	Cprec，Cch Cexc，Cinc，Cacc	Cycti	TD	MH
文献[110]	DTL	（S1） + 1 + 12	Wf，MCS	Tqeti，Tdst	Cprec，Cinc，Cch	Cycti，SI	TD	PSO

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