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面向订单的航空制造业多工厂生产与运输综合计划模型

沈广亚 李立恒 张宁

沈广亚, 李立恒, 张宁等 . 面向订单的航空制造业多工厂生产与运输综合计划模型[J]. 北京航空航天大学学报, 2020, 46(7): 1422-1436. doi: 10.13700/j.bh.1001-5965.2020.0028
引用本文: 沈广亚, 李立恒, 张宁等 . 面向订单的航空制造业多工厂生产与运输综合计划模型[J]. 北京航空航天大学学报, 2020, 46(7): 1422-1436. doi: 10.13700/j.bh.1001-5965.2020.0028
SHEN Guangya, LI Liheng, ZHANG Ninget al. An integrated planning model for production and transportation in make-to-order multi-site aviation manufacturing industry[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(7): 1422-1436. doi: 10.13700/j.bh.1001-5965.2020.0028(in Chinese)
Citation: SHEN Guangya, LI Liheng, ZHANG Ninget al. An integrated planning model for production and transportation in make-to-order multi-site aviation manufacturing industry[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(7): 1422-1436. doi: 10.13700/j.bh.1001-5965.2020.0028(in Chinese)

面向订单的航空制造业多工厂生产与运输综合计划模型

doi: 10.13700/j.bh.1001-5965.2020.0028
详细信息
    作者简介:

    沈广亚 男, 博士研究生。主要研究方向:制造资源优化配置

    李立恒  女, 硕士研究生。主要研究方向:生产运作管理

    张宁  男, 教授, 博士生导师。主要研究方向:交通运输规划

    通讯作者:

    张宁, E-mail: nzhang@buaa.edu.cn

  • 中图分类号: V2-9;C935

An integrated planning model for production and transportation in make-to-order multi-site aviation manufacturing industry

More Information
  • 摘要:

    在多个异质性离散型生产工厂的航空零部件集成制造环境下,以最小化生产与运输总成本为目标,研究了订单的分配以及零部件加工和成品装配、产品运输的综合计划制定问题,构建了整数规划模型。所建模型既不需要单独引入订单分配决策变量,也不需要在生产量和运输量的决策变量中添加订单维度,而是通过成品配送约束解决了订单分配决策问题,大幅度减少了决策变量数量,显著降低了模型的复杂度,提升了模型的实用性。以某航空制造企业为例验证了模型的有效性。

     

  • 图 1  装配型企业多工厂生产全流程示意图

    Figure 1.  Schematic diagram of whole multi-site production process of assembly enterprise

    图 2  最优生产计划下的2类工厂负荷

    Figure 2.  Loads of two types of factory under optimal production plan

    图 3  最优解的各项成本占比

    Figure 3.  Proportion of various costs of optimal solution

    图 4  零部件加工工厂最大产能变化的影响

    Figure 4.  Effect of variation of maximum production capacity of parts processing factories

    图 5  装配工厂最大产能变化的影响

    Figure 5.  Effect of variation of maximum production capacity of assembly factories

    图 6  零部件加工工厂单位生产成本变化的影响

    Figure 6.  Effect of variation of unit production cost of parts processing factories

    图 7  零部件单位运输成本变化的影响

    Figure 7.  Effect of the variation of unit transportation cost of parts

    图 8  产品需求量变化的影响

    Figure 8.  Effect of product demand variation

    表  1  数学符号含义

    Table  1.   Notation of mathematical symbols

    符号 定义
    I 接收到的订单集I={i1, i2, …, i}
    I′ 指定装配工厂的订单集,I′⊂I
    J 零部件加工工厂集J={j1, j2, …, j}
    J′ 不具备生产全品类零部件的加工工厂集,J′⊂J
    P 装配工厂集P={p1, p2, …, p}
    K 零部件类型集K={k1, k2, …, k}
    Kj 零部件加工工厂jJ′不能生产的零部件类型集,KjK
    M 可加工产品集M={m1, m2, …, m}
    Mi 订单iI′指定装配工厂组装的产品集,MiM
    Pim 订单iI′指定产品mMi的装配工厂集,PimP
    L 销售地集L={l1, l2, …, l}
    Lim 订单iI′指定将产品mMi运往的销售地集,LimL
    deiml 订单i要求生产并运往销售地l的产品m的数量
    C 生产和运输中成本
    C1jk 零部件加工工厂j生产单位零件k的生产成本
    C2pm 装配工厂p组装单位产品m的生产成本
    C3jp 运输单位零部件从加工工厂j至装配工厂p的成本
    C4pl 运输单位产品从装配工厂p至销售地l的运输成本
    djk 零部件加工工厂j生产单位零件k所花费的工时
    dpm 装配工厂p组装单位产品m所花费的工时
    D1j 零部件加工工厂j的可用工时
    D2p 装配工厂p的可用工时
    βkm 产品m和零部件k的物料关系
    Xjk 零部件加工工厂j生产零件k的数量
    Ypm 装配工厂p生产产品m的数量
    Tjpk 零部件加工工厂j运输零件k到装配工厂p的数量
    Spml 装配工厂p运输产品m到销售地l的数量
    下载: 导出CSV

    表  2  订单i1需求的7种产品的装配工厂分配

    Table  2.   Allocation of 7 types of product for order i1 to assembly plant

    销售地 m1 m2 m3 m4 m5 m6 m7
    l1 p4 p4 p4 p4 p4 p4 p4
    l2
    l3
    l4
    l5
    l6
    下载: 导出CSV

    表  3  订单i2需求的7种产品的装配工厂分配

    Table  3.   Allocation of 7 types of product for order i2 to assembly plant

    销售地 m1 m2 m3 m4 m5 m6 m7
    l1
    l2 p3 p2 p2 p1, p3 p2, p4 p2 p1
    l3 p3, p5 p1 p6 p6 p4 p3 p1
    l4 p5 p1 p6 p6 p4 p3 p1
    l5 p5 p1, p5 p5 p3, p6 p5 p3, p5 p1
    l6 p3 p2 p2 p3 p1, p3 p3 p1
    下载: 导出CSV

    表  4  订单i3需求的7种产品的装配工厂分配

    Table  4.   Allocation of 7 types of product for order i3 to assembly plant

    销售地 m1 m2 m3 m4 m5 m6 m7
    l1
    l2 p3 p2 p2 p1, p3 p2, p4 p2 p1
    l3 p3, p5 p1 p6 p6 p4 p3 p1
    l4 p5 p1 p6 p6 p4 p3 p1
    l5 p5 p1, p5 p5 p3, p6 p5 p3, p5 p1
    l6 p3 p2 p2 p3 p1, p3 p3 p1
    下载: 导出CSV

    表A-1  7种产品的物料清单

    表A-1.   Bill of materials of 7 types of products

    零部件 m1 m2 m3 m4 m5 m6 m7
    k1 1 0 0 0 0 0 0
    k2 0 0 1 0 0 0 0
    k3 0 1 0 1 0 0 0
    k4 0 0 0 0 0 1 0
    k5 0 0 0 0 1 0 0
    k6 0 0 0 0 0 0 1
    k7 1 1 1 1 1 1 1
    k8 1 1 0 0 0 0 0
    k9 0 0 0 0 1 0 0
    k10 0 0 0 1 0 1 1
    k11 0 0 1 0 0 0 0
    k12 0 0 0 0 0 0 1
    k13 1 1 0 1 1 0 0
    k14 0 0 0 0 0 1 0
    k15 0 0 1 0 0 0 0
    k16 0 0 0 0 0 0 1
    k17 1 1 0 1 1 1 0
    k18 0 0 1 0 0 0 0
    k19 6 7 8 11 11 8 8
    下载: 导出CSV

    表 A-2  订单i1对7种产品的需求量

    表 A-2.   Demand of 7 types of products in order i1

    销售地 m1 m2 m3 m4 m5 m6 m7
    l1 300 350 200 300 220 150 230
    l2 0 0 0 0 0 0 0
    l3 0 0 0 0 0 0 0
    l4 0 0 0 0 0 0 0
    l5 0 0 0 0 0 0 0
    l6 0 0 0 0 0 0 0
    下载: 导出CSV

    表 A-3  订单i2对7种产品的需求量

    表 A-3.   Demand of 7 types of products in order i2

    销售地 m1 m2 m3 m4 m5 m6 m7
    l1 0 0 0 0 0 0 0
    l2 100 100 100 100 100 50 100
    l3 100 150 50 100 100 60 100
    l4 100 50 50 100 50 100 75
    l5 50 50 100 50 50 100 50
    l6 150 200 150 100 200 200 100
    下载: 导出CSV

    表 A-4  订单i3对7种产品的需求量

    表 A-4.   Demand of 7 types of products in order i3

    销售地 m1 m2 m3 m4 m5 m6 m7
    l1 0 0 0 0 0 0 0
    l2 150 100 100 150 70 50 80
    l3 100 100 50 100 20 140 30
    l4 100 200 50 100 70 100 55
    l5 50 50 100 100 100 100 50
    l6 200 200 150 100 50 0 100
    下载: 导出CSV

    表 A-5  零部件加工工厂的生产成本

    表 A-5.   Production cost of parts processing factories  元/件

    零部件 j1 j2 j3 j4 j5
    k1 0 0 20 18 20
    k2 0 0 15 15 13
    k3 0 0 13 13 13
    k4 0 0 12 12 13
    k5 0 0 10 10 10
    k6 0 0 10 10 10
    k7 0 0 15 15 15
    k8 1000 800 700 720 700
    k9 2000 1800 1800 1850 1800
    k10 2500 2000 2000 2000 2000
    k11 3000 2500 2500 2500 2500
    k12 0 0 200 200 180
    k13 0 0 400 450 400
    k14 0 0 600 600 650
    k15 0 0 800 750 750
    k16 0 0 70 70 70
    k17 0 0 100 100 100
    k18 160 150 150 150 150
    k19 60 50 50 50 50
    下载: 导出CSV

    表 A-6  装配工厂的生产成本

    表 A-6.   Production cost of assembly plants  元/件

    装配工厂 m1 m2 m3 m4 m5 m6 m7
    p1 10 10 80 65 50 60 30
    p2 10 10 80 65 50 60 30
    p3 15 15 90 70 70 70 40
    p4 20 20 100 70 70 80 55
    p5 15 10 75 70 65 70 50
    p6 12 12 95 75 85 80 75
    下载: 导出CSV

    表 A-7  零部件加工工厂生产各零部件消耗的工时

    表 A-7.   Working-hours consumed for production of various parts in parts processing factories  h

    零部件 j1 j2 j3 j4 j5
    k1 0 0 0.06 0.08 0.06
    k2 0 0 0.06 0.06 0.06
    k3 0 0 0.06 0.06 0.08
    k4 0 0 0.05 0.06 0.05
    k5 0 0 0.06 0.06 0.06
    k6 0 0 0.06 0.05 0.06
    k7 0 0 0.06 0.05 0.06
    k8 0.16 0.2 0.2 0.21 0.2
    k9 0.18 0.2 0.2 0.21 0.2
    k10 0.2 0.21 0.2 0.21 0.2
    k11 0.23 0.25 0.23 0.23 0.25
    k12 0.1 0.13 0.1 0.11 0.1
    k13 0.1 0.11 0.13 0.15 0.11
    k14 0.11 0.13 0.13 0.15 0.11
    k15 0.13 0.13 0.13 0.11 0.15
    k16 0 0 0.1 0.1 0.13
    k17 0 0 0.1 0.11 0.11
    k18 0 0 0.1 0.13 0.15
    k19 0 0 0.05 0.06 0.05
    下载: 导出CSV

    表 A-8  装配工厂组装各产品所耗工时

    表 A-8.   Working-hours consumed for assembly of various products in assembly plants  h

    装配工厂 m1 m2 m3 m4 m5 m6 m7
    p1 1 1.3 1.3 1.2 1.2 1.1 1.1
    p2 1 1.3 1.3 1.2 1.2 1.1 1.1
    p3 1 2 1.7 1.6 1.5 1.2 1.6
    p4 1 1 2 1.5 1 1 1
    p5 1.2 1.6 1.3 1.6 1.7 1.2 1.6
    p6 1.2 1.7 1.3 1.5 1.6 1.8 1.4
    下载: 导出CSV

    表 A-9  零部件加工工厂的最大可用工时

    表 A-9.   Maximum working-hours of parts processing plants  h

    加工工厂 j1 j2 j3 j4 j5
    最大可用工时 1500 1500 1800 2000 2000
    下载: 导出CSV

    表 A-10  装配工厂的最大可用工时

    表 A-10.   Maximum working hours of assembly plants  h

    装配工厂 p1 p2 p3 p4 p5 p6
    最大可用工时 2000 2000 2500 2500 1200 1000
    下载: 导出CSV

    表 A-11  零部件加工工厂与装配工厂间的运输成本

    表 A-11.   Transportation cost between processing plant and assembly plants  元/件

    加工工厂 p1 p2 p3 p4 p5 p6
    j1 80 80 70 50 20 80
    j2 30 30 35 40 80 30
    j3 50 50 45 5 45 45
    j4 50 50 45 5 45 45
    j5 50 50 45 5 45 45
    下载: 导出CSV

    表 A-12  装配工厂与销售地之间的运输成本

    表 A-12.   Transportation costs between assembly plant and sales location  元/件

    销售地 p1 p2 p3 p4 p5 p6
    l1 50 50 55 10 80 30
    l2 30 30 25 20 50 30
    l3 60 60 50 20 40 40
    l4 60 60 50 20 30 40
    l5 90 90 80 80 20 80
    l6 50 50 30 60 100 70
    下载: 导出CSV

    表A-13  订单在各销售地的7种产品需求量

    表A-13.   Demand for 7 types of products of orders at each sales location  

    销售地 m1 m2 m3 m4 m5 m6 m7
    l1 300 350 200 300 220 150 230
    l2 250 200 200 250 170 100 180
    l3 200 250 100 200 120 200 130
    l4 200 250 100 200 120 200 130
    l5 100 100 200 150 150 200 100
    l6 350 400 300 200 250 200 200
    下载: 导出CSV

    表 B-1  零部件加工工厂生产计划

    表 B-1.   Production plan of parts processing plants  

    零部件 j1 j2 j3 j4 j5
    k1 0 0 1100 0 300
    k2 0 0 0 1100 0
    k3 0 0 0 2850 0
    k4 0 0 1050 0 0
    k5 0 0 0 1030 0
    k6 0 0 0 970 0
    k7 0 0 0 8400 0
    k8 419 1102 0 1429 0
    k9 150 880 0 0 0
    k10 0 3320 0 0 0
    k11 1 705 0 394 0
    k12 969 0 0 1 0
    k13 3497 1783 0 0 0
    k14 1050 0 0 0 0
    k15 902 0 0 198 0
    k16 0 0 0 970 0
    k17 0 0 521 5809 0
    k18 0 0 1100 0 0
    k19 0 0 30241 0 39599
    下载: 导出CSV

    表 B-2  装配工厂生产计划

    表 B-2.   Production plan of assembly plants  

    装配工厂 m1 m2 m3 m4 m5 m6 m7
    p1 0 502 0 174 3 0 740
    p2 0 600 500 0 10 100 0
    p3 779 0 0 333 247 681 0
    p4 300 350 200 300 620 150 230
    p5 321 98 200 0 150 119 0
    p6 0 0 200 493 0 0 0
    下载: 导出CSV

    表 B-3  装配工厂运输计划

    表 B-3.   Transportation plan of assembly plants  

    装配工厂 销售地 m1 m2 m3 m4 m5 m6 m7
    p1 l1 0 0 0 0 0 0 0
    l2 0 0 0 174 0 0 180
    l3 0 250 0 0 0 0 130
    l4 0 250 0 0 0 0 130
    l5 0 2 0 0 0 0 100
    l6 0 0 0 0 3 0 200
    p2 l1 0 0 0 0 0 0 0
    l2 0 200 200 0 10 100 0
    l3 0 0 0 0 0 0 0
    l4 0 0 0 0 0 0 0
    l5 0 0 0 0 0 0 0
    l6 0 400 300 0 0 0 0
    p3 l1 0 0 0 0 0 0 0
    l2 250 0 0 76 0 0 0
    l3 179 0 0 0 0 200 0
    l4 0 0 0 0 0 200 0
    l5 0 0 0 57 0 81 0
    l6 350 0 0 200 247 200 0
    p4 l1 300 350 200 300 220 150 230
    l2 0 0 0 0 160 0 0
    l3 0 0 0 0 120 0 0
    l4 0 0 0 0 120 0 0
    l5 0 0 0 0 0 0 0
    l6 0 0 0 0 0 0 0
    p5 l1 0 0 0 0 0 0 0
    l2 0 0 0 0 0 0 0
    l3 21 0 0 0 0 0 0
    l4 200 0 0 0 0 0 0
    l5 100 98 200 0 150 119 0
    l6 0 0 0 0 0 0 0
    p6 l1 0 0 0 0 0 0 0
    l2 0 0 0 0 0 0 0
    l3 0 0 100 200 0 0 0
    l4 0 0 100 200 0 0 0
    l5 0 0 0 93 0 0 0
    l6 0 0 0 0 0 0 0
    下载: 导出CSV

    表 B-4  零部件加工工厂j1运输计划

    表 B-4.   Transportation plan of parts processing plant j1

    零部件 p1 p2 p3 p4 p5 p6
    k1 0 0 0 0 0 0
    k2 0 0 0 0 0 0
    k3 0 0 0 0 0 0
    k4 0 0 0 0 0 0
    k5 0 0 0 0 0 0
    k6 0 0 0 0 0 0
    k7 0 0 0 0 0 0
    k8 0 0 0 0 419 0
    k9 0 0 0 0 150 0
    k10 0 0 0 0 0 0
    k11 0 0 0 1 0 0
    k12 739 0 0 230 0 0
    k13 0 0 1358 1570 569 0
    k14 0 100 681 150 119 0
    k15 0 500 0 2 200 200
    k16 0 0 0 0 0 0
    k17 0 0 0 0 0 0
    k18 0 0 0 0 0 0
    k19 0 0 0 0 0 0
    下载: 导出CSV

    表 B-5  零部件加工工厂j2运输计划

    表 B-5.   Transportation plan of parts processing plant j2

    零部件 p1 p2 p3 p4 p5 p6
    k1 0 0 0 0 0 0
    k2 0 0 0 0 0 0
    k3 0 0 0 0 0 0
    k4 0 0 0 0 0 0
    k5 0 0 0 0 0 0
    k6 0 0 0 0 0 0
    k7 0 0 0 0 0 0
    k8 502 600 0 0 0 0
    k9 3 10 247 620 0 0
    k10 914 100 1014 680 119 493
    k11 0 500 0 5 0 200
    k12 0 0 0 0 0 0
    k13 679 610 1 0 0 493
    k14 0 0 0 0 0 0
    k15 0 0 0 0 0 0
    k16 0 0 0 0 0 0
    k17 0 0 0 0 0 0
    k18 0 0 0 0 0 0
    k19 0 0 0 0 0 0
    下载: 导出CSV

    表 B-6  零部件加工工厂j3运输计划

    表 B-6.   Transportation plan of parts processing plant j3

    零部件 p1 p2 p3 p4 p5 p6
    k1 0 0 779 0 321 0
    k2 0 0 0 0 0 0
    k3 0 0 0 0 0 0
    k4 0 100 681 150 119 0
    k5 0 0 0 0 0 0
    k6 0 0 0 0 0 0
    k7 0 0 0 0 0 0
    k8 0 0 0 0 0 0
    k9 0 0 0 0 0 0
    k10 0 0 0 0 0 0
    k11 0 0 0 0 0 0
    k12 0 0 0 0 0 0
    k13 0 0 0 0 0 0
    k14 0 0 0 0 0 0
    k15 0 0 0 0 0 0
    k16 0 0 0 0 0 0
    k17 521 0 0 0 0 0
    k18 0 500 0 200 200 200
    k19 1 0 4207 19010 0 7023
    下载: 导出CSV

    表 B-7  零部件加工工厂j4运输计划

    表 B-7.   Transportation plan of parts processing plant j4

    零部件 p1 p2 p3 p4 p5 p6
    k1 0 0 0 0 0 0
    k2 0 500 0 200 200 200
    k3 676 600 333 650 98 493
    k4 0 0 0 0 0 0
    k5 3 10 247 620 150 0
    k6 740 0 0 230 0 0
    k7 1419 1210 2040 2150 888 693
    k8 0 0 779 650 0 0
    k9 0 0 0 0 0 0
    k10 0 0 0 0 0 0
    k11 0 0 0 194 200 0
    k12 1 0 0 0 0 0
    k13 0 0 0 0 0 0
    k14 0 0 0 0 0 0
    k15 0 0 0 198 0 0
    k16 740 0 0 230 0 0
    k17 158 710 2040 1720 688 493
    k18 0 0 0 0 0 0
    k19 0 0 0 0 0 0
    下载: 导出CSV

    表 B-8  零部件加工工厂j5运输计划

    表 B-8.   Transportation plan of parts processing plant j5

    零部件 p1 p2 p3 p4 p5 p6
    k1 0 0 0 300 0 0
    k2 0 0 0 0 0 0
    k3 0 0 0 0 0 0
    k4 0 0 0 0 0 0
    k5 0 0 0 0 0 0
    k6 0 0 0 0 0 0
    k7 0 0 0 0 0 0
    k8 0 0 0 0 0 0
    k9 0 0 0 0 0 0
    k10 0 0 0 0 0 0
    k11 0 0 0 0 0 0
    k12 0 0 0 0 0 0
    k13 0 0 0 0 0 0
    k14 0 0 0 0 0 0
    k15 0 0 0 0 0 0
    k16 0 0 0 0 0 0
    k17 0 0 0 0 0 0
    k18 0 0 0 0 0 0
    k19 11380 9110 12295 0 6814 0
    下载: 导出CSV
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  • 收稿日期:  2020-01-18
  • 录用日期:  2020-02-07
  • 刊出日期:  2020-07-20

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