An integrated planning model for production and transportation in make-to-order multi-site aviation manufacturing industry
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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。
Abstract:An integer programming model is built to solve the integrated planning problems including order allocation, components and parts processing, product assembly and product transportation in aviation parts integrated manufacturing environment with multiple heterogenic discrete manufacturing plants. The objective of the proposed model is the minimization of the total cost in the whole process of production and transportation. The proposed model handles the order allocation problem through constructing the product shipment constraint rather than separately introducing order allocation decision variables or adding order dimensions to the production and transportation decision variables so as to reduce a large number of unnecessary decision variables, which significantly reduces the complexity of the model and improves its practicability. The effectiveness of the proposed model is confirmed by an instance from an aviation manufacturing enterprise.
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Key words:
- production planning /
- transportation /
- multi-site /
- order allocation /
- aviation manufacturing industry
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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 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
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j∈J′不能生产的零部件类型集，Kj⊂K M 可加工产品集M={m1, m2, …, m} Mi 订单i∈I′指定装配工厂组装的产品集，Mi⊂M Pim 订单i∈I′指定产品m∈Mi的装配工厂集，Pim⊂P L 销售地集L={l1, l2, …, l} Lim 订单i∈I′指定将产品m∈Mi运往的销售地集，Lim⊂L 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 
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
件 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
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表 B-1 零部件加工工厂生产计划
表 B-1. Production plan of parts processing plants
件 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
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表 B-2 装配工厂生产计划
表 B-2. Production plan of assembly plants
件 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
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表 B-3 装配工厂运输计划
表 B-3. Transportation plan of assembly plants
件 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
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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
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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
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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
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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
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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
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