Dynamic scheduling for aircraft mobile production line considering material supply interference
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摘要:
针对飞机装配过程中出现的物料供应延期干扰问题,对飞机移动生产线装配作业调度进行了研究。通过对物料供应信息的动态分析,将反应调度决策划分为固定决策和不同场景下的预测决策,并建立了物料供应干扰环境下的动态调度框架。在滚动决策点,以最小化与模板装配计划的偏差及工期的加权和期望值为目标函数,建立了二阶段近似优化模型。针对模型的决策逻辑,设计了以两阶段禁忌搜索算法为框架的启发式算法,求解滚动决策点的优化问题。不同规模下的数值实验表明,所提出的动态调度方法能够有效利用不断更新的物料供应信息,获得接近后验精确解的调度结果,且相比于传统的调度方法,所提方法能更有效地应对物料供应干扰。
Abstract:To solve the problem of material supply delay during the assembly process of aircraft, the assembly operation scheduling problem of aircraft mobile production line is studied. Through the dynamic analysis of material supply information, reactive scheduling decisions were divided into fixed decisions and predictive decisions in different scenarios, and a dynamic scheduling framework in the environment of material supply interference was established. At each rolling decision point, a two-stage approximate optimization model was established with the objective function of minimizing the expected weighted sum of the deviation from the template plan and the makespan. On the basis of the decision logic of the model, a two-stage tabu search based heuristic was designed to solve the optimization problem of each rolling decision point. Numerical experiments with different scales indicate that the proposed dynamic scheduling method can effectively utilize the constantly updated material supply information to obtain scheduling results which is close to the posterior exact solution, and compared to the traditional scheduling strategies, the proposed method can more effectively deal with the interference of material supply.
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Key words:
- aircraft mobile production line /
- material supply /
- uncertainty /
- dynamic scheduling /
- rolling decision
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表 1 参数与决策变量
Table 1. Parameters and decision variables
参数 定义 J 作业集合 n 作业数量 j∈[0, 1, …, n, n+1] 作业序号 K 可更新资源集合 k∈K 资源种类编号 T 时间集合 t∈T 时间编号 pj 作业j的执行工期 Pj 作业j的紧前作业集合 rjk 作业j对第k种资源的需求量 Rk 第k种资源总量 sj0 作业j的模板计划开始时间 Aj0 作业j的物料计划到达时间 d 作业的物料配送提前期 决策变量 定义 sj 整数变量, 作业j的开始时间 xjt 0/1变量, 作业j在时刻t开始取1, 否则取0 表 2 修正的参数与决策变量
Table 2. Modified parameters and decision variables
参数 定义 q∈[0, 1, …, ε] 干扰编号, 0代表无干扰, ε为干扰总数 Tq 第q次干扰发生时刻 JF, JD, JP 3类作业集合 sR, j(j∈JF) JF类作业j的实际开始时间 ω1, ω2 ω1为与模板装配计划偏差的单位时间成本权重, ω2为工期的单位时间成本权重, 且满足ω1+ω2=1 Θ 物料到达场景集合 N 场景数量 θ∈Θ 场景编号 Aj, θ 场景θ下, 作业j的物料到达时间 决策变量 定义 sj, θ 整数变量, 场景θ下, 作业j的开始时间 xjt, θ 0/1变量, 场景θ下, 作业j在时刻t开始取1, 否则取0 表 3 基于后验信息的实验结果
Table 3. Experiment results based on posterior information
V 算例 实验1 实验2 实验3 Z t/min Z t/min G Z t/min G 20 1 260.0 0 260.0 0.1 0 287.0 0.1 10.4 2 304.5 0.1 304.5 0 0 304.5 0 0 3 300.0 0 300.0 0.1 0 304.5 0 1.5 4 242.0 0 245.0 0.1 1.2 261.5 0 8.1 5 281.0 0 281.0 0.1 0 287.0 0.1 2.1 6 264.5 0.1 264.5 0.1 0 267.0 0 0.9 7 328.0 0 356.0 0.1 8.5 356.5 0.1 8.7 8 358.5 0.3 358.5 0.1 0 360.0 0 0.4 9 232.0 0.1 232.0 0.1 0 243.0 0.1 4.7 10 346.5 0.4 362.0 0.1 4.5 370.5 0.1 6.9 均值 291.7 0.1 296.4 0.1 1.4 304.2 0.1 4.4 30 1 315.5 0.6 315.5 0.2 0 315.5 0.2 0 2 262.5 0.7 300.0 0.2 14.3 300.0 0.1 14.3 3 344.0 0.6 369.5 0.3 7.4 369.5 0.2 7.4 4 353.5 0.6 353.5 0.1 0 353.5 0.1 0 5 250.5 0.9 250.5 0.4 0 250.5 0.2 0 6 249.0 0.7 256.0 0.3 2.8 256.0 0.3 2.8 7 398.5 1.4 398.5 0.8 0 406.0 0.6 1.9 8 261.0 0.7 261.0 0.4 0 261.0 0.1 0 9 448.5 1.8 448.5 0.6 0 448.5 0.4 0 10 383.0 1.1 394.5 0.5 3.0 416.5 0.3 8.7 均值 326.6 0.9 334.8 0.4 2.8 337.7 0.3 3.5 60 1 543.5 126 543.5 4.6 0 544.0 3.3 0.1 2 538.5 42 541.0 3.8 0.5 541.0 2.9 0.5 3 815.0 137 848.0 4.7 4.0 903.5 3.3 10.9 4 667.5 92 667.5 3.5 0 682.0 2.1 2.2 5* 803.5 180 803.5 4.6 0 835.0 3.4 3.9 6 547.0 38 552.0 3.1 0.9 567.0 2.9 3.7 7 440.5 30 458.0 3.7 4.0 458.0 2.8 4.0 8* 665.5 180 750.0 3.0 12.7 756.0 2.8 13.6 9 506.0 142 506.0 4.7 0 522.0 4.1 3.2 10 587.0 83 618.5 3.7 5.4 618.5 2.4 5.4 均值 611.4 105 628.8 3.9 2.8 642.7 3.0 4.8 表 4 小规模算例实验结果
Table 4. Experiment results of small-scale example
V 算例 实验4 实验5 实验6 实验7 实验8 Z GAP1 Z GAP2 Z GAP3 Z GAP4 Z GAP5 20 1 260.0 0 260.0 0 260.0 0 307.5 18.3 265.0 1.9 2 309.5 1.6 310.5 0.3 310.5 0.3 358.5 15.8 313.5 1.3 3 300.0 0 300.5 0.2 304.5 1.5 363.5 21.2 324.5 8.2 4 262.0 8.3 262.0 0 266.5 1.7 356.5 36.1 271.5 3.6 5 281.0 0 284.0 1.1 281.0 0 357.0 27.0 299.0 6.4 6 271.0 2.5 275.5 1.7 268.5 -0.9 390.0 43.9 285.5 5.4 7 356.0 8.5 361.0 1.4 356.0 0 369.5 3.8 368.0 3.4 8 366.5 2.2 366.5 0 364.5 -0.5 419.0 14.3 378.5 3.3 9 234.5 1.1 234.5 0 241.5 3.0 356.0 51.8 243.0 3.6 10 364.0 5.1 365.0 0.3 370.0 1.6 392.5 7.8 370.0 1.6 均值 300.5 2.9 302.0 0.5 302.3 0.7 367.0 24.0 311.9 3.9 30 1 315.5 0 319.0 1.1 315.5 0 317.5 0.6 315.5 0 2 302.5 15.2 303.5 0.3 307.5 1.7 331.0 9.4 323.0 6.8 3 369.5 7.4 370.0 0.1 369.5 0 378.5 2.4 370.0 0 4 353.5 0 355.0 0.4 356.5 0.8 353.5 0 358.5 1.4 5 259.0 3.4 260.5 0.6 260.5 0.6 314.5 21.4 279.5 7.9 6 257.5 3.4 260.0 1.0 256.0 -0.6 268.0 4.1 264.0 2.5 7 402.5 1.0 405.0 0.6 407.0 1.1 418.5 4.0 410.5 2.0 8 261.0 0 261.0 0 261.0 0 261.0 0 261.0 0 9 448.5 0 451.0 0.6 457.5 2.0 487.5 8.7 467.5 4.2 10 401.5 4.8 408.5 1.7 420.0 4.6 483.5 20.4 442.5 10.2 均值 337.1 3.5 339.4 0.6 341.1 1.0 361.4 7.1 349.2 3.5 60 1 543.5 0 548.0 0.9 549.5 1.1 558.0 2.8 555.5 2.2 2 542.5 0.7 547.5 0.9 538.5 -0.7 547.0 0.8 546.5 0.7 3 852.5 4.6 875.5 2.7 913.5 7.3 974.5 14.3 941.0 10.4 4 674.5 1.0 678.0 0.5 676.5 0.3 780.5 15.7 702.0 4.1 5* 810.5 0.9 824.5 1.7 824.5 1.7 827.5 2.1 827.0 2.0 6 558.0 2.0 565.5 1.3 552.0 -1.1 633.0 13.4 573.5 2.8 7 465.5 5.7 472.5 1.5 504.5 8.4 522.0 12.1 495.5 6.4 8* 722.5 8.6 730.0 1.0 750.0 3.8 857.5 18.7 765.5 6.0 9 511.0 1.0 515.0 0.8 548.5 7.3 548.5 7.3 529.0 3.5 10 622.5 6.0 631.5 1.4 635.5 2.1 631.5 1.4 632.5 1.6 均值 630.3 3.1 638.8 1.3 649.3 3.0 688.0 8.9 656.8 4.0 表 5 大规模算例实验结果
Table 5. Experiment results of large-scale example
V 算例 后验结果 实验4 实验5 实验6 实验7 实验8 Z Z GAP1 Z GAP2 Z GAP3 Z GAP4 Z GAP5 90 1 652.5 668.5 2.5 702.5 5.1 802.5 20.0 859.5 28.6 739.0 10.5 2 654.0 674.5 3.1 691.5 2.5 918.0 36.1 962.5 42.7 849.5 25.9 3 918.0 930.0 1.3 949.0 2.0 1 155.5 24.2 1 016.5 9.3 1 005.0 8.1 4 891.0 921.0 3.4 965.0 4.8 1 162.5 26.2 1 104.5 19.9 993.5 7.9 5 702.5 774.0 10.2 796.5 2.9 952.5 23.1 962.5 24.4 871.5 12.6 6 776.5 808.0 4.1 814.5 0.8 776.5 -3.9 914.0 13.1 867.5 7.4 7 652.5 715.0 9.6 715.0 0 728.0 1.8 864.0 20.8 782.5 9.4 8 823.5 843.5 2.4 850.5 0.8 843.5 0 1 281.0 51.9 922.5 9.4 9 988.0 1 002.0 1.4 1 032.5 3.0 1 063.0 6.1 1 071.0 6.9 1 071.0 6.9 10 946.0 959.0 1.4 967.5 0.9 974.0 1.6 1 124.0 17.2 1 008.5 5.2 均值 800.5 829.6 3.9 848.5 2.3 937.6 13.5 1 016.0 23.5 911.1 10.3 120 1 1 224.5 1 269.5 3.7 1 335.5 5.2 1 582.5 24.7 1 684.0 32.7 1 405.5 10.7 2 1 239.5 1 279.0 3.2 1 343.0 5.0 1 520.5 18.9 1 678.0 31.2 1 414.5 10.6 3 1 228.0 1 275.0 3.8 1 339.5 5.1 2 283.0 79.1 1 626.0 27.5 1 471.0 15.4 4 1 247.0 1 314.0 5.4 1 374.0 4.6 1 380.0 5.0 1 548.0 17.8 1 445.0 10.0 5 1 035.5 1 057.5 2.1 1 134.0 7.2 1 691.5 60.0 1 476.0 39.6 1 267.0 19.8 6 1 086.5 1 208.0 11.2 1 263.5 4.6 1 281.0 6.0 1 743.0 44.3 1 363.5 12.9 7 855.0 904.5 5.8 945.0 4.5 1 117.5 23.5 1 395.0 54.2 1 073.5 18.7 8 965 968.0 0.3 983.0 1.5 1 003.0 3.6 1 003.5 3.7 1 003.0 3.6 9 1 282 1 370.5 6.9 1 413.0 3.1 1 433.5 4.6 1 735.5 26.6 1 510.5 10.2 10 1 270 1 302.0 2.5 1 392.5 7.0 1 539.0 18.2 1 756.5 34.9 1 496.5 14.9 均值 1 143.3 1 194.8 4.5 1 252.3 4.8 1 483.2 24.4 1 564.6 31.3 1 345.0 12.7 表 6 尾翼装配工位模板装配计划
Table 6. Template assembly plan of tail assembly station
作业编号 开始时间 装配工时 物料计划到达时间 资源占用 紧后作业 AO15001 0 0 [0,0,0,0] 2,3,4 AO15002 0 12 0 [2,1,1,2] 7,8 AO15003 0 12 0 [2,1,1,2] 5,6,11 AO15004 0 14 0 [2,2,1,2] 10 AO15005 12 24 6 [3,2,1,2] 9 AO15006 12 52 0 [5,2,1,5] 8 AO15007 12 8 2 [2,2,1,5] 11,12 AO15008 132 21 126 [2,2,1,4] 18 AO15009 92 60 77 [4,3,1,5] 17 AO15010 14 48 7 [4,2,1,2] 13 AO15011 20 18 12 [6,4,1,5] 14,16,19 AO15012 132 48 117 [4,2,1,2] 16,18 AO15013 64 13 47 [4,3,1,4] 15 AO15014 64 28 48 [6,4,1,5] 15 AO15015 92 40 85 [6,4,1,5] 20 AO15016 180 16 175 [5,2,1,5] 21 AO15017 152 35 146 [6,4,1,5] 20 AO15018 187 14 180 [5,4,1,2] 20 AO15019 38 10 30 [2,1,1,2] 22 AO15020 201 32 196 [2,1,1,2] 21,22 AO15021 233 25 226 [2,1,1,2] 23 AO15022 233 11 228 [2,1,1,2] 23 AO15023 258 0 [0,0,0,0] 注:紧后作业一栏为简写, 如2表示作业编号为AO15002的作业。 -
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