Balancing optimization of parallel production lines for group products considering process complexity and employee variance
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摘要: 针对具有产品关联性的成组产品并行生产线平衡优化问题，采用分阶段研究思路，先后考虑工序复杂性与员工技能水平差异，提出工序与员工分配优化方案。首先以工序优先关系和设备属性为约束，以生产节拍、时间均衡指数和复杂性平滑系数为优化目标建立优化模型，将工序合理分配于工位中。然后根据成组产品特性和各工位技能需求建立员工指派模型，将不同技能员工与工位匹配，减少并行生产线之间节拍差异，实现成组产品的均衡生产。采用遗传算法和拟退火算法分别求解工序分配问题和员工指派问题，并结合实例验证了优化思路与方法的有效性。Abstract: Aiming at the balance optimization problem of group product parallel production line with product correlation, a phased research idea was adopted to propose an optimization scheme for process and employee assignment by successively considering process complexity and employee skill level differences. First, by taking the process precedence relation and equipment attributes as the constraints and the production cycle time, time balance index and complexity smoothing coefficient as the optimization objectives, the optimization model was established, so that the processes can be reasonably allocated to the workstations. Then, according to the characteristics of group products and the skill requirements of each workstation, the employee assignment model was established to match employees with different skills to workstations, so as to reduce the difference in the beat between parallel production lines and achieve balanced production of group products. Genetic algorithm and quasi-annealing algorithm were used to solve the process assignment problem and the employee assignment problem respectively, and the effectiveness of the optimization idea and method was verified with the example.
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Key words:
- process complexity /
- employee skill level /
- group product /
- parallel production line /
- line balance
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表 1 工序相对操作难度分级
$ {D}_{iv} $ A1 A2 B1 B2 $ {D}_{i} $ 1 0.875 0.75 0.625 $ {D}_{iv} $ C1 C2 D1 D2 $ {D}_{i} $ 0.5 0.375 0.25 0.125 
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表 2 工序信息表
$ i $ $ {t}_{i} $ $ {D}_{iv} $ $ {S}_{i1} $ $ {P}_{i1} $ $ {M}_{i} $ $ {H}_{C}\left(i\right) $ $ i $ $ {t}_{i} $ $ {D}_{iv} $ $ {S}_{i1} $ $ {P}_{i1} $ $ {M}_{i} $ $ {H}_{C}\left(i\right) $ $ i $ $ {t}_{i} $ $ {D}_{iv} $ $ {S}_{i1} $ $ {P}_{i1} $ $ {M}_{i} $ $ {H}_{C}\left(i\right) $ 1 15.1 D2 0 1 5 0.415 04 29 31.4 C2 0 4 4 1.119 74 57 22 D2 5 4 2 0.943 66 2 23.5 C2 0 1 3 0.719 16 30 26 D1 0 25 4 0.842 55 58 10.2 D2 0 6 2 0.706 18 3 32.2 C1 2 2 4 1.407 88 31 62 B2 1 25 5 1.910 65 59 51.1 C2 1 6 5 1.598 46 4 36.8 B1 3 2 2 1.221 43 32 59.7 B2 27 1 2 1.582 92 60 41.3 C2 2 6 2 1.181 78 5 32.4 C1 4 2 2 1.023 57 33 95 B1 30 1 7 3.036 78 61 49 C2 3 6 2 1.231 58 6 23.8 C1 5 2 2 1.066 80 34 93 B1 31 1 8 3.161 33 62 52.4 C1 10 2 3 1.541 48 7 24.1 D2 0 2 2 0.313 24 35 38 D1 29 1 4 1.448 38 63 90 B1 1 11 8 2.954 71 8 50.5 C2 1 2 3 0.911 69 36 40 C1 33 1 2 1.334 57 64 43.8 D1 2 11 6 1.447 39 9 19.2 C1 2 5 2 1.066 80 37 40 C1 32 1 2 1.332 76 65 50.2 B2 3 11 2 1.495 24 10 19.2 C1 2 5 2 1.066 80 38 47.5 C1 35 3 4 1.745 00 66 41.4 B2 4 4 2 1.398 70 11 32.2 D1 0 2 12 1.098 93 39 47.5 C1 34 2 4 1.818 49 67 41.4 B2 4 5 2 1.460 02 12 60 C2 1 2 13 1.716 37 40 23.5 B2 39 0 2 1.355 02 68 20 D2 18 4 3 1.019 79 13 60 C2 1 2 13 1.716 37 41 12.1 B2 39 1 2 0.855 12 69 20 D1 19 4 2 1.007 84 14 46 B2 3 5 3 1.622 29 42 10.8 A2 39 1 2 1.105 12 70 71.1 B2 20 4 5 2.131 46 15 46 B2 3 5 3 1.622 29 43 16 B1 39 1 2 0.980 12 71 20 D2 5 5 3 1.042 21 16 44 B1 4 5 2 1.435 24 44 22.5 B2 39 1 3 1.220 72 72 20 D1 6 5 2 1.085 02 17 44 B1 4 5 2 1.435 24 45 11.5 B2 39 1 2 0.855 12 73 71.1 B2 7 5 4 2.057 00 18 32 C1 2 2 3 1.200 15 46 10.6 B2 39 1 2 0.855 12 74 48 D2 0 5 5 0.854 25 19 32 C1 2 2 3 1.200 15 47 26.9 B2 39 1 2 0.855 12 75 24.5 D1 1 5 4 1.193 43 20 30.8 C2 5 2 2 0.946 02 48 44.3 A2 39 1 2 1.105 12 76 34 C2 0 1 4 0.842 83 21 27 C1 5 5 2 1.229 94 49 46.8 A2 39 1 2 1.105 12 77 65 C1 1 1 16 2.305 63 22 27 C1 5 5 2 1.229 94 50 42 B1 49 0 3 1.188 72 78 60.2 C2 0 2 16 1.824 83 23 65 B1 6 5 2 1.517 24 51 21.2 D2 0 4 8 0.826 21 79 46.6 C1 3 26 3 0.979 98 24 65 B1 6 5 2 1.517 24 52 32.3 D2 0 11 5 0.832 54 80 47 C1 4 26 6 1.464 66 25 16.7 D1 6 2 2 0.858 32 53 35 C1 1 4 2 1.106 39 81 40 C2 2 5 7 1.374 18 26 15.3 D2 0 28 2 0.415 19 54 48.3 B1 2 4 2 1.444 96 82 93 B2 31 0 20 2.901 83 27 15 D2 0 3 2 0.431 55 55 23.7 D2 3 4 2 0.880 43 83 89.2 B2 32 0 25 2.902 41 28 40 D2 0 33 20 0.913 40 56 43.9 B2 4 4 2 1.420 57
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表 3 优化后生产线1工序分配方案
工位 工序 时间/s 复杂性/bit 1 1-2-27-28 93.6 2.479 15 2 3-4-7 93.1 2.942 55 3 8-9-30 95.7 2.821 04 4 14-16 90 3.057 53 5 11-12 92.2 2.815 30 6 5-6-10-26 90.7 3.572 37 7 13-19 92 2.916 52 8 21-23 92 2.757 18 9 15-17 90 3.057 53 10 22-24 92 2.747 18 11 18-20-29 94.2 3.265 90 12 25-31 78.7 2.768 97 13 32-35 97.7 3.031 29 14 33 95 3.036 78 15 34 93 3.161 33 16 37-39 87.5 3.151 24 17 36-38 87.5 3.079 57 18 40-44-48 90.3 3.680 85 19 41-42-43-49 85.7 4.045 47 20 45-46-47-50 91 3.754 07
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表 4 优化后生产线2工序分配方案
工位 工序 时间/s 复杂性/bit 1 76-78 94.2 2.667 66 2 51-74-55 93.7 2.873 89 3 52-77 97.3 3.138 17 4 63 90 2.954 71 5 53-58-79 91.8 2.792 55 6 59-64 94.9 3.045 85 7 65-67 91.6 2.955 26 8 60-66 82.7 2.580 48 9 54-55-71 92 3.367 61 10 72-73 91.1 3.142 01 11 56-61 92.9 2.652 15 12 57-62-68 94.4 3.504 92 13 69-70 91.1 3.139 30 14 80-81 87 2.838 84 15 82 93 2.901 83 16 83 89.9 2.902 41
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表 5 工序–技能对照表
$ r $ $ i $ $ r $ $ i $ $ r $ $ i $ $ r $ $ i $ $ r $ $ i $ 1 1-51-52 11 64-78 21 8 31 81 41 68-71 2 2 12 75 22 9-10 32 33 42 69-72 3 11 13 76 23 14-15 33 34 43 70-73 4 12-13 14 77 24 16-17 34 35 44 82 5 18-19 15 3 25 21-22 35 36-37 45 83 6 20 16 4-53-55 26 23-24 36 38-39 46 40 7 27 17 5-56 27 25-57-60-61 37 58 47 41-43-44-45-46-47 8 28-74 18 4-54 28 26-79 38 62-80 48 42 9 29 19 6 29 30 39 63 49 50 10 59 20 7 30 31-32 40 65-66-67 50 48-49
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表 6 员工技能水平
$ r $1 $ r $2 $ r $3 $ r $4 $ r $5 $ r $6 … $ j $1 2.0 2.1 2.2 2.3 2.4 2.0 … $ j $2 2.1 2 1.0 1.1 1.2 1.3 … $ j $3 1.8 1.6 2.0 1.7 1.9 2.1 … … … … … … … … … $ j $11 1.0 1.9 2.0 2.2 2.3 1.7 … $ j $12 2.1 1.8 2.0 2.3 2.4 1.8 … … … … … … … … …
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表 7 优化后生产线1员工分配方案
工位 员工 时间/s 工位 员工 时间/s 1 2 97.6 11 3 96.2 2 8 98.1 12 21 84.2 3 19 98.2 13 10 97.7 4 16 99.5 14 26 96.5 5 17 96.7 15 9 97 6 6 96.2 16 22 93.5 7 25 98.5 17 27 91.5 8 12 97 18 36 89.3 9 5 95.5 19 30 90.7 10 34 89.5 20 33 92.5
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表 8 优化后生产线2员工分配方案
工位 员工 时间/s 工位 员工 时间/s 1 32 95.7 9 15 97 2 4 96.7 10 35 95.6 3 1 97.3 11 14 96.4 4 23 95 12 18 97.9 5 7 97.3 13 29 99.6 6 20 96.9 14 11 95 7 28 97.6 15 24 98 8 31 91.2 16 13 92.2
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