Journal of Jilin University(Engineering and Technology Edition) ›› 2021, Vol. 51 ›› Issue (3): 900-909.doi: 10.13229/j.cnki.jdxbgxb20200063

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Multi⁃objective flow shop optimal scheduling considering worker's load

Bao-feng SUN1(),Xin-xin REN1,Zai-si ZHENG1,2,Guo-yi Li1   

  1. 1.College of Transportation，Jilin University，Changchun 130022，China
    2.Department of Product，FAW-Volkswagen Auntomobile Co. ，Ltd. ，Changchun 130011，China
  • Received:2020-02-06 Online:2021-05-01 Published:2021-05-07

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Abstract:

To solve the problem of workers' load imbalance in the flow shop scheduling， a dual-objective optimization scheduling model is proposed in this paper with the minimum delay time and the workers' workload standard deviation. A NSGA-II based on two-gene chromosome coding is designed to obtain Pareto-optimal solutions. Two embedded heuristic rules， the earliest due date （EDD） rule and the shortest processing time （SPT） rule， are introduced together with NSGA-II to form the NSGA-II-EDD and NSGA-II-SPT for comparison. Computation experimental analysis shows that NSGA-II performs better in case of evaluation indexes with the average non-dominated solutions N， error ratio ER，spacing evaluation index S and Pareto front span K， but is worse in operation time T.

Key words: computer application, flow shop scheduling, multi-objective optimization, worker's load, two-gene chromosome coding, NSGA-II algorithm

CLC Number: 

  • TP29

Fig.1

Distribution of processing tasks"

Table 1

Weekly order production time"

工件号工序一工序二工序三工序四交货期
166867965296
261806464538
356856965550
452856273272
558668170275
655787967558
759648163267
869778466296
967867568296
1070787764289
1165627479280
1269758579308
1355736679546
1468858579317
1559698369280
1657636677263
1767718561284
1866658569570
1952866975564
2068788673305

Table 2

Team, worker and process"

班组名称工序一工序二工序三工序四
16787
26877
36777
47888

Table 3

Partial worker basic information table"

工序人员编号身高/cm体重/kg年龄BMRRMRm
一1159553264112
2172724368124
3177622872123
4179593274119
5170633376117
6162623570116
二1172652870125
2167523267114
3164532963112
4162623374124
5167582876110
6169604375119
7172592972126
三1174673269123
2176632265119
3168642663104
4172692761106
5164592572103
6158623364112
7163632967109
8157593662114

Table 4

Model basic parameters"

参数符号数值
低负荷延误概率λ10.064
高负荷延误概率λ20.104
单位时间工人能量阈值E10.056
经验参数β7.02

Fig.2

Solution of the algorithm NSGA-II"

Table 5

Result of frontier solution"

订单规模运行时间/sPareto
Tσ
903.2308.44
1004.34012.55
4.1111.53
5.2310.39
15.4110.31
1105.121.1147.66
5.5723.65
16.6917.41
34.3116.91
38.2315.85
67.4914.58
71.3214.51
72.4114.49
80.9913.08
107.5312.79
1206.3881.0423.49
140.3423.02
140.3518.46
162.2014.93
219.4814.49
272.3113.53
281.8813.15
464.7412.83
523.8512.82
528.5712.48

Fig.3

Iteration curve trend of target value"

Fig.4

Comparison of the number of non-dominated solutions in the frontier of Pareto"

Fig.5

Comparison of the error ratio (ER) in Pareto frontier solution"

Fig.6

Comparison of spacing evaluation index inPareto frontier solution"

Fig.7

Comparison of the frontier span"

Fig.8

Comparison of running time"

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