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March  2021, 17(2): 779-803. doi: 10.3934/jimo.2019134

Simulated annealing and genetic algorithm based method for a bi-level seru loading problem with worker assignment in seru production systems

Lan Luo 1, , Zhe Zhang 1,, and  Yong Yin 2,

1. 

School Economics and Management, Nanjing University of Science and Technology, Nanjing 210094, China
2. 

Graduate School of Business, Doshisha University, Karasuma-Imadegawa, Kamigyo-ku, Kyoto, 602-8580, Japan

* Corresponding author: Zhe Zhang

Received  April 2019 Revised  July 2019 Published  March 2021 Early access  October 2019

Fund Project: This research was sponsored by Natural Science Foundation of China (NSFC Grant no. 71401075). We thank Professor Xiuli Wang and Ding Zhang for their valuable discussions and comments, and we would like to express our appreciation to all the reviewers and editors who contributed to this research

Seru production is one of the latest manufacturing modes arising from Japanese production practice. Seru can achieve efficiency, flexibility, and responsiveness simultaneously. To accommodate the current business environment with volatile demands and fierce competitions, seru has attracted more and more attention both from researchers and practitioners. A new planning management system, just-in-time organization system (JIT-OS), is used to manage and control a seru production system. The JIT-OS contains two decisions: seru formation and seru loading. By seru formation, a seru system with one or multiple appropriate serus is configured; by seru loading, customer ordered products are allocated to serus to implement production plans. In the process of seru formation, workers have to be assigned to serus. In this paper, a seru loading problem with worker assignment is constructed as a bi-level programming model, and the worker assignment on the upper level is to minimize total idle time while the lower level is to minimize the makespan by finding out optimal product allocation. A product lot can be splitted and allocated to different serus. The problem of this paper is shown to be NP-hard. Therefore, a simulated annealing and genetic algorithm (SA-GA) is developed. The SA is for the upper level programming and the GA is for the lower level programming. The practicality and effectiveness of the model and algorithm are verified by two numerical examples, and the results show that the SA-GA algorithm has good scalability.

Keywords: Seru loading, bi-level programming, lot-splitting, worker assignment, hybrid intelligent algorithm.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: Lan Luo, Zhe Zhang, Yong Yin. Simulated annealing and genetic algorithm based method for a bi-level seru loading problem with worker assignment in seru production systems. Journal of Industrial & Management Optimization, 2021, 17 (2) : 779-803. doi: 10.3934/jimo.2019134
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show all references

References:
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A. Aboelfotoh, G. A. Süer and M. Abdullah, Selection of Assembly Systems; Assembly Lines vs. Seru Systems, Procedia Comput. Sci., 140 (2018), 351-358.  doi: 10.1016/j.procs.2018.10.304.  Google Scholar

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C. Kasemset and V. Kachitvichyanukul, Bi-level multi-objective mathematical model for job-shop scheduling: the application of theory of constraints, International Journal of Production Research, 48 (2010), 6137-6154. doi: 10.1080/00207540903176705.  Google Scholar

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[20]

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J. Lian, C. G. Liu, W. J. Li and Y. Yin, A multi-skilled worker assignment problem in seru production systems considering the worker heterogeneity, Comput. Industr. Engineering, 118 (2018), 366-382.  doi: 10.1016/j.cie.2018.02.035.  Google Scholar

[22]

C. G. Liu, F. Dang, W. J. Li, J. Lian, S. Evans and Y. Yin, Production planning of multi-stage multi-option seru production systems with sustainable measures, J. Cleaner Produc., 105 (2014), 285-299.  doi: 10.1016/j.jclepro.2014.03.033.  Google Scholar

[23]

C. G. Liu, J. Lian, Y. Yin and W. J. Li, Seru Seisan - An innovation of the production management mode in Japan, Asian Journal of Technology Innovation, 18 (2010), 89-113.  doi: 10.1080/19761597.2010.9668694.  Google Scholar

[24]

C. G. Liu, K. E. Stecke, J. Lian and Y. Yin, An implementation framework for seru production, Internat. Transactions in Oper. Res., 21 (2014), 1-19.  doi: 10.1111/itor.12014.  Google Scholar

[25]

C. G. Liu, N. Yang, W. J. Li, J. Lian, S. Evans and Y. Yin, Training and assignment of multi-skilled workers for implementing seru production systems, Internat. J. Advanced Manufac. Tech., 69 (2013), 937-959. doi: 10.1007/s00170-013-5027-5.  Google Scholar

[26]

C. Low, C. M. Hsu and K. I. Huang, Benefits of lot splitting in job-shop scheduling, Internat. J. Advanced Manufac. Tech., 24 (2004), 773-780.  doi: 10.1007/s00170-003-1785-9.  Google Scholar

[27]

H. Luo, A. Zhang and G. Q. Huang, Active scheduling for hybrid flowshop with family setup time and inconsistent family formation, Jo. Intelligent Manufac., 26 (2015), 169-187.  doi: 10.1007/s10845-013-0771-9.  Google Scholar

[28]

L. Luo, Z. Zhang and Y. Yin, Modelling and numerical analysis of seru loading problem under uncertainty, European J. of Industr. Engineering, 11 (2017), 185-204.  doi: 10.1504/EJIE.2017.083255.  Google Scholar

[29]

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, Equation of state calculations by fast computing machines, J. Chem. Physics, 21 (1953), 1087-1092.  doi: 10.2172/4390578.  Google Scholar

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Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, Berlin, 1994. doi: 10.1007/978-3-662-07418-3.  Google Scholar

[31]

D. I. Miyake, The shift from belt conveyor line to work-cell based assembly systems to cope with increasing demand variation in Japanese industries, Internat. J. Automotive Tech. and Management, 6 (2006), 419-439.  doi: 10.1504/IJATM.2006.012234.  Google Scholar

[32]

Not only Toyota - miraculous Canon manufacturing system, Weekly Toyo Keizen, 2003. Google Scholar

[33]

J. Pei, X. Liu, P. M. Pardalos, A. Migdalas and S. Yang, Serial-batching scheduling with time-dependent setup time and effects of deterioration and learning on a single-machine, J. Global Optim., 67 (2017), 1-12.  doi: 10.1007/s10898-015-0320-5.  Google Scholar

[34]

A. Roth, J. Singhal, K. Singhal and C. S. Tang, Knowledge creation and dissemination in operations and supply chain management, Produc. and Oper. Management, 25 (2016), 1473-1488.  doi: 10.1111/poms.12590.  Google Scholar

[35]

H. Sakamaki, The Change of Consciousness and Company by Cellular Manufacturing in Canon Way, Japan Management Association-Management Center, Tokyo, 2006. Google Scholar

[36]

Y. Sakazume, Is Japanese cell manufacturing a new system? A comparative study between Japanese cell manufacturing and cellular manufacturing, J. Japan Industr. Management Assoc., 55 (2005), 341-349.   Google Scholar

[37]

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Figure 1.  Three types seru
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Figure 2.  Whole bi-level decision procedure
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Figure 3.  The outline of SA-GA algorithm
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Figure 4.  An example of SA encoding
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Figure 5.  The genetic encoding based on allocation ratios
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Figure 6.  The flowchart of SA-GA algorithm
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Figure 7.  The minimum idle time in each iteration of SA
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Figure 8.  Idle time and makespan
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Figure 9.  The worker assignment decision
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Figure 10.  Loading results
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Figure 11.  The worker assignment decision
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Figure 12.  Loading results
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Table 1.  The parameter setting of SA-GA algorithm
Level Algorithm Parameters
Upper SA $ T\_max=10000 $ $ T\_min=0.1 $
$ II=20 $ $ \alpha=0.9 $
Lower GA $ pop\_size=300 $ $ GEN=500 $
$ p\_zero1=0.75 $ $ p\_zero2=0.25 $
$ p\_cross=0.9 $ $ p\_muta=0.1 $
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Level Algorithm Parameters
Upper SA $ T\_max=10000 $ $ T\_min=0.1 $
$ II=20 $ $ \alpha=0.9 $
Lower GA $ pop\_size=300 $ $ GEN=500 $
$ p\_zero1=0.75 $ $ p\_zero2=0.25 $
$ p\_cross=0.9 $ $ p\_muta=0.1 $
Table 2.  Data about products
Product Worker's processing time (min) Demand Setup
(min)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 23 23 21 22 21 24 22 – 21 24 22 – 24 24 23 95 4
2 – 32 37 32 – 34 37 31 34 31 – 31 36 36 37 100 9
3 41 43 – – 44 47 42 42 – 41 47 45 44 42 – 130 8
4 29 28 29 28 26 27 26 27 27 28 26 31 31 – 28 105 6
5 17 – 17 16 19 17 – 18 16 16 20 20 18 16 17 120 5
6 42 23 20 33 38 33 27 29 – 34 33 29 30 36 19 145 6
7 – 68 48 63 43 71 49 21 66 59 53 – – 70 83 50 4
8 14 15 14 20 – 19 19 17 22 19 17 18 – 15 10 115 1
1 The '-' means that the worker cannot produce the product.
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Product Worker's processing time (min) Demand Setup
(min)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 23 23 21 22 21 24 22 – 21 24 22 – 24 24 23 95 4
2 – 32 37 32 – 34 37 31 34 31 – 31 36 36 37 100 9
3 41 43 – – 44 47 42 42 – 41 47 45 44 42 – 130 8
4 29 28 29 28 26 27 26 27 27 28 26 31 31 – 28 105 6
5 17 – 17 16 19 17 – 18 16 16 20 20 18 16 17 120 5
6 42 23 20 33 38 33 27 29 – 34 33 29 30 36 19 145 6
7 – 68 48 63 43 71 49 21 66 59 53 – – 70 83 50 4
8 14 15 14 20 – 19 19 17 22 19 17 18 – 15 10 115 1
1 The '-' means that the worker cannot produce the product.
Table 3.  Data about products
1 2 3 4 5 6 7 8
1 – 100 – – 80 – 50 115
2 – – 130 – – 116 – –
3 95 – – 105 40 29 – –
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1 2 3 4 5 6 7 8
1 – 100 – – 80 – 50 115
2 – – 130 – – 116 – –
3 95 – – 105 40 29 – –
Table 4.  Production timetable
Product 1 2 3 4 5
Seru 3 1 2 3 1
Starting time Monday 8:00 Monday 8:00 Monday 8:00 Tuesday 9:13 Tuesday10:22
Finishing time Tuesday 9:07 Tuesday 10:17 Wednesday 11:30 Wednesday 15:54 Tuesday 16:09
Product 5 6 6 7 8
Seru 3 2 3 1 1
Starting time Wednesday 15:59 Wednesday 11:36 Thursday 9:25 Tuesday 16:13 Thursday 8:05
Finishing time Thursday 9:19 Thursday 17:12 Thursday 16:29 Thursday 8:04 Thursday 17:07
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Product 1 2 3 4 5
Seru 3 1 2 3 1
Starting time Monday 8:00 Monday 8:00 Monday 8:00 Tuesday 9:13 Tuesday10:22
Finishing time Tuesday 9:07 Tuesday 10:17 Wednesday 11:30 Wednesday 15:54 Tuesday 16:09
Product 5 6 6 7 8
Seru 3 2 3 1 1
Starting time Wednesday 15:59 Wednesday 11:36 Thursday 9:25 Tuesday 16:13 Thursday 8:05
Finishing time Thursday 9:19 Thursday 17:12 Thursday 16:29 Thursday 8:04 Thursday 17:07
Table 5.  Results of the small case
No. Idle time (min) Makespan (min) CPU time (s)
1 2381.7 1910 8242.5
2 2629.4 1907.8 8193.5
3 2438.6 1932.3 8222.2
4 2446 1936 8228
5 2723.1 1933 8228.6
6 2022.3 1893 8064.8
7 2461.2 1895 8095.2
8 2300 1906.3 8098.5
9 2819 1859.5 8051.9
10 2566.8 1874.1 8135
Average 2478.81 1904.7 8156.02
SD 214.16 24.07 70.94
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No. Idle time (min) Makespan (min) CPU time (s)
1 2381.7 1910 8242.5
2 2629.4 1907.8 8193.5
3 2438.6 1932.3 8222.2
4 2446 1936 8228
5 2723.1 1933 8228.6
6 2022.3 1893 8064.8
7 2461.2 1895 8095.2
8 2300 1906.3 8098.5
9 2819 1859.5 8051.9
10 2566.8 1874.1 8135
Average 2478.81 1904.7 8156.02
SD 214.16 24.07 70.94
Table 6.  Results of GA-GA algorithm for small case
No. Idle time (min) Makespan (min) CPU time (s)
1 2519.5 1913.8 8220.8
2 nonconvergent
3 2384.4 1851.8 8278.8
4 2375.6 1898.3 8230.3
5 nonconvergent
6 2409.5 1829 8284.8
7 2882 1894.2 9085.2
8 2213.2 1941.3 8244.5
9 2526 1941 8190.9
10 2526.9 1918 8289.3
Average 2479.64 1898.43 8353.08
SD 181.55 37.55 278.59
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No. Idle time (min) Makespan (min) CPU time (s)
1 2519.5 1913.8 8220.8
2 nonconvergent
3 2384.4 1851.8 8278.8
4 2375.6 1898.3 8230.3
5 nonconvergent
6 2409.5 1829 8284.8
7 2882 1894.2 9085.2
8 2213.2 1941.3 8244.5
9 2526 1941 8190.9
10 2526.9 1918 8289.3
Average 2479.64 1898.43 8353.08
SD 181.55 37.55 278.59
Table 7.  Workers' processing time for each product
Worker Workers' processing time for each product (min)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 22 39 47 29 - 34 64 23 50 71 20 21 11 32 39 15 20 27 29 24
2 23 37 47 29 20 35 54 21 55 77 24 20 12 30 38 19 21 21 26 20
3 22 38 46 - 22 35 50 26 56 77 24 15 11 34 43 - 17 23 29 21
4 - 37 46 32 - 35 56 - 50 78 22 19 12 34 42 17 21 21 25 23
5 23 40 47 27 - 34 59 20 50 81 - 17 10 34 42 15 17 22 28 -
6 22 38 47 29 23 33 61 25 - - 21 20 10 32 39 18 17 27 28 21
7 21 37 - 28 19 32 59 - 52 73 23 21 11 30 35 16 22 22 25 19
8 23 38 49 27 18 - - 22 48 78 21 20 10 31 44 18 - 23 26 22
9 21 40 50 - 21 33 56 26 53 87 - 18 10 32 40 17 22 21 27 20
10 24 - 49 28 19 38 58 26 52 - 24 18 10 37 41 - 17 25 26 23
11 22 38 47 30 18 33 61 27 53 77 21 19 - 33 41 - 19 21 29 23
12 23 36 49 29 21 34 57 22 53 86 21 20 10 33 36 17 21 21 27 24
13 23 39 47 29 22 - 65 21 53 86 22 19 12 30 38 15 19 22 27 21
14 23 39 - 31 18 30 50 29 57 85 24 - 10 37 36 19 21 27 27 21
15 21 36 49 30 - 36 59 24 50 81 24 17 11 37 35 18 19 26 26 22
16 25 36 49 31 19 37 58 22 54 82 24 19 12 39 39 17 18 23 29 22
17 - 37 45 30 22 38 60 23 55 - 21 18 - 37 44 - 21 22 27 -
18 23 37 49 31 21 37 61 - 48 - 21 21 12 34 - 17 17 - 26 20
19 21 35 48 - 19 37 61 28 48 69 20 19 10 33 36 18 22 25 25 20
20 21 38 - 30 23 32 55 29 53 72 22 16 10 - 35 16 17 21 29 23
21 21 36 50 30 22 35 64 29 53 86 22 17 11 39 - 17 18 24 26 23
22 22 38 50 29 - 33 61 22 48 69 23 17 11 40 - 15 - 22 28 21
23 25 39 47 29 19 37 59 26 - - 24 16 12 39 - 17 22 25 25 23
24 20 37 49 29 22 30 62 22 47 71 21 18 12 40 42 19 21 27 25 21
25 23 39 47 30 21 38 63 - 55 - 23 15 11 31 38 19 22 27 27 24
26 - 37 - 32 23 32 58 28 50 72 24 16 11 32 44 17 19 22 25 -
27 24 37 49 30 22 - 56 30 51 78 24 19 11 34 40 - 19 - 29 21
28 24 39 47 - 18 37 - 24 47 85 23 16 10 39 35 17 22 20 26 20
29 25 - 47 29 19 36 54 20 49 79 24 16 11 35 41 18 - 23 25 -
30 20 37 47 28 22 40 51 22 51 78 - 21 11 37 39 16 18 - 25 -
31 23 38 48 29 19 35 53 20 56 72 22 16 11 - 37 16 20 25 25 20
32 23 36 45 29 - 37 63 29 50 79 20 16 11 37 - 18 21 27 29 25
33 23 38 47 30 23 40 59 26 56 78 23 18 11 41 40 - 21 22 - 23
34 21 35 50 27 23 38 65 22 47 71 24 16 10 38 36 16 20 27 27 24
35 20 35 48 32 21 33 61 25 - - 21 21 10 38 - 19 18 24 29 19
36 - 38 45 30 19 31 63 24 56 85 23 - 10 41 37 19 19 24 26 21
37 24 36 - 30 22 38 55 24 50 87 23 19 12 - 39 17 20 26 - 25
38 24 39 49 32 21 37 52 - - 71 24 19 12 35 38 15 19 23 25 22
39 21 39 49 31 19 35 57 29 55 77 21 19 11 40 43 15 19 - 28 19
40 25 35 47 30 20 34 59 25 48 72 23 - 10 41 35 18 20 20 26 18
41 22 36 48 32 20 - 55 25 49 71 23 19 12 31 43 17 19 22 26 24
42 23 39 47 27 19 39 64 24 53 74 24 21 12 32 - 19 18 - 29 22
43 23 36 46 32 20 35 - 21 55 80 21 16 12 32 40 18 20 23 26 22
44 - - 45 31 22 37 52 - 57 72 22 16 11 37 - 18 22 20 27 24
45 20 40 47 29 21 32 52 29 55 82 21 15 10 33 - 16 20 27 - 19
46 20 40 - 30 20 38 58 23 50 82 23 20 11 31 38 19 - - 25 19
47 23 39 49 - 21 39 61 25 - 78 24 19 11 38 39 17 22 27 27 25
48 22 38 49 28 18 33 - 25 49 74 23 18 12 30 43 16 20 21 29 -
49 20 39 47 29 21 - 60 22 52 81 23 21 12 30 40 16 20 24 25 19
50 22 - 47 28 20 32 64 27 49 77 - 18 10 33 37 17 20 20 25 24
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Worker Workers' processing time for each product (min)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 22 39 47 29 - 34 64 23 50 71 20 21 11 32 39 15 20 27 29 24
2 23 37 47 29 20 35 54 21 55 77 24 20 12 30 38 19 21 21 26 20
3 22 38 46 - 22 35 50 26 56 77 24 15 11 34 43 - 17 23 29 21
4 - 37 46 32 - 35 56 - 50 78 22 19 12 34 42 17 21 21 25 23
5 23 40 47 27 - 34 59 20 50 81 - 17 10 34 42 15 17 22 28 -
6 22 38 47 29 23 33 61 25 - - 21 20 10 32 39 18 17 27 28 21
7 21 37 - 28 19 32 59 - 52 73 23 21 11 30 35 16 22 22 25 19
8 23 38 49 27 18 - - 22 48 78 21 20 10 31 44 18 - 23 26 22
9 21 40 50 - 21 33 56 26 53 87 - 18 10 32 40 17 22 21 27 20
10 24 - 49 28 19 38 58 26 52 - 24 18 10 37 41 - 17 25 26 23
11 22 38 47 30 18 33 61 27 53 77 21 19 - 33 41 - 19 21 29 23
12 23 36 49 29 21 34 57 22 53 86 21 20 10 33 36 17 21 21 27 24
13 23 39 47 29 22 - 65 21 53 86 22 19 12 30 38 15 19 22 27 21
14 23 39 - 31 18 30 50 29 57 85 24 - 10 37 36 19 21 27 27 21
15 21 36 49 30 - 36 59 24 50 81 24 17 11 37 35 18 19 26 26 22
16 25 36 49 31 19 37 58 22 54 82 24 19 12 39 39 17 18 23 29 22
17 - 37 45 30 22 38 60 23 55 - 21 18 - 37 44 - 21 22 27 -
18 23 37 49 31 21 37 61 - 48 - 21 21 12 34 - 17 17 - 26 20
19 21 35 48 - 19 37 61 28 48 69 20 19 10 33 36 18 22 25 25 20
20 21 38 - 30 23 32 55 29 53 72 22 16 10 - 35 16 17 21 29 23
21 21 36 50 30 22 35 64 29 53 86 22 17 11 39 - 17 18 24 26 23
22 22 38 50 29 - 33 61 22 48 69 23 17 11 40 - 15 - 22 28 21
23 25 39 47 29 19 37 59 26 - - 24 16 12 39 - 17 22 25 25 23
24 20 37 49 29 22 30 62 22 47 71 21 18 12 40 42 19 21 27 25 21
25 23 39 47 30 21 38 63 - 55 - 23 15 11 31 38 19 22 27 27 24
26 - 37 - 32 23 32 58 28 50 72 24 16 11 32 44 17 19 22 25 -
27 24 37 49 30 22 - 56 30 51 78 24 19 11 34 40 - 19 - 29 21
28 24 39 47 - 18 37 - 24 47 85 23 16 10 39 35 17 22 20 26 20
29 25 - 47 29 19 36 54 20 49 79 24 16 11 35 41 18 - 23 25 -
30 20 37 47 28 22 40 51 22 51 78 - 21 11 37 39 16 18 - 25 -
31 23 38 48 29 19 35 53 20 56 72 22 16 11 - 37 16 20 25 25 20
32 23 36 45 29 - 37 63 29 50 79 20 16 11 37 - 18 21 27 29 25
33 23 38 47 30 23 40 59 26 56 78 23 18 11 41 40 - 21 22 - 23
34 21 35 50 27 23 38 65 22 47 71 24 16 10 38 36 16 20 27 27 24
35 20 35 48 32 21 33 61 25 - - 21 21 10 38 - 19 18 24 29 19
36 - 38 45 30 19 31 63 24 56 85 23 - 10 41 37 19 19 24 26 21
37 24 36 - 30 22 38 55 24 50 87 23 19 12 - 39 17 20 26 - 25
38 24 39 49 32 21 37 52 - - 71 24 19 12 35 38 15 19 23 25 22
39 21 39 49 31 19 35 57 29 55 77 21 19 11 40 43 15 19 - 28 19
40 25 35 47 30 20 34 59 25 48 72 23 - 10 41 35 18 20 20 26 18
41 22 36 48 32 20 - 55 25 49 71 23 19 12 31 43 17 19 22 26 24
42 23 39 47 27 19 39 64 24 53 74 24 21 12 32 - 19 18 - 29 22
43 23 36 46 32 20 35 - 21 55 80 21 16 12 32 40 18 20 23 26 22
44 - - 45 31 22 37 52 - 57 72 22 16 11 37 - 18 22 20 27 24
45 20 40 47 29 21 32 52 29 55 82 21 15 10 33 - 16 20 27 - 19
46 20 40 - 30 20 38 58 23 50 82 23 20 11 31 38 19 - - 25 19
47 23 39 49 - 21 39 61 25 - 78 24 19 11 38 39 17 22 27 27 25
48 22 38 49 28 18 33 - 25 49 74 23 18 12 30 43 16 20 21 29 -
49 20 39 47 29 21 - 60 22 52 81 23 21 12 30 40 16 20 24 25 19
50 22 - 47 28 20 32 64 27 49 77 - 18 10 33 37 17 20 20 25 24
Table 8.  Setup time and demand of products
Product 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Setup time (min) 4 9 8 6 5 6 4 1 10 12 24 2 5 7 11 3 15 4 2 7
Demand 145 107 134 105 140 145 115 87 145 126 125 150 118 106 75 80 132 83 65 89
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Product 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Setup time (min) 4 9 8 6 5 6 4 1 10 12 24 2 5 7 11 3 15 4 2 7
Demand 145 107 134 105 140 145 115 87 145 126 125 150 118 106 75 80 132 83 65 89
Table 9.  Results of large case
No. Idle time (min) Makespan (min) CPU time (s)
1 5587.3 1932 16236
2 5457.4 1848.30 16376
3 5164.9 1865.4 16221
4 5258.9 1919 15754
5 5757.2 1806 15743
Average 5445.14 1874.14 16066
SD 214.92 46.36 264.84
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No. Idle time (min) Makespan (min) CPU time (s)
1 5587.3 1932 16236
2 5457.4 1848.30 16376
3 5164.9 1865.4 16221
4 5258.9 1919 15754
5 5757.2 1806 15743
Average 5445.14 1874.14 16066
SD 214.92 46.36 264.84
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