American Institute of Mathematical Sciences

Advanced
April  2019, 15(2): 855-879. doi: 10.3934/jimo.2018074

An integrated Principal Component Analysis and multi-objective mathematical programming approach to agile supply chain network design under uncertainty

Azam Moradi 1, , Jafar Razmi 1, , Reza Babazadeh 2,, and  Ali Sabbaghnia 1,

1. 

School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
2. 

Faculty of Engineering, Urmia University, Urmia, West Azerbaijan Province, Iran

* Corresponding author: Tel.: +98 441 2972854; Fax: +98 441 2773591, Email address: r.babazadeh@urmia.ac.ir

Received  January 2018 Revised  January 2018 Published  April 2019 Early access  June 2018

Fund Project: The authors are supported by INSF grant (Iran National Science Foundation).

The design of agile supply chain networks has attracted more attention in recent years according to the competitive business environment. Further, due to high degree of uncertainty in agile supply chains (SCs), developing robust and efficient decision making tools are of interest. In this study, an integrated approach based on principal component analysis (PCA) and multi-objective possibilistic mixed integer programming (MOPMIP) approaches is proposed to optimally design agile supply chain network under uncertainty. The PCA method is used for ranking and filtering the suppliers, constituting the first layer of the supply chain, based on agility criteria. The proposed MOPMIP model is employed to construct the agile supply chain network under uncertainty. In the proposed MOPMIP model, three objective functions including 1) total costs minimization, 2) total delivery time minimization and 3) maximization of flexibility are considered. An interactive fuzzy solution approach is used to solve the proposed MOPMILP model. Two numerical examples, is conducted to evaluate the performance and efficiency of the proposed integrated approach for agile supply chain network design under uncertainty.

Keywords: Principal component analysis, agile supply chain, mathematical programming, fuzzy multi-objective programming, uncertainty.
Mathematics Subject Classification: Primary: 35Q90, 97N60, 65K05; Secondary: 90C70, 90C10, 90C29.
Citation: Azam Moradi, Jafar Razmi, Reza Babazadeh, Ali Sabbaghnia. An integrated Principal Component Analysis and multi-objective mathematical programming approach to agile supply chain network design under uncertainty. Journal of Industrial & Management Optimization, 2019, 15 (2) : 855-879. doi: 10.3934/jimo.2018074
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Figure 1.  Here is the Caption of your figure
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Figure 2.  Eigenvalue scree plot
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Figure 3.  The Pareto optimal solutions for normalized values of first test problem
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Table 1.  The primary defined input attributes for suppliers selection
RowInput attributeRowInput attribute
1Number of facilities21Working hours
2Staff training22Bureaucratic
3Education managers23Defective products
4Standard simple mentation in organizations24Material requirements planning
5In Stock25Distribution plan
6Product price26The geographical location of the factory
7Product variety27The geographical area covered
8Transportation28The political situation in the regions covered
9Waste29Infrastructure
10Market share30After Sales Service
11Career Opportunities31Technical Support
12The use of new technology32Management
13Production Volume33Response to Customer Request
14Automation34E-commerce Capability
15Communication System35JIT
16Delivery36Packing Ability
17Time of preparation37Position in the industry
18Lot Size38Product appearance
19Work in process (WIP)39Quality
20Specialist operators
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RowInput attributeRowInput attribute
1Number of facilities21Working hours
2Staff training22Bureaucratic
3Education managers23Defective products
4Standard simple mentation in organizations24Material requirements planning
5In Stock25Distribution plan
6Product price26The geographical location of the factory
7Product variety27The geographical area covered
8Transportation28The political situation in the regions covered
9Waste29Infrastructure
10Market share30After Sales Service
11Career Opportunities31Technical Support
12The use of new technology32Management
13Production Volume33Response to Customer Request
14Automation34E-commerce Capability
15Communication System35JIT
16Delivery36Packing Ability
17Time of preparation37Position in the industry
18Lot Size38Product appearance
19Work in process (WIP)39Quality
20Specialist operators
Table 2.  The most important agility criteria filtered through conducting brain storming meeting
Input indicatorsRow
1Specialist operators
2The use of new technology
3Material requirements planning
4Distribution plan
5Response to Customer Request
6Technical Support
7E-commerce Capability
8Product variety
9Production Volume
10Transportation
11After Sales Service
12Automation
13Communication System
14JIT
15Quality
16The geographical area covered
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Input indicatorsRow
1Specialist operators
2The use of new technology
3Material requirements planning
4Distribution plan
5Response to Customer Request
6Technical Support
7E-commerce Capability
8Product variety
9Production Volume
10Transportation
11After Sales Service
12Automation
13Communication System
14JIT
15Quality
16The geographical area covered
Table 3.  The performance indicators of suppliers
Output indicatorsRow
1Product price
2Bureaucratic
3Delivery time
4Work in Process (WIP)
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Output indicatorsRow
1Product price
2Bureaucratic
3Delivery time
4Work in Process (WIP)
Table 4.  Total Variance of components
ComponentInitial Eigenvalue
TotalPercentage of VarianceCumulative Percentage
12.07412.96512.965
21.80311.26724.232
31.5759.84334.075
41.3808.62542.700
51.3348.33651.036
61.1817.38358.419
71.0276.41864.836
80.9355.84170.677
90.8845.52376.200
100.7934.95981.159
110.7204.49885.656
120.6243.89889.554
130.5803.62493.178
140.4232.64295.820
150.3622.26598.086
160.3061.914100.000
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ComponentInitial Eigenvalue
TotalPercentage of VarianceCumulative Percentage
12.07412.96512.965
21.80311.26724.232
31.5759.84334.075
41.3808.62542.700
51.3348.33651.036
61.1817.38358.419
71.0276.41864.836
80.9355.84170.677
90.8845.52376.200
100.7934.95981.159
110.7204.49885.656
120.6243.89889.554
130.5803.62493.178
140.4232.64295.820
150.3622.26598.086
160.3061.914100.000
Table 5.  Total Variance of components
ComponentExtraction Sums of Squared LoadingsRotation Sums of Squared Loadings
TotalPercentage of VarianceCumulative PercentageTotalPercentage of VarianceCumulative Percentage
12.07412.96512.9651.5489.6759.675
21.80311.26724.2321.5479.67219.347
31.5759.84334.0751.5109.44028.787
41.3808.62542.7001.5069.41038.197
51.3348.33651.0361.4609.12647.324
61.1817.38358.4191.4018.75756.081
71.0276.41864.8361.4018.75564.836
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ComponentExtraction Sums of Squared LoadingsRotation Sums of Squared Loadings
TotalPercentage of VarianceCumulative PercentageTotalPercentage of VarianceCumulative Percentage
12.07412.96512.9651.5489.6759.675
21.80311.26724.2321.5479.67219.347
31.5759.84334.0751.5109.44028.787
41.3808.62542.7001.5069.41038.197
51.3348.33651.0361.4609.12647.324
61.1817.38358.4191.4018.75756.081
71.0276.41864.8361.4018.75564.836
Table 6.  Rotated components
VariablesComponents
1234567
X10.042-0.1920.615-0.2110.159-0.273-0.029
X2-0.1750.176-0.015-0.065-0.709-0.101-0.061
X3-0.083-0.096-0.1450.479-0.4400.219-0.067
X40.1200.177-0.2200.6090.221-0.251-0.108
X5-0.208-0.8270.0650.1390.0480.2630.109
X6-0.2230.571-0.2070.0990.2560.1820.418
X70.133-0.1340.2050.753-0.0700.0730.037
X8-0.0730.004-0.090-0.018-0.016-0.729-0.123
X90.8410.0350.1350.0220.083-0.0110.014
X100.551-0.016-0.1000.309-0.0350.370-0.010
X11-0.1100.2280.6950.2210.1900.141-0.097
X12-0.2580.5410.1550.034-0.2830.2920.244
X130.175-0.166-0.147-0.2810.1510.506-0.591
X14-0.1770.115-0.6370.0140.262-0.176-0.120
X15-0.4640.1590.031-0.0860.629-0.029-0.048
X160.1110.005-0.030-0.1630.0720.1910.861
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VariablesComponents
1234567
X10.042-0.1920.615-0.2110.159-0.273-0.029
X2-0.1750.176-0.015-0.065-0.709-0.101-0.061
X3-0.083-0.096-0.1450.479-0.4400.219-0.067
X40.1200.177-0.2200.6090.221-0.251-0.108
X5-0.208-0.8270.0650.1390.0480.2630.109
X6-0.2230.571-0.2070.0990.2560.1820.418
X70.133-0.1340.2050.753-0.0700.0730.037
X8-0.0730.004-0.090-0.018-0.016-0.729-0.123
X90.8410.0350.1350.0220.083-0.0110.014
X100.551-0.016-0.1000.309-0.0350.370-0.010
X11-0.1100.2280.6950.2210.1900.141-0.097
X12-0.2580.5410.1550.034-0.2830.2920.244
X130.175-0.166-0.147-0.2810.1510.506-0.591
X14-0.1770.115-0.6370.0140.262-0.176-0.120
X15-0.4640.1590.031-0.0860.629-0.029-0.048
X160.1110.005-0.030-0.1630.0720.1910.861
Table 7.  Suppliers scores driven out via PCA approach
SupplierScoreSupplierScoreSupplierScoreSupplierScore
1-0.4414316-0.4509331-0.70673460.22046
2-0.3994817-0.16193320.52357470.646209
30.079517180.41908330.57433948-0.2407
4-0.0185419-0.05046340.054961490.430716
50.06819200.01026435-0.3108500.175306
6-0.1633921-0.2980536-0.2968151-0.12202
7-0.47472220.283236370.379933520.065461
8-0.2640923-0.10214380.08338653-0.80726
90.35943424-0.387439-0.1178554-0.19505
10-0.48728250.278027400.092893550.258526
110.044161260.19624741-0.19233560.570286
120.50004270.194767420.121639570.265066
131.064131280.00978343-0.39538580.098087
14-0.7230529-0.08439440.67646459-0.50213
15-0.19635300.26665345-0.0272160-0.39293
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SupplierScoreSupplierScoreSupplierScoreSupplierScore
1-0.4414316-0.4509331-0.70673460.22046
2-0.3994817-0.16193320.52357470.646209
30.079517180.41908330.57433948-0.2407
4-0.0185419-0.05046340.054961490.430716
50.06819200.01026435-0.3108500.175306
6-0.1633921-0.2980536-0.2968151-0.12202
7-0.47472220.283236370.379933520.065461
8-0.2640923-0.10214380.08338653-0.80726
90.35943424-0.387439-0.1178554-0.19505
10-0.48728250.278027400.092893550.258526
110.044161260.19624741-0.19233560.570286
120.50004270.194767420.121639570.265066
131.064131280.00978343-0.39538580.098087
14-0.7230529-0.08439440.67646459-0.50213
15-0.19635300.26665345-0.0272160-0.39293
Table 8.  The sources of random generation of the most likely values
ParameterValueParameterValue
$\tilde fs_{st}$ $ \sim Uniform(1800000, 4300000)$$\tilde Tr4_{idclt}$ $ \sim Uniform(80, 100)$
$\tilde fp_{pt}$$ \sim Uniform(1700000, 4000000)$$\tilde Cost_{mspt}$$ \sim Uniform(20, 40)$
$\tilde fd_{dt}$$ \sim Uniform(1600000, 3000000)$$\tilde MI_{id}$$ \sim Uniform(100, 120)$
$\tilde fse_{st}$$ \sim Uniform(180000, 480000)$$\tilde CPA1_{pft}$$ \sim Uniform(50000, 60000)$
$\tilde fpe_{pt}$$ \sim Uniform(170000, 400000)$$\tilde CPA2_{djt}$$ \sim Uniform(30000, 35000)$
$\tilde fde_{dt}$$ \sim Uniform(160000, 300000)$$\tilde CPA_{pdt}$$ \sim Uniform(60000, 70000)$
$\tilde de_{ict}$$ \sim Uniform(100, 200)$$\tilde td_{pclt}$$ \sim Uniform(16, 20)$
$\tilde vp_{ipt}$$ \sim Uniform(120, 150)$$\tilde tc_{dclt}$$ \sim Uniform(2, 4)$
$\tilde Hd_{idt}$$ \sim Uniform(10, 30)$$\tilde te_{pdlt}$$ \sim Uniform(10, 16)$
$\tilde Hp_{ipt}$$ \sim Uniform(15, 40)$$\tilde dis1_{pcl}$$ \sim Uniform(200, 600)$
$\tilde Tr1_{isplt}$$ \sim Uniform(80, 100)$$\tilde dis2_{dcl}$$ \sim Uniform(300, 500)$
$\tilde Tr2_{ipdlt}$$ \sim Uniform(40, 60)$$\tilde dis3_{pdl}$$ \sim Uniform(100, 200)$
$\tilde Tr3_{ipclt}$$ \sim Uniform(110, 200)$
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ParameterValueParameterValue
$\tilde fs_{st}$ $ \sim Uniform(1800000, 4300000)$$\tilde Tr4_{idclt}$ $ \sim Uniform(80, 100)$
$\tilde fp_{pt}$$ \sim Uniform(1700000, 4000000)$$\tilde Cost_{mspt}$$ \sim Uniform(20, 40)$
$\tilde fd_{dt}$$ \sim Uniform(1600000, 3000000)$$\tilde MI_{id}$$ \sim Uniform(100, 120)$
$\tilde fse_{st}$$ \sim Uniform(180000, 480000)$$\tilde CPA1_{pft}$$ \sim Uniform(50000, 60000)$
$\tilde fpe_{pt}$$ \sim Uniform(170000, 400000)$$\tilde CPA2_{djt}$$ \sim Uniform(30000, 35000)$
$\tilde fde_{dt}$$ \sim Uniform(160000, 300000)$$\tilde CPA_{pdt}$$ \sim Uniform(60000, 70000)$
$\tilde de_{ict}$$ \sim Uniform(100, 200)$$\tilde td_{pclt}$$ \sim Uniform(16, 20)$
$\tilde vp_{ipt}$$ \sim Uniform(120, 150)$$\tilde tc_{dclt}$$ \sim Uniform(2, 4)$
$\tilde Hd_{idt}$$ \sim Uniform(10, 30)$$\tilde te_{pdlt}$$ \sim Uniform(10, 16)$
$\tilde Hp_{ipt}$$ \sim Uniform(15, 40)$$\tilde dis1_{pcl}$$ \sim Uniform(200, 600)$
$\tilde Tr1_{isplt}$$ \sim Uniform(80, 100)$$\tilde dis2_{dcl}$$ \sim Uniform(300, 500)$
$\tilde Tr2_{ipdlt}$$ \sim Uniform(40, 60)$$\tilde dis3_{pdl}$$ \sim Uniform(100, 200)$
$\tilde Tr3_{ipclt}$$ \sim Uniform(110, 200)$
Table 9.  The Pareto optimal solution for different values of importance coefficients
r1r2r3Problem No.Obj1Obj2Obj3CPU time (Sec)
10013.69E+111.38E+080.00E+00134
23.82E+121.26E+090.00E+00646
01016.61E+122.44E+070.00E+00164
22.50E+152.53E+080.00E+00655
00116.61E+121.38E+087.46E+07132
22.50E+151.26E+093.74E+11692
0.450.450.113.39E+127.89E+071.42E+07210
21.13E+156.58E+088.33E+10512
0.350.350.313.99E+129.30E+072.76E+07167
21.30E+157.29E+081.46E+11472
0.250.250.514.55E+121.06E+084.70E+07173
21.58E+159.41E+082.31E+11627
0.150.150.715.50E+121.16E+085.67E+07159
21.80E+159.91E+083.07E+11679
0.050.050.916.20E+121.25E+087.02E+07134
22.25E+151.13E+093.48E+11646
0.20.30.515.20E+129.83E+074.78E+07164
21.68E+158.90E+082.25E+11655
0.20.50.314.93E+127.21E+072.76E+07132
21.70E+156.48E+081.23E+11690
0.30.20.514.38E+121.13E+084.63E+07210
21.53E+159.81E+082.31E+11512
0.30.50.214.24E+126.65E+071.72E+07167
21.53E+156.38E+088.61E+10472
0.50.20.313.12E+121.08E+082.84E+07173
29.27E+149.84E+081.12E+11627
0.50.30.212.93E+129.59E+071.79E+07159
29.47E+148.90E+089.36E+10679
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r1r2r3Problem No.Obj1Obj2Obj3CPU time (Sec)
10013.69E+111.38E+080.00E+00134
23.82E+121.26E+090.00E+00646
01016.61E+122.44E+070.00E+00164
22.50E+152.53E+080.00E+00655
00116.61E+121.38E+087.46E+07132
22.50E+151.26E+093.74E+11692
0.450.450.113.39E+127.89E+071.42E+07210
21.13E+156.58E+088.33E+10512
0.350.350.313.99E+129.30E+072.76E+07167
21.30E+157.29E+081.46E+11472
0.250.250.514.55E+121.06E+084.70E+07173
21.58E+159.41E+082.31E+11627
0.150.150.715.50E+121.16E+085.67E+07159
21.80E+159.91E+083.07E+11679
0.050.050.916.20E+121.25E+087.02E+07134
22.25E+151.13E+093.48E+11646
0.20.30.515.20E+129.83E+074.78E+07164
21.68E+158.90E+082.25E+11655
0.20.50.314.93E+127.21E+072.76E+07132
21.70E+156.48E+081.23E+11690
0.30.20.514.38E+121.13E+084.63E+07210
21.53E+159.81E+082.31E+11512
0.30.50.214.24E+126.65E+071.72E+07167
21.53E+156.38E+088.61E+10472
0.50.20.313.12E+121.08E+082.84E+07173
29.27E+149.84E+081.12E+11627
0.50.30.212.93E+129.59E+071.79E+07159
29.47E+148.90E+089.36E+10679
Table 10.  The studies mentioning the agility indicators in the literature
IndexRazmi et al. (2011)Yauch (2011)Ghodsypour and O'Brien (1998)Min and Shin (2008)Weber et al. (1991)Abratt and Kleyn (2012)Dickson (1996)Prater et al. (2001)Kassaee et al. (2014)Dahmardeh et al. (2010)Kumar et al. (2011)Aktepe et al. (1999)Lin (2009)Chan and Thong (2009)This study
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Table Options

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IndexRazmi et al. (2011)Yauch (2011)Ghodsypour and O'Brien (1998)Min and Shin (2008)Weber et al. (1991)Abratt and Kleyn (2012)Dickson (1996)Prater et al. (2001)Kassaee et al. (2014)Dahmardeh et al. (2010)Kumar et al. (2011)Aktepe et al. (1999)Lin (2009)Chan and Thong (2009)This study
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Table 11.  Agile suppliers attributes
No.In1In2In3In4In5In6In7In8In9In10In11In12In13In14In15In16
10.540.820.50.620.750.450.620.640.710.60.50.570.520.350.230.6
20.50.040.630.630.950.460.60.760.40.770.50.60.80.530.380.47
30.270.660.720.970.930.480.780.120.370.780.680.630.80.350.120.33
40.430.340.710.750.920.560.720.440.530.680.640.680.720.370.320.3
50.720.130.540.730.680.50.520.650.710.790.620.610.540.550.190.35
60.710.450.810.520.90.520.550.020.310.720.70.650.70.340.10.34
70.50.430.890.940.850.410.580.50.580.610.630.530.760.520.760.34
80.340.770.740.550.740.420.70.060.80.760.40.630.790.440.240.49
90.520.290.860.570.730.620.590.310.710.710.650.650.770.460.740.69
100.390.580.650.760.670.660.620.40.210.610.420.60.520.560.940.36
110.40.530.970.810.960.470.760.170.690.770.420.740.670.240.240.51
120.580.070.750.540.650.60.530.10.860.720.630.740.70.30.060.55
130.40.120.620.870.620.70.730.040.620.790.60.80.790.210.590.64
140.340.810.870.860.630.670.520.940.20.730.490.520.770.50.220.32
150.80.730.890.50.80.590.580.940.260.740.650.620.570.10.440.52
160.620.270.570.891.000.440.70.670.20.620.440.560.590.410.860.65
170.260.010.860.710.910.510.540.610.370.80.420.640.650.290.370.66
180.330.630.960.930.610.650.730.230.440.710.70.640.540.520.170.63
190.50.540.910.860.860.530.740.610.650.710.570.610.740.550.940.48
210.330.890.680.620.810.590.510.380.510.750.510.770.790.410.860.35
220.610.40.560.540.830.70.530.370.630.70.560.640.580.330.970.67
230.680.840.980.90.880.440.690.030.60.740.430.590.720.140.250.61
240.410.810.810.950.730.460.770.660.50.680.470.630.690.230.310.3
250.270.440.630.550.940.690.720.180.280.740.610.710.580.210.000.59
260.280.370.530.550.850.470.680.330.750.780.460.650.670.180.350.7
270.640.790.630.70.890.450.570.150.690.770.660.710.650.250.550.52
280.310.890.990.620.670.60.790.250.380.720.510.80.540.390.110.55
290.60.020.760.730.640.70.50.670.530.640.420.790.620.450.990.36
300.420.230.760.90.810.660.790.960.690.780.560.510.760.20.510.36
310.80.480.80.510.830.430.660.840.30.780.480.580.690.480.120.31
320.580.050.660.60.730.610.730.230.870.740.490.670.770.320.030.68
330.570.210.860.710.640.540.780.450.550.740.680.770.560.310.990.41
340.760.630.650.930.660.440.680.990.750.720.520.80.50.20.50.38
350.280.040.710.670.720.430.570.440.720.710.450.50.750.410.290.47
360.450.750.870.70.620.410.570.920.630.730.620.780.670.340.360.35
370.730.10.750.980.730.550.560.340.750.690.620.520.730.230.610.57
380.750.20.750.720.950.510.670.720.460.720.660.660.750.490.910.58
390.80.980.520.860.860.680.50.310.690.650.630.640.760.170.270.43
410.330.440.840.840.680.70.580.980.370.60.50.780.540.520.270.7
420.660.970.590.70.780.590.770.720.440.680.670.710.660.160.340.54
430.320.720.750.580.730.580.560.260.210.620.510.660.780.280.620.62
440.520.170.560.990.760.650.770.590.460.730.670.670.50.410.870.56
450.590.530.80.780.930.460.710.070.780.660.520.590.680.160.710.36
460.460.010.770.770.990.50.710.760.90.780.590.60.790.480.460.54
470.790.070.820.680.810.590.740.30.640.750.650.620.720.120.410.6
480.410.180.640.590.790.460.730.890.760.640.620.540.580.530.220.41
490.450.090.530.860.650.640.740.270.280.770.620.580.710.460.840.4
500.40.490.910.620.880.580.750.390.350.710.650.780.640.130.390.44
510.660.470.710.610.670.570.660.020.310.60.610.750.760.510.690.35
520.620.420.810.540.930.540.520.110.220.690.680.790.620.350.550.69
530.70.930.660.520.90.450.570.650.310.640.560.580.80.230.250.43
540.250.910.820.990.630.650.580.880.360.760.460.780.640.520.170.62
550.280.370.520.550.690.60.650.630.280.630.70.720.620.150.880.67
560.640.421.001.000.910.690.710.110.890.770.510.620.560.420.210.63
570.490.630.910.820.840.540.80.010.530.790.620.560.520.480.190.49
580.490.970.560.70.60.660.580.260.820.80.420.610.770.460.590.56
590.710.090.620.50.790.520.670.590.210.660.440.510.730.290.60.4
600.270.060.970.680.980.590.580.250.20.690.40.750.680.540.720.49
Table Options

Download as excel

No.In1In2In3In4In5In6In7In8In9In10In11In12In13In14In15In16
10.540.820.50.620.750.450.620.640.710.60.50.570.520.350.230.6
20.50.040.630.630.950.460.60.760.40.770.50.60.80.530.380.47
30.270.660.720.970.930.480.780.120.370.780.680.630.80.350.120.33
40.430.340.710.750.920.560.720.440.530.680.640.680.720.370.320.3
50.720.130.540.730.680.50.520.650.710.790.620.610.540.550.190.35
60.710.450.810.520.90.520.550.020.310.720.70.650.70.340.10.34
70.50.430.890.940.850.410.580.50.580.610.630.530.760.520.760.34
80.340.770.740.550.740.420.70.060.80.760.40.630.790.440.240.49
90.520.290.860.570.730.620.590.310.710.710.650.650.770.460.740.69
100.390.580.650.760.670.660.620.40.210.610.420.60.520.560.940.36
110.40.530.970.810.960.470.760.170.690.770.420.740.670.240.240.51
120.580.070.750.540.650.60.530.10.860.720.630.740.70.30.060.55
130.40.120.620.870.620.70.730.040.620.790.60.80.790.210.590.64
140.340.810.870.860.630.670.520.940.20.730.490.520.770.50.220.32
150.80.730.890.50.80.590.580.940.260.740.650.620.570.10.440.52
160.620.270.570.891.000.440.70.670.20.620.440.560.590.410.860.65
170.260.010.860.710.910.510.540.610.370.80.420.640.650.290.370.66
180.330.630.960.930.610.650.730.230.440.710.70.640.540.520.170.63
190.50.540.910.860.860.530.740.610.650.710.570.610.740.550.940.48
210.330.890.680.620.810.590.510.380.510.750.510.770.790.410.860.35
220.610.40.560.540.830.70.530.370.630.70.560.640.580.330.970.67
230.680.840.980.90.880.440.690.030.60.740.430.590.720.140.250.61
240.410.810.810.950.730.460.770.660.50.680.470.630.690.230.310.3
250.270.440.630.550.940.690.720.180.280.740.610.710.580.210.000.59
260.280.370.530.550.850.470.680.330.750.780.460.650.670.180.350.7
270.640.790.630.70.890.450.570.150.690.770.660.710.650.250.550.52
280.310.890.990.620.670.60.790.250.380.720.510.80.540.390.110.55
290.60.020.760.730.640.70.50.670.530.640.420.790.620.450.990.36
300.420.230.760.90.810.660.790.960.690.780.560.510.760.20.510.36
310.80.480.80.510.830.430.660.840.30.780.480.580.690.480.120.31
320.580.050.660.60.730.610.730.230.870.740.490.670.770.320.030.68
330.570.210.860.710.640.540.780.450.550.740.680.770.560.310.990.41
340.760.630.650.930.660.440.680.990.750.720.520.80.50.20.50.38
350.280.040.710.670.720.430.570.440.720.710.450.50.750.410.290.47
360.450.750.870.70.620.410.570.920.630.730.620.780.670.340.360.35
370.730.10.750.980.730.550.560.340.750.690.620.520.730.230.610.57
380.750.20.750.720.950.510.670.720.460.720.660.660.750.490.910.58
390.80.980.520.860.860.680.50.310.690.650.630.640.760.170.270.43
410.330.440.840.840.680.70.580.980.370.60.50.780.540.520.270.7
420.660.970.590.70.780.590.770.720.440.680.670.710.660.160.340.54
430.320.720.750.580.730.580.560.260.210.620.510.660.780.280.620.62
440.520.170.560.990.760.650.770.590.460.730.670.670.50.410.870.56
450.590.530.80.780.930.460.710.070.780.660.520.590.680.160.710.36
460.460.010.770.770.990.50.710.760.90.780.590.60.790.480.460.54
470.790.070.820.680.810.590.740.30.640.750.650.620.720.120.410.6
480.410.180.640.590.790.460.730.890.760.640.620.540.580.530.220.41
490.450.090.530.860.650.640.740.270.280.770.620.580.710.460.840.4
500.40.490.910.620.880.580.750.390.350.710.650.780.640.130.390.44
510.660.470.710.610.670.570.660.020.310.60.610.750.760.510.690.35
520.620.420.810.540.930.540.520.110.220.690.680.790.620.350.550.69
530.70.930.660.520.90.450.570.650.310.640.560.580.80.230.250.43
540.250.910.820.990.630.650.580.880.360.760.460.780.640.520.170.62
550.280.370.520.550.690.60.650.630.280.630.70.720.620.150.880.67
560.640.421.001.000.910.690.710.110.890.770.510.620.560.420.210.63
570.490.630.910.820.840.540.80.010.530.790.620.560.520.480.190.49
580.490.970.560.70.60.660.580.260.820.80.420.610.770.460.590.56
590.710.090.620.50.790.520.670.590.210.660.440.510.730.290.60.4
600.270.060.970.680.980.590.580.250.20.690.40.750.680.540.720.49
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