Table 7 Average RPDs (%) and running time for small-scale instances.

From: Single machine scheduling problems with sequence-dependent setup times and precedence delays

n

Processing Time

SDST

Delay Time

MILP

LIG

VNS

RPD

Time

RPD

Time

RPD

Time

10

[10, 20]

[5, 10]

[20,40]

0.000

3.76

0.000

1.002

0.597

4.56

10

[10, 20]

[5, 10]

[40,60]

0.000

2.96

0.000

1.010

0.052

4.45

10

[10, 20]

[10, 15]

[20,40]

0.000

5.51

0.000

1.009

0.238

4.44

10

[10, 20]

[10, 15]

[40,60]

0.000

3.12

0.000

1.009

0.574

4.53

10

[10, 20]

[5, 10]

[20,40]

0.000

4.83

0.000

1.009

0.196

4.47

10

[20, 30]

[5, 10]

[40,60]

0.000

3.73

0.000

1.009

0.663

4.42

10

[20, 30]

[10, 15]

[20,40]

0.000

6.91

0.000

1.009

0.000

4.48

10

[20, 30]

[10, 15]

[40,60]

0.000

4.35

0.000

1.007

0.433

4.49

15

[20, 30]

[5,10]

[20,40]

1.181

3600.02

1.079

1.509

2.801

5.44

15

[10, 20]

[5, 10]

[40,60]

1.141

3359.48

1.105

1.509

3.416

5.47

15

[10, 20]

[10, 15]

[20,40]

0.782

3600.02

0.756

1.510

1.723

5.49

15

[10, 20]

[10, 15]

[40,60]

0.950

3600.02

0.894

1.510

2.288

5.44

15

[20, 30]

[5, 10]

[20,40]

0.618

3600.03

0.618

1.509

1.412

5.42

15

[20, 30]

[5, 10]

[40,60]

0.776

3600.02

0.731

1.510

1.984

5.45

15

[20, 30]

[10, 15]

[20,40]

0.531

3600.02

0.512

1.509

1.256

5.41

15

[20, 30]

[10, 15]

[40,60]

0.611

3600.02

0.611

1.508

1.573

5.48

Total Ave

   

0.412

1787.18

0.394

1.259

1.200

4.96