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A Simple Metaheuristic for the FleetSize and Mix Problem with TimeWindows

  • Conference paper
  • First Online:
Computational Methods and Models for Transport (ECCOMAS 2015)

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 45))

  • 770 Accesses

Abstract

This paper presents a powerful new single-parameter metaheuristic to solve the Fleet Size and Mix Vehicle Routing Problem with Time Windows. The key idea of the new metaheuristic is to perform a random number of random-sized jumps in random order through four well-known local search operators. Computational testing on the 600 large-scale benchmarks of Bräysy et al. (Expert Syst Appl 36(4):8460–8475, 2009) show that the new metaheuristic outperforms previous best approaches, finding 533 new best-known solutions. Despite the significant number of random components, it is demonstrated that the variance of the results is rather low. Moreover, the suggested metaheuristic is shown to scale almost linearly up to 1000 customers.

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Authors and Affiliations

Authors

Corresponding author

Correspondence to Olli Bräysy .

Editor information

Editors and Affiliations

Appendix

Appendix

Data set

MSDAL

Normal

New

Data set

MSDAL

Normal

New

Best

CPU

Best

CPU

Best

CPU

Best

CPU

Best

CPU

Best

CPU

C121A

17478.35

95.30

17456.15

7.55

16146.77

14.32

C121C

4216.08

106.09

4216.08

8.34

3801.05

19.15

C122A

17056.41

96.25

17095.62

7.58

16929.05

10.69

C122C

4165.48

119.16

4164.70

7.58

4162.99

13.53

C123A

16897.70

92.95

16820.15

7.86

16629.48

14.45

C123C

4104.72

114.55

4093.93

8.72

4068.95

14.80

C124A

16563.86

95.13

16529.97

6.58

16364.38

16.10

C124C

4009.70

108.95

3988.11

7.89

3966.33

15.27

C125A

17452.85

108.22

17450.12

6.91

17311.40

8.07

C125C

4210.44

114.11

4210.35

7.58

4210.35

8.85

C126A

17528.25

114.49

17466.85

8.09

17407.42

10.83

C126C

4210.35

108.91

4210.35

8.47

4210.35

10.17

C127A

17539.70

106.81

17427.81

7.80

17280.28

10.31

C127C

4196.00

125.78

4191.71

7.84

4191.71

9.69

C128A

17366.06

107.13

17284.68

9.03

17118.19

11.56

C128C

4165.85

121.14

4169.79

7.84

4165.50

12.64

C129A

16963.26

85.86

17018.38

7.64

16810.15

12.17

C129C

4106.18

131.17

4086.01

7.31

4069.22

10.39

C1210A

16884.73

102.50

16749.52

7.41

16618.35

12.90

C1210C

4051.22

102.95

4038.56

8.11

4001.34

13.67

C221A

17787.35

69.27

17901.59

6.53

17281.46

8.10

C221C

3530.70

82.17

3547.22

7.75

3533.53

9.31

C222A

17591.14

54.52

17649.04

6.09

16955.05

9.81

C222C

3465.22

70.08

3462.97

7.39

3420.01

8.30

C223A

17139.14

62.72

16984.26

6.28

16946.04

12.50

C223C

3397.72

75.94

3396.56

7.05

3356.29

11.69

C224A

17048.28

86.38

17177.17

5.83

16823.39

9.21

C224C

3381.71

89.45

3333.64

6.83

3294.95

10.81

C225A

17627.05

58.06

17567.03

6.14

17175.93

9.34

C225C

3483.03

67.34

3496.70

7.14

3462.77

7.74

C226A

17321.54

65.31

17415.59

6.25

16999.21

6.19

C226C

3447.47

74.23

3439.13

7.39

3415.59

7.30

C227A

17496.18

66.75

17477.99

6.38

17015.52

8.08

C227C

3507.58

67.89

3491.72

7.11

3419.37

10.05

C228A

17399.34

60.69

17177.48

7.31

16890.76

8.96

C228C

3451.61

69.92

3425.01

7.58

3372.27

7.27

C229A

17600.02

62.81

17478.95

5.98

16991.30

9.88

C229C

3481.13

78.67

3439.75

7.06

3415.39

9.39

C2210A

17324.16

63.83

17024.78

6.19

16805.04

10.28

C2210C

3363.75

68.09

3408.34

6.92

3334.50

6.49

R121A

13904.64

90.36

13897.19

5.78

13790.32

9.19

R121C

5713.38

100.48

5700.76

6.03

5669.65

9.67

R122A

12467.81

84.94

12367.64

7.36

12234.33

11.59

R122C

4931.09

85.88

4889.25

7.59

4833.51

14.40

R123A

11207.92

80.00

11122.32

6.80

11026.50

12.98

R123C

4211.11

85.06

4125.01

7.48

4092.97

13.26

R124A

10466.36

74.38

10388.10

6.28

10267.04

13.00

R124C

3576.54

93.22

3517.42

7.41

3497.69

12.92

R125A

12336.34

81.27

12294.94

7.33

12110.40

7.60

R125C

4974.72

89.55

4941.12

7.69

4857.98

10.50

R126A

11620.63

79.56

11332.67

6.74

11269.22

10.67

R126C

4331.41

80.02

4340.97

6.94

4283.74

10.92

R127A

10868.82

76.19

10669.74

7.23

10569.21

9.89

R127C

3823.36

80.72

3759.99

8.06

3719.42

12.09

R128A

10361.97

72.53

10216.89

6.22

10167.08

12.18

R128C

3445.34

81.13

3421.79

7.70

3362.84

14.88

R129A

11812.63

73.99

11639.96

7.53

11443.92

8.96

R129C

4567.00

77.06

4553.55

7.69

4471.58

8.96

R1210A

10890.60

71.27

10780.94

7.39

10641.88

10.20

R1210C

3922.18

75.00

3867.58

7.25

3817.39

11.61

R221A

14355.06

71.61

14840.05

6.30

14874.75

6.01

R221C

4972.08

52.34

4805.18

6.98

4758.35

12.62

R222A

13543.70

52.16

14209.18

6.19

13799.69

12.36

R222C

4526.72

63.00

4344.74

6.64

4258.26

13.06

R223A

12103.17

57.30

12706.39

6.28

12008.67

10.52

R223C

3984.50

61.58

3795.58

6.97

3767.15

13.45

R224A

10520.72

57.80

11122.21

6.11

10514.71

11.39

R224C

3143.03

72.02

3097.62

6.98

2887.55

10.37

R225A

13081.80

38.53

13444.59

6.48

13383.36

10.97

R225C

4369.26

54.05

4375.84

6.77

4278.22

7.49

R226A

12543.67

48.02

12599.55

6.20

12098.39

10.97

R226C

4046.82

49.58

3947.06

7.05

3873.87

11.86

R227A

11137.18

52.20

11657.07

6.33

11325.15

11.65

R227C

3648.21

58.73

3477.60

6.69

3409.74

11.67

R228A

10274.93

65.78

10717.99

6.59

10004.11

11.59

R228C

2935.01

73.13

2896.26

7.23

2792.17

9.83

R229A

12586.96

34.84

12636.17

6.24

12183.42

9.39

R229C

4173.26

44.49

4138.39

7.36

4026.33

11.54

R2210A

11347.19

41.95

12182.76

6.08

11263.86

10.25

R2210C

3843.46

36.20

3817.64

6.42

3672.94

10.34

RC121A

10995.16

94.88

10885.35

6.52

10814.30

7.15

RC121C

4239.52

95.44

4239.69

7.24

4181.93

10.20

RC122A

10413.91

83.36

10214.64

6.94

10103.06

8.75

RC122C

3919.43

91.63

3882.92

7.33

3828.64

9.55

RC123A

9909.46

77.89

9644.62

6.97

9590.68

12.43

RC123C

3587.59

81.97

3498.29

7.53

3431.44

11.09

RC124A

9494.38

74.58

9378.79

6.28

9260.15

13.96

RC124C

3289.12

93.98

3197.80

7.81

3167.56

13.42

RC125A

10603.03

93.73

10509.68

7.41

10299.01

10.33

RC125C

4021.30

89.45

3984.16

7.70

3932.96

9.75

RC126A

10526.77

86.44

10368.06

7.47

10145.36

8.42

RC126C

3945.98

96.44

3926.56

8.06

3839.79

11.51

RC127A

10179.64

83.75

10030.10

7.83

9941.54

10.17

RC127C

3799.75

88.03

3728.42

7.25

3676.90

9.52

RC128A

9856.77

77.39

9714.63

7.42

9655.27

10.19

RC128C

3552.67

85.84

3564.54

7.78

3472.88

12.73

RC129A

9813.89

80.84

9737.70

7.56

9609.07

10.28

RC129C

3532.69

85.20

3541.33

7.47

3452.41

12.01

RC1210A

9645.79

74.55

9558.28

7.49

9425.92

9.77

RC1210C

3358.61

76.81

3361.24

7.61

3306.65

11.64

RC221A

14529.34

61.31

14520.71

6.09

14427.00

4.74

RC221C

4149.91

62.95

4114.66

7.09

4047.60

6.05

RC222A

13425.73

64.33

13705.36

5.89

13105.64

14.07

RC222C

3807.73

67.23

3784.42

7.49

3687.16

9.74

RC223A

11976.30

64.14

12827.49

5.53

11738.56

7.15

RC223C

3701.30

78.53

3498.41

7.03

3386.92

8.14

RC224A

10811.14

91.09

11279.77

6.16

10850.91

12.59

RC224C

3219.43

101.28

2980.75

6.66

2968.82

13.02

RC225A

13392.72

51.97

14359.90

5.52

13170.90

11.47

RC225C

3887.52

51.31

3769.78

6.91

3684.16

13.00

RC226A

13295.09

45.20

13565.32

5.63

12916.40

13.31

RC226C

3820.37

52.39

3761.27

7.31

3663.62

13.35

RC227A

12345.43

52.80

12879.30

6.33

12363.69

11.36

RC227C

3545.04

57.17

3572.29

7.41

3463.24

12.07

RC228A

11989.91

55.75

12449.37

5.33

11600.87

12.25

RC228C

3440.13

54.98

3351.74

7.31

3244.29

12.22

RC229A

11640.05

41.98

12109.84

8.09

11136.85

14.42

RC229C

3326.45

63.41

3257.88

6.84

3165.38

11.03

RC2210A

11345.16

51.19

11603.96

5.30

10339.85

9.25

RC2210C

3005.69

48.02

3142.97

6.97

2984.82

9.02

C141A

37156.67

368.98

37097.84

13.89

37004.00

10.30

C141C

10186.68

366.30

10185.25

14.16

10183.32

12.71

C142A

36287.65

375.16

36456.97

15.70

36095.64

18.77

C142C

10084.39

382.86

10130.08

14.64

10067.15

22.07

C143A

35443.86

366.56

35281.26

14.61

34936.70

23.37

C143C

9703.27

370.94

9848.58

15.34

9683.62

29.11

C144A

34483.09

353.73

33896.21

15.25

33646.05

28.74

C144C

9149.61

366.09

9134.87

15.75

8999.95

29.38

C145A

37423.25

375.06

37323.54

14.47

36985.55

17.05

C145C

10179.76

392.80

10178.79

13.89

10178.79

17.92

C146A

37640.19

389.23

37632.95

16.36

37006.93

17.80

C146C

10177.34

384.77

10181.25

14.78

10177.34

20.90

C147A

37628.29

368.61

37656.93

16.64

37157.52

18.86

C147C

10162.34

432.42

10260.60

16.11

10162.03

19.63

C148A

37268.20

356.30

37174.88

18.25

36643.17

20.09

C148C

10121.30

407.55

10150.06

17.09

10078.15

23.57

C149A

36408.62

371.00

36532.43

16.80

35952.34

25.65

C149C

9949.86

405.22

9968.79

16.86

9832.26

26.16

C1410A

35691.67

354.22

35847.06

17.11

35442.90

27.16

C1410C

9660.06

381.63

9763.37

17.48

9580.12

27.00

C241A

37214.21

305.72

37088.94

9.75

35018.11

16.01

C241C

7574.53

339.64

7511.11

12.08

7265.86

16.86

C242A

35332.57

296.28

34896.10

11.27

34394.99

18.63

C242C

7507.78

324.50

7289.22

13.11

7087.05

18.41

C243A

35391.65

296.09

35503.71

10.48

34322.87

20.97

C243C

7460.24

337.22

7092.95

12.33

7020.11

19.86

C244A

34815.47

358.92

34546.07

10.81

33721.40

20.08

C244C

7172.85

387.73

6943.14

12.81

6816.11

24.32

C245A

37085.14

297.52

36290.36

10.78

34785.97

17.38

C245C

7493.45

317.08

7367.54

12.70

7152.30

16.68

C246A

36175.26

291.80

35696.75

11.72

34489.11

19.05

C246C

7331.15

324.31

7182.54

13.78

7036.19

18.49

C247A

36025.56

304.25

36003.90

11.55

34384.41

19.00

C247C

7407.89

316.39

7387.50

12.80

7140.91

17.33

C248A

35900.06

307.61

35860.75

10.55

34167.01

17.89

C248C

7317.89

306.81

7243.95

12.75

6922.05

16.83

C249A

36117.04

320.34

36265.80

10.64

34482.65

20.52

C249C

7395.61

325.31

7192.29

13.11

7072.88

21.11

C2410A

35373.19

321.88

35217.67

10.52

33999.22

16.99

C2410C

7076.80

327.58

7156.69

12.47

6826.55

18.24

R141A

28667.92

329.58

28416.94

10.45

28106.24

17.72

R141C

12254.98

370.05

12212.22

11.89

12152.43

19.69

R142A

25397.84

318.11

25291.12

13.14

24902.38

21.37

R142C

10502.18

349.16

10560.12

14.31

10332.34

25.94

R143A

23134.81

297.03

22818.20

12.55

22602.52

26.43

R143C

8956.00

318.00

8795.12

14.61

8672.50

28.85

R144A

21970.88

303.78

21715.80

12.41

21503.57

26.97

R144C

8043.02

343.14

7870.61

14.59

7747.60

30.97

R145A

25347.71

317.28

25250.04

13.11

24774.88

16.47

R145C

10608.92

334.73

10656.56

14.33

10487.93

18.85

R146A

23905.30

301.91

23641.90

15.19

23373.36

19.55

R146C

9713.02

327.27

9633.82

15.55

9475.35

23.32

R147A

22687.50

301.45

22352.49

13.59

22121.96

25.02

R147C

8555.58

323.72

8417.54

13.22

8236.43

25.43

R148A

21909.69

298.95

21606.92

13.14

21444.98

29.13

R148C

7905.12

335.55

7772.45

14.66

7630.77

25.96

R149A

24180.08

297.16

24065.69

13.56

23661.41

17.94

R149C

9921.21

318.06

9832.68

14.64

9670.65

20.75

R1410A

23130.23

285.44

22884.25

13.03

22603.72

21.92

R1410C

9078.38

308.25

8944.72

12.83

8793.32

23.20

R241A

30752.74

321.22

31463.53

13.16

31502.10

22.75

R241C

10799.49

185.02

10370.89

13.03

10066.55

19.47

R242A

27372.86

220.03

30025.97

12.03

28893.61

28.46

R242C

9635.11

267.55

9171.98

12.80

9010.48

21.33

R243A

24922.94

264.44

27621.15

11.81

25112.82

15.38

R243C

8338.94

330.72

8089.29

11.75

7779.07

14.93

R244A

21552.34

331.88

21894.05

10.66

21645.36

19.66

R244C

6809.50

306.08

6493.74

13.39

6283.62

23.13

R245A

27302.03

179.00

30007.57

11.42

28472.48

18.74

R245C

9644.09

204.39

9447.63

12.55

9028.41

17.61

R246A

24400.15

183.64

26785.61

11.17

25635.31

21.90

R246C

9092.40

240.33

8528.13

12.92

8189.75

17.41

R247A

22749.95

248.61

24206.06

10.49

22908.83

22.82

R247C

8004.41

269.05

7449.61

12.17

7137.50

17.55

R248A

21298.98

362.19

20392.97

10.58

20334.21

16.19

R248C

6552.64

313.17

6176.44

14.64

5950.25

15.49

R249A

25891.73

155.73

27132.32

11.38

26350.33

23.49

R249C

8991.19

196.50

8864.43

12.95

8435.10

24.06

R2410A

23894.38

184.95

25154.26

12.39

24447.99

26.19

R2410C

8567.66

200.52

8386.89

13.20

7923.03

19.13

RC141A

23667.18

348.45

23429.93

12.98

23161.68

12.79

RC141C

9839.00

360.55

9812.02

14.42

9708.76

17.25

RC142A

22066.80

327.91

21860.59

13.50

21533.88

18.77

RC142C

8970.15

349.41

8859.79

15.70

8699.61

21.87

RC143A

20597.40

316.80

20446.10

12.78

20142.14

24.04

RC143C

8140.88

337.50

8089.51

15.17

7924.20

25.69

RC144A

20080.59

331.70

19809.80

13.38

19672.56

26.75

RC144C

7723.72

361.88

7558.39

14.28

7470.42

28.39

RC145A

22271.61

341.41

22197.31

14.45

21979.77

17.38

RC145C

9306.67

341.63

9147.86

15.50

8985.27

19.38

RC146A

22257.21

338.55

21760.79

14.47

21678.32

19.77

RC146C

9150.17

338.03

9127.43

15.36

8904.58

16.77

RC147A

21663.84

327.77

21460.28

15.36

21218.09

20.44

RC147C

8844.62

328.13

8754.82

13.91

8557.48

20.70

RC148A

21004.48

313.55

20879.27

14.20

20577.53

21.26

RC148C

8391.29

323.69

8427.69

14.56

8197.76

22.64

RC149A

20841.74

311.05

20742.67

15.06

20401.44

21.61

RC149C

8297.20

309.86

8318.95

13.50

8099.14

23.76

RC1410A

20439.53

306.94

20197.91

12.97

20101.92

23.35

RC1410C

8085.39

320.97

8025.24

13.89

7838.42

23.60

RC241A

30354.46

348.42

29970.85

12.50

29280.00

23.96

RC241C

9035.96

267.58

8849.39

11.27

8558.49

22.83

RC242A

26847.73

341.09

28733.62

11.44

26869.42

20.62

RC242C

8567.81

356.14

7984.16

11.16

7856.42

22.51

RC243A

24497.60

345.91

26844.11

10.47

23597.58

22.67

RC243C

7763.58

361.31

7137.48

12.00

6910.54

23.10

RC244A

21047.48

359.88

20679.44

14.63

20859.13

19.13

RC244C

6609.23

375.17

5769.86

13.31

5621.26

21.03

RC245A

28217.45

264.09

28456.96

11.42

27225.33

22.84

RC245C

8289.54

272.08

8142.32

12.47

7793.09

21.26

RC246A

27157.56

292.84

28627.03

11.56

26486.60

21.81

RC246C

8063.89

302.53

8022.63

11.59

7695.75

20.76

RC247A

26655.32

247.58

27342.13

11.20

25504.91

23.28

RC247C

7724.78

259.39

7589.56

12.14

7306.26

21.14

RC248A

25030.18

250.05

25521.11

12.03

23869.02

22.81

RC248C

7338.61

257.86

7197.08

13.39

6922.08

21.70

RC249A

23893.36

255.91

23348.97

13.08

22760.50

21.68

RC249C

7235.74

287.03

7003.77

13.14

6664.64

19.20

RC2410A

23346.33

231.13

22963.14

16.47

21397.63

20.86

RC2410C

6931.63

258.11

6567.66

13.45

6377.35

14.01

C161A

59689.55

760.17

59586.47

21.09

59481.40

18.72

C161C

18707.09

793.52

18716.49

19.03

18699.39

21.22

C162A

58755.09

785.00

58571.76

24.34

58079.81

35.99

C162C

18526.04

793.52

18502.45

22.34

18454.09

37.94

C163A

57563.30

771.61

56829.20

24.06

56346.77

43.54

C163C

17911.72

799.81

17970.54

22.67

17700.27

48.14

C164A

56426.93

783.73

55567.63

22.53

55186.06

48.70

C164C

17264.42

779.80

17123.40

22.58

16981.84

48.02

C165A

59855.49

757.41

59943.50

21.64

59422.74

23.34

C165C

18706.06

822.45

18693.84

17.95

18686.38

26.47

C166A

60653.99

801.13

60318.27

23.66

59381.65

30.25

C166C

18717.27

813.41

18707.56

21.69

18686.50

31.57

C167A

60286.25

776.58

60294.54

24.36

59443.34

29.58

C167C

18704.18

863.47

18701.59

21.66

18683.86

32.06

C168A

59920.91

776.97

59595.55

25.70

58996.74

36.13

C168C

18571.11

801.09

18682.18

23.31

18510.70

36.61

C169A

58156.55

786.81

58567.22

27.03

57804.33

38.11

C169C

17887.99

815.83

18242.30

23.27

17763.93

41.73

C1610A

57870.92

754.78

57896.52

27.27

57194.78

43.93

C1610C

17639.89

815.38

17887.74

24.09

17646.48

45.05

C261A

58825.82

714.53

58082.40

17.44

55132.04

26.85

C261C

13015.11

716.86

13332.62

15.05

12604.76

23.92

C262A

58081.86

741.48

57698.77

19.27

54475.36

26.47

C262C

13020.56

742.78

12918.37

18.03

12457.44

28.70

C263A

55943.84

775.75

55292.05

16.86

53935.22

29.47

C263C

12849.37

779.22

12715.31

16.64

12328.78

31.97

C264A

55141.06

863.83

54421.80

16.83

52625.95

33.85

C264C

12532.26

830.28

12377.14

16.34

11918.71

35.80

C265A

58023.94

714.28

57227.76

19.17

54984.43

24.76

C265C

13424.80

703.59

13080.26

17.11

12461.79

24.76

C266A

57196.13

738.19

56603.26

17.83

54784.32

26.93

C266C

13769.02

745.63

13050.43

17.91

12337.14

22.76

C267A

57811.18

739.98

56829.07

19.36

54898.39

29.03

C267C

13399.36

711.77

13223.82

17.24

12577.49

24.41

C268A

56595.38

776.39

56119.74

18.13

54172.38

27.21

C268C

13038.78

764.05

12680.30

17.27

12237.35

26.69

C269A

56210.82

761.52

56183.81

19.19

54197.74

27.92

C269C

13054.19

754.39

12995.09

17.88

12148.71

26.55

C2610A

55862.66

735.16

55607.16

18.30

53561.63

26.63

C2610C

13189.45

753.11

12730.64

16.95

12113.26

30.75

R161A

48768.16

724.11

48035.25

16.31

47810.70

28.94

R161C

24292.87

751.25

24277.93

15.97

23991.86

35.52

R162A

43036.65

683.81

42172.33

21.94

42115.37

36.02

R162C

20600.75

697.09

20575.01

20.86

20243.80

38.00

R163A

39796.18

668.28

39089.63

21.48

38733.18

40.65

R163C

18382.28

691.66

17908.61

20.52

17597.84

43.62

R164A

37493.03

683.09

36769.21

20.94

36402.21

49.48

R164C

16321.85

718.95

15765.01

19.45

15657.10

45.60

R165A

43303.32

671.16

42517.05

23.97

41881.58

27.78

R165C

21421.98

674.55

21118.63

18.58

20607.54

26.61

R166A

41316.95

658.94

40314.96

21.25

39953.39

37.32

R166C

19323.65

672.50

19015.45

20.27

18759.35

33.51

R167A

38989.63

672.41

38234.20

20.67

37851.14

41.22

R167C

17921.75

681.05

17025.78

20.81

17023.24

40.89

R168A

36982.48

694.75

36390.44

21.97

36175.07

45.49

R168C

16051.66

722.38

15616.18

21.83

15418.46

41.71

R169A

41915.91

654.11

40960.30

23.81

40522.86

29.89

R169C

20085.27

656.09

19767.32

20.03

19380.68

30.42

R1610A

40068.23

637.75

39521.70

23.38

39093.56

30.67

R1610C

18891.04

652.08

18449.85

19.89

18111.24

36.10

R261A

55926.79

826.92

53192.13

20.61

51291.20

28.98

R261C

20981.80

470.61

19697.79

17.81

19035.79

29.30

R262A

48401.15

473.86

49406.02

18.70

46659.77

36.07

R262C

18525.78

562.38

17182.59

17.03

16909.31

32.01

R263A

40919.19

586.42

44327.34

17.02

40101.74

31.67

R263C

16550.00

616.45

14510.42

17.45

14184.89

33.37

R264A

35706.92

678.59

35083.09

17.39

33980.67

26.96

R264C

13157.25

707.73

11449.41

17.55

11008.94

27.53

R265A

49199.77

372.17

50693.53

20.89

49223.50

31.12

R265C

19533.05

447.58

18294.03

17.56

17771.90

33.01

R266A

42134.19

405.91

46572.58

17.70

43295.07

31.87

R266C

18749.86

404.58

16356.36

17.83

15661.50

30.06

R267A

39024.05

526.75

42750.32

16.58

38492.23

23.85

R267C

14898.00

544.27

13805.47

15.74

13255.61

31.87

R268A

35947.38

688.89

34233.23

17.80

32580.85

32.46

R268C

13082.88

702.95

10865.64

19.80

10454.96

28.00

R269A

45496.03

447.63

49347.98

19.33

45496.03

29.91

R269C

18567.27

469.55

17034.98

17.20

16551.68

29.67

R2610A

42371.50

437.70

42719.16

19.41

42085.73

32.28

R2610C

17087.31

521.34

16213.20

18.38

15482.84

27.36

RC161A

38981.34

723.89

38568.22

21.20

37966.63

20.78

RC161C

18691.07

742.28

18469.16

19.52

17829.78

24.06

RC162A

36931.09

701.08

36115.10

22.45

35558.83

27.46

RC162C

17192.16

703.69

16864.48

20.17

16400.23

30.90

RC163A

35118.63

694.70

34183.42

22.06

33888.57

36.54

RC163C

15987.36

703.31

15442.62

19.81

15227.84

43.97

RC164A

34036.86

714.39

33177.38

22.61

33100.75

42.06

RC164C

15029.87

729.91

14541.66

20.72

14395.73

44.37

RC165A

37890.20

698.89

37031.67

21.27

36368.56

26.66

RC165C

18122.45

700.42

17505.80

20.86

17015.78

27.02

RC166A

36917.19

688.64

36479.06

24.06

36087.67

24.17

RC166C

17417.86

692.80

17359.22

18.42

16924.63

25.93

RC167A

36045.20

673.61

35613.49

23.75

35130.32

27.58

RC167C

16906.27

687.48

16801.52

20.08

16317.85

29.50

RC168A

35731.11

658.69

34989.07

21.52

34769.63

32.99

RC168C

16665.67

667.88

16303.91

20.06

15989.32

35.12

RC169A

35355.26

661.61

34969.48

24.63

34614.31

32.03

RC169C

16387.88

667.16

16224.11

19.67

15867.19

33.63

RC1610A

35048.50

647.77

34707.66

22.63

34405.79

34.49

RC1610C

16380.54

666.22

15828.02

21.30

15625.16

37.94

RC261A

50965.70

728.20

49713.11

20.45

48026.06

35.41

RC261C

16887.29

517.75

16473.45

16.48

15836.79

27.77

RC262A

45977.09

669.75

46584.05

18.78

43708.88

26.18

RC262C

15607.40

611.44

14470.66

15.52

14027.61

28.72

RC263A

40652.52

675.24

40861.20

15.86

38816.75

30.87

RC263C

14175.00

716.31

12795.89

17.36

12445.42

25.99

RC264A

34595.77

711.36

34942.97

18.14

33183.89

27.61

RC264C

11806.37

749.49

10402.35

18.97

10039.03

24.60

RC265A

46462.01

552.95

47600.73

18.58

46462.01

31.39

RC265C

16152.60

525.72

15449.32

16.30

14886.59

30.69

RC266A

47640.27

589.58

47295.00

18.53

45939.67

27.96

RC266C

15578.28

581.92

15413.57

17.66

14649.05

25.77

RC267A

44631.66

655.25

44216.27

18.97

44922.08

28.47

RC267C

15535.85

542.03

14576.06

17.66

13939.88

26.18

RC268A

41694.33

487.59

42675.06

17.70

41694.33

31.84

RC268C

14289.59

536.38

14095.21

18.23

13314.74

26.62

RC269A

40365.67

514.88

39103.91

17.44

39103.91

25.82

RC269C

14628.42

614.84

13627.13

16.22

12864.97

30.58

RC2610A

38217.84

485.91

37492.89

18.00

40310.55

24.01

RC2610C

13745.89

578.67

13019.75

17.02

12191.27

22.83

C181A

85904.80

1331.39

85377.70

24.34

85118.97

27.71

C181C

31846.67

1306.95

31306.21

26.94

31287.09

27.80

C182A

84580.95

1330.84

83500.72

30.70

82931.70

41.08

C182C

31581.31

1348.14

30995.73

32.52

30758.37

42.99

C183A

80617.52

1296.75

80226.37

29.25

79244.66

54.23

C183C

29319.89

1433.02

29599.34

33.39

28994.36

60.33

C184A

77870.83

1309.70

77236.34

31.89

76324.25

55.79

C184C

27860.33

1410.50

27715.07

33.94

27226.22

64.46

C185A

86500.22

1329.36

85756.73

33.09

85178.09

28.85

C185C

31521.56

1433.78

31268.45

31.39

31255.85

34.35

C186A

86386.20

1319.61

86476.10

32.55

85170.68

37.39

C186C

31456.02

1448.78

31312.16

31.77

31258.70

40.11

C187A

86215.78

1350.13

86513.45

33.97

85384.66

41.17

C187C

31456.56

1478.83

31284.95

30.66

31239.50

41.04

C188A

86156.11

1319.23

85234.16

35.94

84384.02

46.14

C188C

31424.64

1447.25

31179.57

34.95

30981.25

48.24

C189A

84033.43

1313.17

83810.09

36.45

82275.05

49.51

C189C

30327.43

1438.94

30582.53

35.94

29660.17

52.90

C1810A

82053.96

1331.73

82036.56

37.22

81018.18

59.02

C1810C

29490.43

1418.89

29925.15

34.31

29143.52

59.14

C281A

81655.68

1297.78

78151.77

24.05

76114.02

30.62

C281C

18867.04

1433.24

19104.26

25.02

18067.45

30.89

C282A

79202.33

1341.41

76323.83

24.59

75577.78

35.96

C282C

19618.88

1445.19

19022.27

25.55

18033.72

38.50

C283A

78244.81

1319.11

76453.56

24.36

75004.70

38.39

C283C

19866.43

1533.70

18778.22

24.98

18271.39

44.69

C284A

74952.77

1458.69

73761.73

23.89

73570.12

44.88

C284C

19095.48

1621.47

18312.74

24.53

17753.38

44.15

C285A

80079.09

1291.39

77151.81

25.80

75848.80

31.31

C285C

18951.86

1323.30

19142.23

23.69

18236.47

30.31

C286A

78828.71

1308.94

77715.28

25.59

75134.46

33.04

C286C

18824.79

1250.08

18883.89

26.00

18202.91

33.96

C287A

80072.08

1317.11

77071.63

25.75

75469.62

30.23

C287C

19959.09

1278.97

19662.82

26.00

18082.19

36.64

C288A

78157.06

1336.98

76148.19

23.06

75053.58

34.74

C288C

19567.56

1278.56

18870.43

26.09

17982.05

31.87

C289A

78640.20

1339.33

76617.84

24.99

75194.23

36.74

C289C

19663.36

1302.88

19153.84

25.03

18247.55

34.02

C2810A

76765.70

1325.14

75010.33

25.22

74068.15

35.91

C2810C

19182.40

1297.06

18528.86

24.08

17875.26

37.60

R181A

73423.38

1262.56

72590.84

21.42

71956.95

38.11

R181C

40738.97

1405.81

40722.32

24.86

39903.48

49.58

R182A

65257.05

1202.75

64562.15

28.84

63415.68

48.31

R182C

35459.84

1326.39

35039.90

28.08

34134.84

54.85

R183A

59820.10

1182.33

57934.34

28.78

57328.28

54.48

R183C

30784.69

1323.24

29859.11

28.67

29384.40

59.03

R184A

55631.60

1226.55

54311.52

31.05

54020.09

65.43

R184C

27472.15

1375.56

26571.09

33.17

26391.02

71.90

R185A

65112.59

1170.44

64073.48

28.22

63164.19

36.65

R185C

36029.45

1318.28

35683.17

29.23

34750.04

44.60

R186A

61688.93

1162.14

59854.79

29.19

59218.27

49.13

R186C

32471.26

1309.08

31401.22

33.06

31239.21

56.55

R187A

57701.16

1170.03

56186.56

33.22

55876.16

54.66

R187C

29303.08

1351.52

28486.17

31.64

28248.58

61.46

R188A

55067.66

1240.86

54076.86

29.63

53756.47

70.31

R188C

27181.22

1423.31

26306.48

31.56

26130.05

65.15

R189A

63014.13

1158.69

61284.97

29.66

60379.76

39.84

R189C

33991.16

1292.28

33099.81

28.00

32487.48

47.46

R1810A

61051.45

1143.00

59296.93

33.11

58539.97

44.10

R1810C

31979.75

1272.61

31285.10

31.86

30639.84

49.64

R281A

76129.39

1142.08

76800.86

29.66

76015.08

48.08

R281C

33865.73

925.58

31588.51

26.33

30305.13

42.73

R282A

68541.41

872.50

69237.10

27.05

68541.41

50.33

R282C

29710.76

1113.41

27601.50

25.88

26647.88

42.20

R283A

60673.82

1112.23

60335.26

23.97

60335.26

51.30

R283C

25814.85

1246.00

23026.31

25.31

22132.13

40.90

R284A

52897.81

1199.94

52007.50

22.39

52007.50

39.33

R284C

19584.68

1263.48

18353.81

25.31

17249.25

39.42

R285A

70570.70

1043.31

73100.38

31.02

70570.70

44.84

R285C

31565.70

830.22

29379.08

25.31

28067.24

40.05

R286A

63607.13

844.80

66345.27

24.20

63607.13

50.94

R286C

28039.16

1109.69

25993.16

25.08

24831.53

45.52

R287A

59941.44

1180.83

59135.41

25.00

59135.41

45.30

R287C

25839.81

1042.83

22317.59

24.44

21110.35

41.98

R288A

50457.42

1234.20

49862.94

25.02

49862.94

42.53

R288C

19474.12

1223.72

17544.24

23.49

16677.97

35.86

R289A

67169.72

783.03

70365.53

27.66

67169.72

46.77

R289C

30039.87

763.03

27794.89

23.05

26471.23

43.24

R2810A

64422.00

634.05

65480.44

26.00

64422.00

42.81

R2810C

28481.98

883.42

26502.74

24.23

25153.17

37.70

RC181A

59150.52

1237.28

58036.37

28.78

56448.46

34.45

RC181C

32201.65

1253.56

31311.17

32.22

30538.56

36.15

RC182A

55364.17

1204.48

53906.74

31.30

53097.49

43.53

RC182C

29402.58

1234.13

28263.09

30.61

27689.98

47.92

RC183A

52680.52

1231.88

51423.03

31.91

51310.77

55.88

RC183C

27766.02

1252.24

26776.21

32.92

26179.77

63.58

RC184A

50474.12

1265.33

49389.16

30.49

49314.78

61.03

RC184C

25379.72

1285.17

24802.80

30.33

24662.89

55.69

RC185A

57066.52

1202.56

55811.28

29.91

54591.68

38.49

RC185C

30521.64

1225.08

30023.54

32.64

29334.44

44.85

RC186A

55904.77

1207.13

55368.05

31.22

54173.58

39.02

RC186C

29693.74

1213.64

29376.62

33.39

28916.35

44.67

RC187A

54825.86

1186.95

53951.41

31.86

53099.90

46.74

RC187C

29040.12

1201.38

28469.93

30.66

27862.34

47.72

RC188A

54077.31

1172.06

52573.27

29.80

52058.95

44.05

RC188C

28744.38

1194.99

27713.70

34.05

27190.09

53.29

RC189A

54060.53

1164.98

52536.89

31.53

51820.68

52.42

RC189C

28365.75

1190.58

27503.60

30.81

27073.12

59.78

RC1810A

52977.40

1158.20

52055.42

30.16

51203.98

55.18

RC1810C

27446.71

1191.06

26982.44

31.91

26730.07

56.44

RC281A

72564.38

1180.42

68932.23

29.66

68932.23

46.29

RC281C

26967.79

1094.53

25510.42

25.92

24403.06

39.81

RC282A

65076.57

1235.95

63429.73

23.53

63429.73

52.39

RC282C

24967.48

1241.05

22564.77

23.78

21796.86

41.23

RC283A

57898.17

1325.23

56750.79

23.84

56750.79

46.47

RC283C

21165.76

1392.27

19486.10

24.56

18750.79

46.96

RC284A

51738.96

1349.83

49084.96

22.77

48176.69

40.01

RC284C

17256.03

1489.83

15650.35

24.39

16048.69

35.16

RC285A

65302.06

1051.83

65449.16

25.58

65302.06

57.86

RC285C

24480.05

1150.34

23440.24

24.03

23403.65

43.96

RC286A

65842.89

1086.66

62731.40

23.25

62731.40

54.91

RC286C

24864.24

1038.98

23389.50

24.44

22937.89

40.26

RC287A

63694.95

1030.31

61200.18

25.38

61200.18

51.48

RC287C

23640.37

1088.58

22536.80

27.53

22031.78

44.43

RC288A

59340.22

977.31

57763.84

22.97

57763.84

52.43

RC288C

22731.98

1052.16

21481.50

24.59

20758.74

36.79

RC289A

57960.22

995.58

56770.02

23.45

56770.02

49.76

RC289C

22423.33

1115.30

20964.52

23.45

20641.88

37.77

RC2810A

54409.41

998.69

54190.70

22.80

54190.70

42.84

RC2810C

21656.00

1091.56

20208.70

25.58

19503.18

35.71

C1101A

118787.14

1983.70

117485.38

35.27

117207.95

35.07

C1101C

50787.86

2021.80

50065.08

36.55

50057.53

36.38

C1102A

116725.88

1987.66

115410.43

46.91

114115.83

58.16

C1102C

49784.06

2048.88

49606.12

45.03

49365.50

64.76

C1103A

112483.80

1981.67

111346.16

47.77

109840.98

65.74

C1103C

47210.25

2058.17

47948.33

49.47

47078.95

73.02

C1104A

106391.73

2042.83

104794.52

44.94

104186.72

83.97

C1104C

43981.17

2177.30

43895.81

48.11

42999.37

83.60

C1105A

118762.64

2028.78

117881.98

42.61

117198.64

43.28

C1105C

50310.32

2201.94

50075.16

45.20

50032.87

45.99

C1106A

120062.98

2027.02

118269.16

46.00

117143.79

51.76

C1106C

50139.08

2208.06

50131.77

42.36

50033.15

48.81

C1107A

118882.44

2044.41

119287.70

43.56

117212.94

47.02

C1107C

50344.85

2201.61

50179.69

43.84

50023.45

51.35

C1108A

118720.60

2010.92

117465.45

47.41

116276.77

57.52

C1108C

50059.20

2206.91

50078.75

44.41

49692.13

65.60

C1109A

115666.78

2043.36

114729.25

49.77

114032.42

70.51

C1109C

48281.63

2239.78

49033.63

45.05

47616.00

69.56

C11010A

113723.05

2018.86

113565.70

48.25

111928.58

70.01

C11010C

47767.31

2189.56

48006.15

48.13

46606.41

82.70

C2101A

104405.41

1895.28

101055.51

33.80

99171.59

41.22

C2101C

27565.94

2273.83

26914.42

33.97

25081.81

38.61

C2102A

104122.18

1910.50

99865.72

35.19

99865.72

45.19

C2102C

27451.23

2237.17

26360.07

34.03

24946.05

52.63

C2103A

100344.77

1969.92

97243.95

32.99

97243.95

52.12

C2103C

27775.83

2340.63

26335.14

33.88

25294.95

51.11

C2104A

99061.77

2187.19

95365.89

32.52

95303.05

60.72

C2104C

26171.65

2457.75

25404.70

35.55

24720.91

64.02

C2105A

102803.17

1850.39

99935.95

34.17

99935.95

42.62

C2105C

27069.58

2163.28

26709.19

35.14

25164.18

44.40

C2106A

102681.81

1896.06

99364.25

32.88

97425.92

43.43

C2106C

27874.57

2252.98

26926.17

31.20

24826.73

47.72

C2107A

103154.60

1881.92

99228.42

33.66

98391.09

47.24

C2107C

27906.83

2217.74

26664.01

32.72

26200.46

51.23

C2108A

101995.64

1915.75

97999.53

34.11

96851.00

42.84

C2108C

27492.01

2220.94

26398.24

34.13

25584.10

47.13

C2109A

101620.37

1898.66

98829.27

33.20

97843.37

46.50

C2109C

27589.01

2241.56

26563.02

33.48

25962.44

51.42

C21010A

101197.13

1938.42

96876.09

32.73

96513.50

46.11

C21010C

26891.55

2240.75

26151.47

32.24

24881.47

50.65

R1101A

100212.48

2040.98

98182.30

30.14

97552.74

49.45

R1101C

58943.11

2178.30

58614.10

28.39

57340.91

72.46

R1102A

89838.07

1853.09

87719.66

39.27

86698.79

66.94

R1102C

51655.98

2084.27

50395.03

42.08

49488.02

75.13

R1103A

81944.28

1725.16

79314.20

40.33

78694.48

76.91

R1103C

45856.57

2062.03

43793.72

40.02

43168.66

90.37

R1104A

76926.73

1806.22

74883.88

40.28

74448.69

92.68

R1104C

41019.65

2139.47

39729.29

41.39

39336.09

95.64

R1105A

90778.97

1703.67

87170.08

36.02

86018.13

55.86

R1105C

53446.32

2078.80

51998.27

40.47

50455.79

65.24

R1106A

85998.64

1694.72

82132.25

39.27

81654.91

67.05

R1106C

48283.29

2045.13

46956.65

42.64

45874.48

81.85

R1107A

80195.64

1733.50

77698.93

40.56

77295.04

86.99

R1107C

44417.54

2087.34

42431.94

40.38

41982.23

91.40

R1108A

76503.94

1761.13

74621.00

43.72

74191.95

90.26

R1108C

40368.48

2159.92

39378.73

44.86

39012.00

95.35

R1109A

88163.81

1688.74

85080.58

37.31

83994.10

59.11

R1109C

50974.68

2044.73

49370.69

41.14

48257.65

69.27

R11010A

85534.08

1671.95

82393.37

39.45

81317.50

64.04

R11010C

48615.96

2017.91

46699.48

42.25

45601.70

72.32

R2101A

110184.33

1313.19

104301.16

42.06

101743.42

61.65

R2101C

49601.56

1829.30

45786.67

35.08

43912.34

58.24

R2102A

97442.41

1501.20

94750.47

38.34

91999.25

68.70

R2102C

45550.71

1918.45

39158.92

33.06

38138.85

65.75

R2103A

83346.44

1714.33

80347.20

38.19

79405.92

67.33

R2103C

37908.70

2233.11

31949.84

30.06

30898.94

55.55

R2104A

70656.05

1757.58

65589.11

28.13

65616.95

58.11

R2104C

28511.63

2028.28

24545.11

33.19

23218.64

58.45

R2105A

104693.34

1206.02

100037.95

42.27

100037.95

63.35

R2105C

46757.77

1514.56

43108.04

34.14

40929.15

57.30

R2106A

90800.22

1400.36

87520.57

35.44

87520.57

53.21

R2106C

42134.09

1608.91

37719.80

30.58

35894.18

57.13

R2107A

76471.25

1706.22

75569.19

34.63

75569.19

63.94

R2107C

35172.42

1887.48

30835.81

33.17

29276.42

62.03

R2108A

69906.48

1778.36

63537.16

31.73

63537.16

55.55

R2108C

27657.81

2122.02

23537.39

32.70

22319.10

50.09

R2109A

96569.63

1050.55

97251.31

40.09

96569.63

61.37

R2109C

44953.75

1488.67

40990.00

34.45

38742.40

56.63

R21010A

90303.81

1071.19

93063.65

37.48

90303.81

60.25

R21010C

43142.36

1199.31

39200.86

35.94

38064.95

48.47

RC1101A

82815.73

1876.09

79959.62

39.94

78031.41

48.69

RC1101C

48849.41

2037.16

47049.28

39.42

45756.90

49.30

RC1102A

77839.84

1885.22

73959.01

42.27

72774.02

53.13

RC1102C

44660.72

2122.11

42589.15

42.98

41655.57

65.68

RC1103A

72778.05

1865.02

70309.67

44.02

69879.53

78.53

RC1103C

41370.69

2157.48

39278.03

41.47

38931.45

82.88

RC1104A

69462.56

1937.08

68081.25

41.99

67776.59

92.87

RC1104C

38606.30

2212.52

37534.31

43.00

37178.45

100.22

RC1105A

79230.56

1877.63

76776.20

40.53

75250.41

54.88

RC1105C

46503.62

2113.03

44786.32

40.30

43533.30

57.16

RC1106A

77781.09

1877.72

75310.20

42.14

73961.84

51.04

RC1106C

46316.18

2081.97

44116.07

40.05

42585.26

44.74

RC1107A

75976.66

1845.33

73748.70

44.55

72905.91

58.67

RC1107C

45117.43

2072.89

43211.56

43.08

42054.25

55.51

RC1108A

75322.36

1837.09

72488.42

40.33

71715.46

60.39

RC1108C

44002.29

2058.11

41422.41

40.25

40985.61

59.87

RC1109A

74556.65

1833.77

72499.64

40.98

71628.86

54.88

RC1109C

43665.91

2002.34

41758.04

40.00

40977.04

57.14

RC11010A

74562.46

1826.00

71752.19

41.52

70987.31

50.56

RC11010C

42647.78

1875.02

40857.08

39.42

40109.00

61.37

RC2101A

96431.08

1718.86

92100.95

36.59

92100.95

53.59

RC2101C

39684.66

1405.31

36591.16

36.44

34879.15

47.97

RC2102A

87586.31

1651.05

82790.18

33.86

82790.18

44.52

RC2102C

36250.77

1799.69

32209.94

31.31

30925.31

58.36

RC2103A

74445.37

1918.56

69548.62

25.39

69548.62

48.25

RC2103C

30443.51

2185.44

26761.99

32.25

25570.40

56.79

RC2104A

64687.95

2113.05

61890.14

33.45

61890.14

49.84

RC2104C

25704.52

2427.97

21596.82

36.56

20690.84

49.12

RC2105A

88789.04

1470.70

87244.16

36.31

87244.16

49.94

RC2105C

36891.79

1587.11

34349.43

36.20

32316.64

48.74

RC2106A

90015.29

1518.77

85087.14

35.89

85087.14

44.62

RC2106C

37837.96

1567.25

34312.05

32.77

32194.44

45.96

RC2107A

86259.89

1397.72

83513.57

34.17

83513.57

47.02

RC2107C

36658.46

1595.92

33036.03

33.45

30571.31

51.40

RC2108A

80197.05

1495.63

80933.86

31.77

80197.05

57.44

RC2108C

33952.09

1539.23

31815.12

33.99

29466.26

42.56

RC2109A

79337.48

1414.70

73604.45

33.33

73604.45

44.85

RC2109C

33757.40

1591.59

30717.02

31.81

28540.66

49.22

RC21010A

75617.04

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Bräysy, O., Dullaert, W., Porkka, P.P. (2018). A Simple Metaheuristic for the FleetSize and Mix Problem with TimeWindows. In: Diez, P., Neittaanmäki, P., Periaux, J., Tuovinen, T., Bräysy, O. (eds) Computational Methods and Models for Transport. ECCOMAS 2015. Computational Methods in Applied Sciences, vol 45. Springer, Cham. https://doi.org/10.1007/978-3-319-54490-8_4

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