Exact and Heuristic Solutions to Minimize Total Waiting Time in the Blood Products Distribution Problem

Table 7

The computational results of the two solution approaches on the generated instances.

Number of hospitals

OFV of Model Flow-SP

Exact

Hybrid heuristic

Instance name

Optimal number of vehicles

OFV of model 1

Ave. gap

Ave. time

Min. gap

Min. time

Max. gap

Max. time

Ave. gap

Ave. time

Min. gap

Min. time

Max. gap

Max. time

50

TRP-S50-R1; TRP-S50-R2; TRP-S50-R3; TRP-S50-R4; TRP-S50-R5; TRP-S50-R6; TRP-S50-R7; TRP-S50-R8; TRP-S50-R9; TRP-S50-R10

2; 2; 2; 2; 3; 2; 2; 2; 3; 2

4607; 4268; 4029; 4627; 6198; 4347; 4029; 4983; 6255; 4689

17.45; 18.89; 9.98; 10.06; 2.73; 18.50; 24.87; 19.60; 5.29; 18.97

283.23; 286.11; 500; 322.95; 195.10; 272.72; 303.61; 500; 333.56; 500

0; 0; 3.71; 0; 0; 0; 0; 14.5; 0; 6.51

66.45; 72.22; 500; 145.89; 10.92; 45.44; 107.22; 500; 0.69; 500

34.9; 37.78; 16.24; 20.11; 0; 37; 49.74; 24.69; 10.6; 31.43

500; 500; 500; 500; 74.39; 500; 500; 500; 500; 500

7.05; 6.43; 7.12; 11.01; 2.74; 11.57; 4.11; 7.65; 4.11; 13.07

3.45; 2.99; 3.16; 7.35; 4.23; 2.17; 3.40; 9.11; 1.76; 5.09

0; 0; 3.71; 0; 0; 0; 0; 12.30; 0; 5.54

0.12; 1.23; 0.67; 0.19; 1.23; 1.02; 0.76; 0.33; 2.45; 1.89

14.59; 7.34; 11.04; 2.10; 0; 14.12; 23.19; 4.99; 0.96; 11.51

8.95; 12.41; 7.56; 8.72; 9.99; 13.24; 12.76; 9.06; 11.63; 7.66

Average

14.63

349.73

2.47

194.88

26.25

457.44

7.49

4.27

2.16

0.99

8.98

10.20

100

TRP-S100-R1; TRP-S100-R2; TRP-S100-R3; TRP-S100-R4; TRP-S100-R5; TRP-S100-R6; TRP-S100-R7; TRP-S100-R8; TRP-S100-R9; TRP-S100-R10

4; 4; 4; 5; 4; 4; 4; 3; 3; 3

9301; 9086; 9495; 11773; 8889; 9680; 8860; 6914; 7213; 8111

13.39; 18.73; 16.38; 3.51; 35.50; 13.03; 11.35; 19.00; 22.69; 26.71

416.56; 399.41; 345.28; 476.09; 500; 500; 500; 500; 500; 500

0; 0; 0; 0; 31.52; 3.15; 8.71; 5.7; 1.58; 13.23

166.23; 97.64; 171.30; 500; 500; 500; 500; 500; 500; 500

19.29; 33.2; 36.52; 9.11; 38.16; 32.04; 13.02; 32.13; 40.44; 34.65

500; 500; 500; 500; 500; 500; 500; 500; 500; 500

10.33; 8.04; 2.17; 5.15; 13.49; 3.03; 9.67; 15.01; 20.79; 22.07

33.34; 42.97; 35.78; 56.03; 43.11; 37.98; 49.67; 51.12; 44.46; 39.57

0; 0; 0; 0; 3.24; 3.13; 7.62; 0.99; 0.76; 3.41

16.23; 22.67; 18.91; 27.33; 29.01; 19.76; 32.19; 33.56; 39.66; 16.96

17.9; 16.21; 14.33; 3.65; 20.71; 9.47; 3.92; 27.49; 18.98; 24.11

103.13; 79.17; 145.22; 183.93; 95.18; 105.62; 186.91; 234.77; 218.39; 399.89

Average

18.03

463.73

6.39

393.52

28.86

500

10.98

43.40

1.92

25.63

15.68

175.22

150

TRP-S150-R1; TRP-S150-R2; TRP-S150-R3; TRP-S150-R4; TRP-S150-R5; TRP-S150-R6; TRP-S150-R7; TRP-S150-R8; TRP-S150-R9; TRP-S150-R10

5; 6; 6; 6; 4; 5; 4; 7; 7; 5

12055; 14885; 13823; 14282; 9626; 12113; 9976; 16982; 16763; 12366

20.57; 8.27; 17.23; 12.28; 29.26; 24.16; 41.05; 7.17; 8.96; 18.01

500; 423.29; 272.39; 345.52; 500; 500; 500; 348.14; 361.39; 500

7.08; 0; 0; 0; 20.02; 7.65; 34.19; 0; 0; 2.88

500; 219.75; 25.53; 36.50; 500; 500; 500 57.06; 31.44; 500

32.70; 41.68; 58.78; 28.92; 51.40; 38.02; 62.04; 32.26; 24.67; 29.91

500; 500; 500; 500; 500; 500; 500; 500; 500; 500

14.22; 5.21; 11.13; 6.08; 12.61; 12.462; 2.78; 3.99; 4.89; 9.17

99.03; 101.11; 84.56; 89.95; 143.10; 105.02; 146.31; 223.90; 117.06; 389.89

7.08; 0; 0; 0; 12.4; 7.65; 13.32; 0; 0; 2.88

76.44; 93.23; 108.02; 66.88; 87.50; 99.10; 109.11; 120.32; 59.34; 140.08

13.34; 1.52; 21.38; 7.12; 19.05; 14.34; 11.44; 7.06; 15.61; 10.31

203.52; 189.01; 500; 123.95; 295.91; 165.55; 293.60; 473.92; 308.86; 500

Average

18.70

425.07

7.18

287.03

40.04

500

9.04

149.99

4.33

96.00

13.42

305.43