The Tractor and Semitrailer Routing Considering Carbon Dioxide Emissions
Table 2
Computational results for the 40 test problems.
Problem
CPLEX
SA
Gap (%)
Tractor quantity
CO2 emissions per ton-kilometer (g/tm)
Tractor quantity
CO2 emissions per ton-kilometer (g/tm)
RAND5-1
11
65.21
14
68.82
5.5
RAND5-2
11
61.35
15
70.91
15.6
RAND5-3
16
62.14
14
67.92
9.3
RAND5-4
12
61.73
16
68.72
11.3
RAND5-5
12
64.22
12
72.83
13.4
RAND5-6
16
62.34
14
66.77
7.1
RAND5-7
19
64.17
13
64.48
0.5
RAND5-8
21
65.78
17
66.33
0.8
RAND5-9
31
79.70
17
65.90
17.3
RAND5-10
17
62.97
17
69.81
10.9
RAND6-1
21
65.78
17
66.88
1.7
RAND6-2
25
61.72
19
62.56
1.4
RAND6-3
24
64.23
19
62.56
2.6
RAND6-4
16
63.58
17
73.91
16.2
RAND6-5
15
61.12
16
70.12
14.7
RAND6-6
32
64.21
20
61.50
4.2
RAND6-7
27
62.14
19
62.77
1.0
RAND6-8
23
63.40
17
64.60
1.9
RAND6-9
22
60.53
18
60.99
0.8
RAND6-10
24
61.95
21
64.79
4.6
RAND7-1
21
61.29
21
67.62
10.3
RAND7-2
21
64.18
17
68.61
6.9
RAND7-3
30
64.49
21
63.00
2.3
RAND7-4
21
62.56
21
73.73
17.9
RAND7-5
23
69.44
18
71.65
3.2
RAND7-6
22
67.50
17
69.99
3.7
RAND7-7
22
68.05
17
68.88
1.2
RAND7-8
24
69.44
17
69.99
0.8
RAND7-9
22
73.86
17
70.82
4.1
RAND7-10
20
68.05
18
72.75
6.9
RAND8-1
28
60.69
33
67.41
11.1
RAND8-2
31
64.14
27
69.95
9.1
RAND8-3
29
62.14
27
68.86
10.8
RAND8-4
29
62.32
27
69.95
12.2
RAND8-5
29
62.14
27
69.95
12.6
RAND8-6
38
73.76
26
70.49
4.4
RAND8-7
30
62.87
25
67.04
6.6
RAND8-8
30
63.23
25
67.04
6.0
RAND8-9
46
65.09
30
62.85
3.4
RAND8-10
53
68.83
32
65.46
4.9
Note: with the total number of tractors (H) enumerated, the computation time for CPLEX12.4 was limited to one hour. The solutions obtained by CPLEX are not absolutely theoretically optimal ones.
