The Linehaul-Feeder Vehicle Routing Problem with Virtual Depots and Time Windows
Table 2
Test results for the LFVRPTW and the VRPTW.
Problem number
Solution algorithm
Objective value
Improve. percentage of initial solution (%)a
No. of small vehicles
CPU time (sec.)
Depot numberb
A32
LFVRPTW
11247
4.36
8
3.52
PD
VRPTW
12541
2.95
10
0.58
—
A34
LFVRPTW
10380
9.95
8
3.21
PD
VRPTW
12444
1.52
11
0.76
—
A38
LFVRPTW
11142
20.81
9
3.42
PD(3)
VRPTW
12651
1.94
11
1.18
—
A45
LFVRPTW
13517
11.35
10
4.66
PD(3)
VRPTW
15857
2.47
14
0.14
—
A46
LFVRPTW
12515
9.37
10
4.75
PD(3)
VRPTW
15499
4.45
14
0.2
—
A60
LFVRPTW
20194
13.63
16
8.43
PD(3)
VRPTW
20816
1.50
17
0.16
—
A61
LFVRPTW
13450
7.32
10
5.45
PD(3)
VRPTW
14545
2.39
13
0.11
—
A64
LFVRPTW
19064
17.04
15
11.74
43,58(3)
VRPTW
22072
3.21
18
0.24
—
A65
LFVRPTW
19423
21.51
12
6.13
PD,24,45(3), 48,61
VRPTW
21440
1.60
19
0.16
—
A69
LFVRPTW
17591
9.19
14
8.21
PD(8)
VRPTW
20923
1.69
19
0.26
—
A80
LFVRPTW
27293
13.28
13
6.76
25(5),43(3),73
VRPTW
27443
1.83
21
0.24
—
C51
LFVRPTW
7896
7.09
6
2.14
—
VRPTW
7940
6.88
7
0.20
—
C81
LFVRPTW
32190
25.75
19
6.37
14,54
VRPTW
39416
0.59
27
0.23
—
C161
LFVRPTW
120176
2.36
66
21.36
PD,43(3),83
VRPTW
125214
1.44
74
1.55
—
F45
LFVRPTW
9704
11.42
7
4.90
PD(3)
VRPTW
9871
4.97
8
0.63
—
F135
LFVRPTW
21750
16.43
15
7.77
PD
VRPTW
22939
2.27
18
2.59
—
Average
LFVRPTW
22970
12.55
14.89
6.79
VRPTW
25101
2.60
18.75
0.59
aThe tabu search is employed in the second stage of the proposed algorithm and the maximum number of iterations set for the tabu search method is 100.
bNumbers in parenthesis denote the frequency of the depot being visited by the small vehicles.
