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A routing and packing problem

We propose a problem which is the union of a Capacitated Vehicle Routing Problem and a Multiple Container Loading Problem. The problem is defined in:

The following table summarizes the features of the instances used in our experiments in terms of number of customers (n), number of box types (bt), total number of boxes (M), number of vehicle types (vt), number of vehicles v, the ratio between the total volume of boxes and the total volume available in vehicles (φ), the ratio between the average demand of customer and the capacity of vehicles(θ),  and the Gini index which gives a measure of heterogeneity of boxes. It is also possible to download our best solutions.

Instances & Best Solutions:

 
Instance Customers Box types Boxes Vehicle types Vehicles φ θGini index 3L-CVRP NO SD SD
Unloaded Volume Cost Download Unloaded Volume Cost Download Unloaded Volume Cost Download
SD-CSS1 11 36 254 1 5 56.47 18.82 98.23 0 5084.053 0 5267.286 0 5025.721
SD-CSS2 25 15 350 1 13 59.57 29.78 88.29 0 11879.928 0 11879.928 0 11922.630
SD-CSS3 33 9 285 1 26 41.55 31.77 76.86 51.13 15475.905 51.13 15475.905 0 16281.905
SD-CSS4 37 13 312 1 12 56.58 17.86 88.49 0 11175.227 0 11286.236 0 11286.236
SD-CSS5 41 47 7035 2 13 5.1 1.57 95.39 0 10451.030 0 17187.010 0 21620.570
SD-CSS6 43 97 8060 1 35 28.53 22.70 93.21 0 21487.564 0 26563.214 0 32909.997
SD-CSS7 45 14 284 2 10 62.57 13.6 88.44 0 10339.704 0 11436.936 0 14443.034
SD-CSS8 48 70 3275 3 36

37.12

27.28 97.19 0 21908.727 5.55 29678.278 0 40627.450
SD-CSS9 56 45 1725 1 23 48.10 19.41 97.44 0 17258.039 0 18230.345 0 28804.275
SD-CSS10 60 29 1840 1 20 23.3 7.64 88.26 0 11865.051 0 17290.009 0 24892.336
SD-CSS11 92 34 3790 2 13 43.79 6.12 88.67 0 24843.111 0 30440.396 0 39436.081
SD-CSS12 129 10 745 1 50 53.67 20.64 97.34 0 34256.077 0 34422.394 0 35755.786
SD-CSS13 129 63 2880 1 35 34.21 9.21 96.53 0 26342.908 0 34216.204 0 60924.859

Best solutions on 3L-CVRP instances

We also make available our best solutions on instances introduced by Gendreau at al. in A Tabu Search Algorithm for a Routing and Container Loading Problem. Transportation Science 40 (3), 342-350.

Instance Customers BoxesVehicles Cost Download
1 15 32 4 302.03
2 15 26 5 334.97
3 20 37 4 397.13
4 20 36 6 437.20
5 21 45 6 444.66
6 21 40 6 498.33
7 22 46 6 752.75
8 22 43 8 805.43
9 25 50 8 630.14
10 29 62 8 823.16
11 29 58 8 790.16
12 30 63 9 612.26
13 32 61 8 2712.64
14 32 72 9 1402.31
15 32 68 9 1364.38
16 35 63 11 698.63
17 40 79 14 864.66
18 44 94 11 1223.52
19 50 99 12 786.13
20 71 147 18 597.53
21 75 155 17 1128.13
22 75 146 18 1188.51
23 75 150 17 1149.33
24 75 143 16 1162.37
25 100 193 22 1435.91
26 100 199 26 1609.88
27 100 198 23 1566.73