Information Technology Reference
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Tabl e 1. Instance characteristics. The first row represents a size categorization based
on the size of the vessel. For each size category, the successive rows present respectively
the capacity of the vessel, the range of locations, the number of instances, and the
average percentage of 20', 40' and release containers. The last row gives a summary of
the ports in the routes and vessel utilization percentages.
Small
Medium
Large
Capacity (TEU)
2000-5000
5000-8000 8000-10,000
Locations
40-74
65-90
80-100
Instances
20
22
38
Avg.% 20'
26
30
19
Avg.% 40'
40
44
46
Avg.% Release
34
26
35
Ports: 3-21
Utilization: 8-88%
comparing the IP and the LNS approach, is that the IP model is only able to find
feasible instances for 50 out of 80 instances, of which only 6 reached optimality
within 3600 seconds. In contrast, the LNS is able to find feasible solutions to
all instances. Since the LNS uses the warm starting procedure to find an initial
solution, it is a logical consequence that the IPWS model also finds feasible
solutions to all instances. In order to have a better overview of the algorithms
performance, Figure 3 shows the objective value (y axis) of for each instance (x
axis) found by the three approaches within 600 seconds (the time-limit given by
the industry). The figure shows how the LNS and IPWS solve more instances
than the IP model and how the LNS, in most of the instances, outperforms the
IPWS. Instances for which a better solution is found by the IPWS, can be solved
to optimality in few seconds.
Fig. 3. Approach comparison. Each vertical dotted line represents an instance, and the
position in the line is the objective value. The lower the value the better the approach.
Timeouts are shown at the top.
 
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