![](bgb.png)
ing) that are useful to model contiguity and visibility
requirements. In the second step, we used the cre-
ated 2D layers to build 3D pallets by using a sim-
ple greedy strategy. Extensive computational exper-
iments on real-world instances proved the effective-
ness of the proposed heuristic.
To evaluate the extreme points, we proposed sev-
eral fitness evaluation functions, and found that the
one based on the concept of Bounding Box gave bet-
ter results than the other ones on average. We also
analyzed the influence of some constraints (e.g., rota-
tion and visibility) when tailoring our heuristic to ba-
sic 2D packing heuristics from the literature, gaining
interesting insights in the difficulty of the real-world
instances that we tested.
As future work, we intend to develop metaheuris-
tic algorithms to try to enhance the quality of the solu-
tions that we generated so far. We also intend to pro-
pose formal mathematical models to express the con-
cept of contiguity and visibility of items, thus filling a
gap in the existing literature. We are also interested in
studying a more complex problem that joins together
the pallet building problem with the vehicle routing
problem, so as to consider the location of pallets into
trucks and their delivery to the clients that required
them. In this case, we should extend the concept of
family, not only relying on the geometric characteris-
tics of the items, but adding new criteria of separation,
in order to help both problems (packing and delivery)
to increase the quality of the final optimization.
ACKNOWLEDGEMENTS
We thank the University of Parma and the University
of Modena and Reggio Emilia (Italy) for the financial
support to this work.
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